Chapter 4: Chemical Kinetics
Rate of Reaction
Rate of Reaction or Reaction Rate in chemistry is defined as the speed or the rate at which a chemical reaction takes place. The rate of a Chemical Reaction is directly proportional to the increase in the concentration of a product per unit of time and to the decrease in the concentration of a reactant per unit of time. This can vary drastically. Chemical reactions proceed at extensively different speeds depending on the nature of the reacting substances, the type of chemical transformation, the temperature, and other factors.
In this article, you will understand the meaning of rate of a chemical reaction, rate of reaction order, the unit of the rate of reaction, and formulas.
Table of Content
What is the Rate of Reaction
Rate of Reaction is the speed at which a chemical reaction occurs. A low-rate reaction means that the rearrangement of molecules by breaking old bonds and creating new bonds is slow. Some reactions can take hundreds of years to occur, whereas others can occur in less than a second. Consider how long it takes plants and ancient fish to become fossils if you want to conceive of an extremely slow reaction (carbonization). The Speed of Reaction is also affected by the type of molecules combined. The reaction will be slower if an essential element or compound is present in low concentrations.
Rate of Reaction Meaning
The Rate of Reaction is defined as the change in the concentration of any one of the reactants or products per unit of time.
Rate of Reaction Formula
The Rate of Reaction is proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. And can be defined as,
- Rate of Reaction = Decrease in the concentration of a reactant R / Time Interval
- Rate of Reaction = Increase in the concentration of a product P / Time interval
If we consider, [R1] and [P1] are the molar concentrations of the reactant and the product respectively at any time t1 and [R2] and [P2] are the concentrations of reactant and product at time t2, then changes in concentrations of the reactant and product will be d [R] = R2 – R1 and d [P] = P2 – P1 and time interval is dt = t2 – t1 and the rate of reaction in terms of reactant or product is given by
- Rate of reaction = -(R2 – R1)/ (t2 – t1) = + (P2 – P1)/(t2 – t1)
- Rate of reaction = – Δ[R]/Δt =+ Δ[P]/Δt.
Significance of Negative and Positive Signs
The sign in the rate of reaction tells about the increase and decrease in the concentration.
- Negative sign indicates that the concentration of the reactant is decreasing.
- Positive sign indicates that the concentration of the product is increasing.
Expressing the Rate of Reaction in terms of different Reactants and Products
Let us consider a reaction ⇒ a A + b B ⇢ x X + y Y
Then the Rate of Reaction is given by
Rate = – 1/a d[A]/dt = – 1/b d[B]/dt = + 1/x d[X]/dt = + 1/y d[Y]/dt
where
- d[A], d[B] represent small decrease in the concentrations of A and B respectively
- d[X] and d[Y] represent small increase in the concentrations of X and Y respectively in the small interval of time dt
Average Rate of Reaction
From beginning to end the rate of reaction does not remain the same, it can vary from time to time. Therefore, the rate of reaction is defined as the ‘Average Rate of Reaction’.
Mathematically, the Average rate of reaction is given by,
rav = -Δ[R]/Δt = +Δ[P]/Δt
Instantaneous Rate of Reaction
The Rate of Reaction at any instant of time is the rate of change of concentration of any one of the reactants or products at that particular instant of time. From the Average Rate of Reaction, we can understand it as when the change in the time interval is very less i.e. Δt→0 then the Rate of Reaction is termed as Instantaneous Rate of Reaction. Let us suppose that the small change in concentration is given dx in the small interval of time dt. Then the rate of reaction at that instant is given by dx/dt. It is given by the tangent to the curve of Concentration of Reactant/Product vs Time.
Mathematically, the Instantaneous Rate of Reaction is given by,
rinst = dx/dt
rinst = -Δ[R]/Δt as Δt ⇢ 0 = -d[R]/dt = -slope
rinst = +Δ[P]/Δt as Δt ⇢ 0 = +d[P]/dt = +slope
Unit of Rate of Reaction
The Rate of Reaction, in general, can be measured as a change in concentration of reactant or product where concentration is denoted in moles/liter and time in seconds or minutes.
So the Unit of Rate of Reaction = mol L-1 s-1 or mol L-1 min-1.
Factors Affecting Rate of Reaction
There are various factors that affect the reaction rate which are listed below:
- Reactant Concentration
- Order of Reaction
- Nature of Reactant
- Pressure
- Temperature
- Solvent
- Electromagnetic Radiation
- Presence of Light
- Presence of Catalyst
- Surface Area
- Activation Energy
Reactants Concentration
From the Collision Theory, we know that the more the reactant more will be the collision and hence more will be the reaction, hence Rate of Reaction is directly proportional to the concentration of Reactants. Also as the concentrations of the reactants decrease, the rate of reaction decreases. Hence, the Rate of Reaction for a given reaction in terms of concentration of Reactant can be given as
aA + bB ⇢ cC + dD
Rate ∝ [A]x [B]y
Rate = k[A]x [B]y
where
- k is the Rate Constant
- x and y may or may not be equal to the coefficient of the reactant.
The above representation of the Rate of Reaction in terms of concentration of Reactant is called Rate Law.
Order of Reaction
In the above reaction, the sum of x and y is called as Order of Reaction. Say for example if (x + y = 0) then the Order of Reaction is Zero and the Rate of Reaction is independent of the concentration of the reactants.
Nature of Reactant
The Rate of Reaction is dependent on the Nature of the Reactant in the manner that the reaction happens fastest if the Reactants are in Gaseous Phase, slower in Liquid Phase, and slowest in the Solid phase.
Pressure
The effect of Pressure is applicable to the reactants in the gaseous phase. The effect is pressure is the same as the effect of concentration in a reaction. High Pressure of gas means higher concentration and hence the rate of reaction increases.
Temperature
The rate of reaction increases with an increase in the temperature. In many cases, the Rate Constant of reaction becomes nearly double for a 10° rise in temperature. However, an accurate explanation of the dependence on temperature was given by Arrhenius. He gave the below expression for the dependence of the rate constant on temperature
k = A -Ea/RT
where,
- k is Rate Constant
- A is the Pre-Exponential Factor or the Frequency Factor
- Ea is Activation Energy
- R is Gas Constant
- T is Temperature
Solvent
Solvent provides the medium for the solute to dissolve. A higher concentration of solute in the solvent will increase the rate of reaction.
Electromagnetic Radiation
Electromagnetic Radiation provides external energy which increases the rate of reaction.
Presence of light
Some reactions do not take place in the dark but can proceed in the presence of light. For Example: H2 + Cl2 ⇢ 2 HCl. This reaction is known as a “photochemical reaction.”
Presence of Catalyst
The main purpose of the catalyst is to increase the rate of reaction without itself involving in the reactions. So the catalyst increases the reaction rate. A catalyst reduces the activation energy barrier and hence provides an alternate path for the reaction to happen.
Surface area
Greater surface area means more collision to take place and hence, greater is the rate of reaction.
Activation Energy
Activation Energy refers to the minimum amount of energy possessed by the reactant to proceed with the reaction. When the molecules of reactant collide they form an intermediate, to form this intermediate minimum amount of energy is required. This minimum energy is called Activation Energy and the intermediate so formed is called Activated Complex. The Rate of Reaction depends on the Activation Energy in the manner that if the Activation Energy is high then the Rate of Reaction will be low and vice versa. Hence, Activation Energy and Rate of Reaction are inversely related to each other.
Learn more about, Factors Affecting Rate of a Chemical Reaction
Difference between Rate of Reaction and Rate Constant
The difference between the Rate of Reaction and Rate Constant is tabulated below:
Rate of Reaction | Rate Constant |
|---|---|
It is the change in the concentration of reactants or the change in the concentration of products per unit of time. | The rate constant is the proportionality constant related to the rate of a particular reaction. |
It depends on the molar concentration of Reactants and Products. | It doesn’t depend on the molar concentration of Reactants and Products. |
It indirectly depends on the temperature. | This directly depends on the temperature |
It is time-dependent. | It is time-independent. |
Related Resources,
FAQs on Rate of Reaction
What is Rate of Reaction Meaning?
The rate of reaction is defined as the change in the concentration of any one of the reactants or products per unit of time.
What is Rate Law?
Rate law refers to the representation of the Rate of Reaction in terms of the concentration of Reactants where the Rate of Reaction is directly proportional to the concentration of the Reactant species each raised to some power which may or may not be equal to the coefficient of the reactants.
What is the Unit of Rate of Reaction?
The Unit of Rate of Reaction is molL-1s-1
What is the Difference between Average and Instantaneous Rate of Reaction?
Instantaneous Rate of Reaction: The rate of reaction at any instant of time is the rate of change of concentration of any one of the reactants or products at that particular instant of time.
Average Rate of Reaction: It is the change is concentration of reactant or product over a time period.
How is Instantaneous Rate of Reaction calculated?
The Instantaneous Rate of Reaction can be calculated by taking tangent to the curve at that particular instant of time.
What is Order of Reaction?
In Rate law, the sum of powers of the concentration of the reactants is called as Order of Reaction. It basically tells the Rate of Reactants is dependent on concentration of how many reactants. For Example, in Zero Order Reaction rate of reaction is independent of the concentration of reactant, in case of First Order reaction, rate is determined by concentration of one of the reactant.
How is Rate of Reaction dependent upon Temperature?
The Rate of Reaction get doubles if temperature is increased by 10°, however accurate dependence is given by Arrhenius Equation given by k = A -Ea/RT
How is the Rate of Reaction dependent upon Activation Energy?
Rate of Reaction and Activation Energy are inversely related to each other. Higher Activation Energy will lead to a lower Rate of Reaction and Vice Versa.
What is the Rate of Reaction Formula?
- Rate of Reaction = Decrease in the concentration of a reactant R / Time Interval
- Rate of Reaction = Increase in the concentration of a product P / Time interval
Factors Affecting Rate of a Chemical Reaction
The rate of reaction is the pace at which the products of a chemical reaction are created from the reactants. It provides some information about the time frame in which a reaction can be accomplished. For example, the reaction rate of cellulose combustion in fire is extremely high, and the reaction is finished in less than a second.
What is Reaction Rate?
The rate of reaction, often known as the reaction rate, refers to the pace at which reactants are converted into products. When we talk about chemical processes, we know that the rate at which they occur varies greatly.
Some chemical reactions are virtually instantaneous, while others take time to achieve their final equilibrium. The rate of a reaction, according to the general definition, is the rate at which a reaction occurs.
Wood combustion, for example, has a high reaction rate because the process is fast, whereas iron rusting has a low reaction rate since the process is sluggish.
Factors Affecting the Rate of Reaction
Chemical reactions occur only when reactant molecules clash with one another. The Collision hypothesis of Chemical Kinetics describes this. According to the collision, for a reaction to occur, the reactants must collide with sufficient energy that is greater than the activation energy Ea. However, other factors can affect the rate of reaction, such as increasing the fraction of molecules with energies greater than the activation energy Ea. The rate of a reaction is influenced by four elements. They are as follows:
Nature of the Reactant
Chemical reactions occur almost instantly in an aqueous solution. Because the chemical bonds of reactant molecules are broken down. The ions’ attractive forces are disrupted, and the ions are hydrated by the water molecules. Furthermore, most ions have equal attractive forces in all directions. In most circumstances, no covalent connections must be disrupted in these situations. Reactions between molecules that require covalent bonds to be broken, on the other hand, tend to be very sluggish. As a result, the pace of reaction is influenced by the structural properties of the reactant molecules, such as bond polarity, geometry, overall size, and orientation.
Concentration of the Reactants
We know that the rate of most reactions increases as the concentration of the reactants increases. Increasing a reactant’s concentration means increasing the number of reactant molecules in the same volume. For many (but not all) reactions, there is a direct link between concentration and rate of reaction. As a result, when the concentration doubles, the rate of reaction doubles as well. This is explained by the collision hypothesis, which states that doubling the number of reactant molecules results in twice as many collisions occurring at the same time.
Temperature of the Reactants
In almost all circumstances, the rate of a reaction increases as the temperature rises. The pace of reaction doubles per 10° increase in temperature! This is a really strong effect. For example, a temperature increase from 20° to 80° (six 10° increments) will result in a reaction rate that is 26 = 64 times faster. That is a significant rate change. The Collision theory can also explain this: the average kinetic energy of all molecules is a direct function of temperature. Because the molecules collide with more energy, their activation energy lowers.
Presence of a Catalyst
A catalyst is a chemical that speeds up a reaction without really participating in it. Catalysts work by giving an alternative chemical pathway. It is the one that uses the least amount of energy to transform the reactants into products. Some catalysts accelerate more than one sort of reaction, but others, such as enzymes in our cells, are specific to a particular reaction or even a single type of reactant molecule. As a result, a catalyst accelerates the process.
Pressure factor
The concentration of gases increases as pressure increases, increasing the rate of reaction. The reaction rate accelerates in the direction of fewer gaseous molecules and slows in the opposite direction. As a result, it is clear that pressure and concentration are related and that they both influence the rate of response.
Sample Questions
Question 1: How does concentration affect the rate of reaction?
Answer:
Collision theory states that increasing the number of reactant molecules increases the number of collisions that occur for a reaction to occur. Similarly, raising the concentration, or the amount of reactant molecules in the solution, will increase the number of collisions that occur in the solution. As a result, the rate of the reaction will accelerate.
Question 2: What is the difference between the chemical kinetics of the reaction and the chemical balancing of the equation?
Answer:
The chemical kinetics of the reaction provides information on the mechanism and pace of the reaction, whereas a balanced chemical equation provides information about the stoichiometry of the reaction.
Question 3: Why does the reaction rate increase with increasing temperature?
Answer:
As the temperature of the reaction rises, the average kinetic energy of the ions and molecules rises as collisions between the ions and molecules become more frequent.
Question 4: What is the difference between chemical thermodynamics and chemical kinetics?
Answer:
Chemical kinetics, often known as reaction kinetics, is concerned with the investigation of reaction rates. Chemical thermodynamics is the study of the interaction of heat and work with chemical processes or physical state changes within the limitations of thermodynamic rules.
Question 5: How do Catalysts speed up reactions?
Answer:
The catalyst speeds up the reaction by allowing a novel reaction pathway to occur at a lower activation energy. It does not consume in the process and also does not alter in chemical properties.
Integrated Rate Laws
Integrated Rate Law is one of the fundamental concepts in the field of chemical kinetics, which is the branch of chemistry that deals with the speed or rate of reactions and various other factors affecting them. Integrated Rate Law tells us about the rate of the reaction for various different reactions such as zeroth order, first order, and second order, etc. Rate Law helps us from measuring rates to predicting the concentration of the reactants, which further helps scientists and scholars to unfold the mysteries of chemical transformations.
This article helps us learn about Integrated Rate Law and its derivation for various reactions. We will also learn how to solve numerical problems based on the Rate Law.
What is Rate Law?
Rate Law is defined as the molar concentration of the reactants with each term raised to some powers which may or may not be the same as the stoichiometric coefficient of the reactant in a balanced chemical equation.
For a Chemical Balanced reaction i.e., A + B
Rate = k[A]α[B]β
Where,
- α and β are the concentration of the A and B respectively
- k is Rate Constant
Rate Constant
The rate constant is defined as the rate of reaction when the molar concentration of all reactants is unity. For a balanced chemical equation of second order, i.e., A + B ⇢ C + D, if [A]=[B]= 1 mol/liter.
Therefore, Rate = K.
Note: Rate Constant depends on the molar concentration of the reactant, so it means the greater the value of the rate constant, the more quickly the reaction takes place.
Unit of Rate Constant: The unit of the rate constant depends on the order of the reaction (time, concentration).
Order of Reaction
The sum of power to which the molar concentrations in the rate law equation are raised to express the observed rate of the reaction is known as the order of the reaction.
Example: What is the Order of Reaction given as follows:
2N2O5 ⇢ 4NO2 + O2
Solution:
For the given Reaction,
Rate of Reaction, R = [N2O5]1
As, rate of reaction only depends on the concentration of N2O5
Thus, Order of Reaction is 1
Note: Order of the reaction is basically integers numbers like 0,1,2 but for some complex species, it can be in fractions as well.
What is Integrated Rate Law?
Integrated Rate Law provides a mathematical representation of the rate of the reaction using an initial and actual concentration of one or more reactants at any given time (t). Using this law we can calculate the rate constant as well as the mechanics of the reactions as well. For each order of reaction, the rate raw is given differently. Let’s discuss the Integrated Rate Law for zeroth, first and second order reaction in detail.
Integrated Rate Law Zero Order
Integrated Rate Law for zero order reaction states that the rate of reaction does not depend on the concentration of the reactants. For a reaction, A ⇢ Product zero order Integrated Rate Law is represented as:
Rate ∝ [A]0
Where,
[A] is the concentration of the Reactant
After integrating and simplifying the above condition, we get the integrated rate law for a zero-order reaction, i.e.,
[A] = [A0] – kt
Where,
- [A] is the concentration of the reactant A at time t
- [A0] is the initial concentration of reactant A
- k is the rate constant of the reaction
- t is the reaction time
Integrated Rate Law First Order
This law states that the rate of the first-order reaction depends upon the first power of the reactant. For a reaction, A ⇢ Product first order Integrated Rate Law is represented as:
Rate ∝ [A]1
After integrating and simplifying the above condition, we get the integrated rate law for a first-order reaction, i.e.,
[A] = [A₀]e-kt
Where,
- [A] is the concentration of the reactant A at time t
- [A0] is the initial concentration of reactant A
- k is the rate constant of the reaction
- t is the reaction time
- e is the mathematical constant i.e., Euler number (e = 2.71828)
Integrated Rate Law Second Order
Integrated Rate Law Second Order states that the rate of the second order reaction depends upon either the second power of the concentration. For a reaction, 2A ⇢ Product first order Integrated Rate Law is represented as:
Rate ∝ [A]2
After integrating and simplifying the above condition, we get the integrated rate law for a second-order reaction, i.e.,
Where,
- [A] is the concentration of the reactant A at time t
- [A0] is the initial concentration of reactant A
- k is the rate constant of the reaction
- t is the reaction time
![\bold{\frac{1}{[A]} = kt + \frac{1}{[A_0]}}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-b5344508baab1bcec971781640b7291e_l3.svg "Rendered by QuickLaTeX.com")
Integrated Rate Equations
For the general reaction aA + bB ⇢ cC + dD, the Rate of this reaction is given as:
Rate = -dR/dt = k[A]a[B]b
Where negative sign signify the decrease in concentration.
This form of the equation is called the differential rate equation. This form is not convenient to determine the rate law and hence the order of the reaction. This is because the instantaneous rate has to be determined to form the slope of the tangent at time t in the plot of concentration versus time.
To overcome the above difficulty, we integrate the differential equation for the reaction of any order. This gives us an equation related directly to the experimental data, i.e., time, concentrations at different times, and rate constant.
Integrated Rate Equation for Zero-Order Reaction
Any reaction for which the rate doesn’t depend on the concentration of the reactant is called Zero Order Reaction. In other words, form A ⇢ Product; is Zero Order Reaction if its rate is independent of the concentration of A.
Consider the general reaction: A ⇢ products
If it is a reaction of zero-order,
Rate = – d[A]/dt = k[A]0 = k
⇒ d[A] = – k dt
Integrating both sides, we get:
[A] = – kt + C . . . (i)
Where C is the constant of Integration.
at t = 0, the Concentration of the reaction is [A0], thus
[A0] = 0 + C ⇒ C = [A0]
Substituting this value of C in Eqn. (i), we get
[A] = – kt + [A0] . . . (ii)
⇒ kt = [A0] – [A]
⇒ k = {[A0] – [A]}/t . . . (iii)
Characteristics of Reactions of Zero Order
The characteristics of the zero-order reaction are,
- Any reaction of zero-order must obey equation, (ii) As it is an equation of a straight line (y = mx + c), the plot of [A] versus t will be a straight line with slope = – k and intercept on the concentration axis = [A0],
- Half-Life Period: The half-life period (t1/2) is the time in which half of the substance has reacted.
This implies that when [A] = [A0]/2, t = t1/2.
Substituting these values in Eqn. (iii), we get
t1/2 = 1/k { [A0] – [A0]/2 } = [A0]/2k
⇒ t1/2 =[A0]/2k . . . (iv)
Thus, the half-life period of a zero-order reaction is directly proportional to the initial concentration, i.e., t1/2 ∝ [A]0.
- Units of Rate Constant (k) for Zeroth Order Reaction = molar conc./time = mol L-1 /time = mol L-1 time-1 .
Integrated Rate Equation for First Order Reactions
A reaction is said to be of the first order if the rate of the reaction depends upon one concentration term only. Thus, we may have
- For the reaction: A ⇢ products, rate the reaction ∝ [A].
- For the reaction: 2A ⇢ products, rate the reaction ∝ [A] only.
- For the reaction: A + B ⇢ products, rate the reaction ∝ [A] or [B] only.
Let us consider the simplest case,
A ⇢ Products
Suppose we start with moles per liter of the reactant A. After time t, suppose x moles per liter of it have decomposed. Therefore, the concentration of A after time t = (a – x) moles per liter. Then according to the law of mass action,
Rate of reaction ∝ (a – x),
i.e.,
dx/dt ∝ (a – x)
⇒ dx/dt = k (a – x) . . . (i)
where k is called the rate constant or the specific reaction rate for the reaction of the first order.
The expression for the rate constant k may be derived as follows:
Equation (i) may be rewritten in the form
dx/a-x =k dt . . . (ii)
Integrating equation (ii), we get
-In (a – x) = kt + I . . . (iii)
where I is a constant of integration.
In the beginning, when t=0, x=0
Putting these values in equation (iii), we get
– In (a – 0) = k x 0 + I
⇒ – In a = I . . . (iv)
Substituting this value of I in equation (iii), we get
– In (a – x) = kt + (- In a)
⇒ kt = a – In (a -x)
⇒ kt = In a/a-x . . . (v)
⇒ k = 1/ t In a/a-x
⇒ k=2.303/t log a/a-x . . . (vi)
If the initial concentration is [A]0 and the concentration after time t is [A], then putting a = [A]0 and (a – x ) = [A],
Equation (vi) becomes:
k = 2.303/t log [A0]/[A] . . . (vii)
Putting a = [A0] and (a – x) = [A] in eqn. (v),
We get,
kt = In [A0]/[A] . . . (viii)
which can be written in the exponential form as:
[A0]/[A] = ekt
⇒ [A]/[A0] =e-kt
⇒ [A] = [A0] e-kt . . . (ix)
Characteristics of First-Order Reactions
The characteristics of the zero-order reaction are,
- Any reaction of the first order must obey equations (vi), (vii), and (ix).
- Half-life Period: The time in which half of the substance is reacted with each other and is converted into the product is called the half-life of the reaction.
As we know, the time taken for substance from concentration a to a-x is given by:
t = 2.303/k log [a/(a – x)]
When half of the reaction is completed, x = a/2. Representing the time taken for half of the reaction to be completed by t1/2,
t1/2 = 2.303/k log a/(a-a/2)
⇒ t1/2 = 2.303/k log 2
t1/2 = 0.693/k
Where,
- t1/2 is the half life of reaction, and
- k is the rate constant.
Learn more about Pseudo First Order Reaction.
Integrated Rate Equation for First-Order Gas-Phase Reaction
Consider the general first-order gas-phase reaction:
A (g) ⇢ B (g) + C (g)
Suppose the initial pressure of A = P0 atm. After time t, suppose the pressure of A decreases by p atm.
Now, as 1 mole of A decomposes to give 1 mole of B and 1 mole of C, the pressure of B and C will increase by p each. Hence, we have
| A(g) ⇢ B (g) + C (g) | |||
|---|---|---|---|
| Initial Pressure | P0 atm | 0 | 0 |
| Pressure After Time, t | P0 – p | p atm | p atm |
The total pressure of the reaction mixture after time t,
Pt = (P0 – p) + p + p = P0 + p atm
⇒ p = Pt – P0
So, pressure of A after time t (PA) = P0 – p = P0 – (Pt – P0) = 2 P0 – Pt
But initial pressure of A (P0) ∝ initial conc. of A, i.e., [A]0
and pressure of A after time t(PA) ∝ conc. of A at time t, i.e., [A]
Substituting these values in the first-order rate equation,
k = 2.303/t log [A]0/[A], We get
k = 2.303/t log [P0/(2P0 – Pt)]
Where,
- P0 is the Intial Pressure of Reactant,
- Pt is the total pressure after time t,
- t is the time in which pressure changes from P0 to Pt, and
- k is the rate constant.
Integrated Rate Equation for Second Order Reactions
Let’s consider a second-order reaction,
2A ⇢ Product
Thus, the rate of the reaction is given by
![\bold{\text { Rate }=-\frac{{d}[{A}]}{{d} {t}}={k}[{A}]^2}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-a1f0e5bcaeb4f0aa0a2fa26385c88161_l3.svg "Rendered by QuickLaTeX.com")
Let’s consider that the initial concentration of the reactant is [A] and in time t, the concentration of the reactant becomes [A0], thus integrating the above equation under the suitable limits, we get
![\Rightarrow \int_{[A]_0}^{[A]} \frac{d[A]}{[A]^2}=-k \int_{t_0}^t d t](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-00788a55a7781b73c4aa0f6bd0bb8b33_l3.svg "Rendered by QuickLaTeX.com")
![-\left.\frac{1}{[A]}\right|_{[A]_0} ^{[A]}=\left.k t\right|_{0} ^t](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-bc5d2f00f40b833ebb322727adcf1828_l3.svg "Rendered by QuickLaTeX.com")
![\Rightarrow \frac{1}{[A]_0}-\frac{1}{[A]}=k\left(t-0\right)](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-8fb6aef2bd388f234d3782c4b14c0cf7_l3.svg "Rendered by QuickLaTeX.com")
![\Rightarrow \frac{1}{[A]}=k t+\frac{1}{[A]_0}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-50b7c3fee29bb22b6a46b5f37cae8dfa_l3.svg "Rendered by QuickLaTeX.com")
Characteristics of Second-Order Reactions
The characteristics of the Second-Order reaction are,
- Half-life Period: Let’s consider the initial concentration of the reactant to be [A0] and after t1/2 time, the concentration becomes [A0]/2, thus half-life is given as follows:
![\frac{1}{[A]_0/2} - \frac{1}{[A_0]} = kt_{1/2}\\ \Rightarrow \frac{2}{[A]_0} - \frac{1}{[A_0]} = kt_{1/2} \\ \Rightarrow \frac{1}{[A]_0} = kt_{1/2} \\ \Rightarrow t_{1/2} = \frac{1}{k[A]_0}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-b57640cc522d2da518314acc23f4877e_l3.svg "Rendered by QuickLaTeX.com")
Summary of Integrated Rate Law
This is the most common method for studying the kinetics of a chemical reaction. For example, consider the reaction:
nA ⇢ products
If we start with a moles/liter of A and in time t, x moles/liter have reacted so that the concentration after time t is (a – x) moles/liter, then
if the reaction is of the first order, dx/dt = k(a – x), and if the reaction is of the second order, dx/dt = k (a – x)2, and so on.
These differential equations can be integrated to get expressions for the rate constants. These are given below for zero, first, and second-order reactions:
- For zero-order reaction, k = 1/t {[A0] – [A]}
- For first-order reaction, k = 2.303/t log [A0]/[A]
- For second-order reaction, k = 1/t {1/[A] – 1/[A0]}
The advantage of the integrated method is that these integrated forms of equations contain the concentration of a reactant at different times and hence can be solved to find the value of k from the data of the run of one experiment only and need not start with different initial concentrations. Moreover, they can be used to find the time for any fraction of the reaction to complete.
Differential vs Integrated Rate Laws
There are some key differences between both differential and integrated rate laws, which are listed in the following table:
Differential Rate Law | Integrated Rate Law |
|---|---|
| Describes the rate of change of concentration with respect to time. | Describes the relationship between concentration and time. |
| Represents the rate equation in terms of initial concentrations and rate constants. | Represents the concentration of reactants or products as a function of time. |
| Provides information about the instantaneous rate of a reaction at a specific moment in time. | Provides information about the overall change in concentration over a given time interval. |
| Can vary with time and is dependent on the concentration of reactants. | Remains constant for a specific reaction under constant conditions. |
| Typically expressed as a differential equation, involving derivatives. | Usually expressed as a mathematical equation, relating concentrations and time. |
| Helpful in determining the order of a reaction and the reaction rate constant. | Useful for determining reaction orders and obtaining information about reaction mechanisms. |
| Represents the rate of change at a specific point on the reaction progress curve. | Represents the cumulative effect of the reaction at different time points. |
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Sample Problems on Integrated Rate Law
Problem 1: At 373 K, the half-life period for the thermal decomposition of N2O5 is 4.6 sec and is independent of the initial pressure of N2O5. Calculate the specific rate constant at this temperature.
Solution:
Since the half-life period is independent of the initial pressure, this shows that the reaction is of the first order.
For a reaction of the first order, we know that t1/2 = 0.693/k
or
k = 0.693/t1/2 = 0.693/4.6s
= 0.1507 s-1
Problem 2: A first-order reaction is found to have a rate constant, k = 5.5 x 10-14s-1. Find the half-life of the reaction.
Solution:
For a first order reaction, t1/2 = 0.693/k
t1/2 = 0.693/5.5×10-14s-1
= 1.26 x 1013 s-1.
Problem 3: Show that in the case of a first-order reaction, the time required for 99.9% of the reaction to take place is about ten times that required for half the reaction.
Solution:
For reaction of first order,
t1/2 = 2.303/k log a/a – a/2
= 2.303/k log 2
= 2.303/k (0.3010)
t99.9% = 2,303/k log
= a/a-0.999a
t99.9% = 2.303/k log 10-3
= 2.303/k x 3
Therefore, t99.9%/t1/2 = 3/0.3010 ≅ 10
Problem 4: The initial concentration of N2O5 in the first-order reaction, N2O5(g) ⇢ 2 NO2(g)+ 1/2 O2(g), was 1.24 x 10-2 mol L-1 at 318 K. The concentration of N2O5 after 60 minutes was 0.20 x 10-2 mol L-1. Calculate the rate constant of the reaction at 318 K.
Solution:
k = 2.303/t log [A]0/[A] = 2.303/t log [N2O5]0/[N2O5]t
2.303/60min log 1.24 x 10-2 mol L-1/0.2 x 10-2 mol L-1
= 2.303/60 log 6.2 min-1 = 2.303/60 x 0.7924min-1
= 0.0304 min-1.
Problem 5: A first-order reaction is found to have a rate constant k = 7.39 x 10-5 sec-1. Find the half-life of the reaction (log 2 = 0.3010).
Solution:
For a first order reaction, k = 2.303/t log a/a-x
For t = t1/2, x = a/2
t1/2 = 2.303/k log a/ a-a/2
= 2.303/k log 2
= 2.303/7.39×10-5s-1 x 0.3010
= 9.38 x 103 s-1.
FAQs on Integrated Rate Law
1. What is Integrated Rate Law?
An integrated rate law is an equation that describes the relationship between the concentration of a reactant and time during a chemical reaction. It integrates the rate equation, which is typically derived from the rate of change of reactant concentrations with respect to time.
2. What are Integrated Rate Laws for Different Order Reactions?
For different order reactions, rate law is given as follows:
- For Zero-order Reaction: Rate ∝ [A]0
- For First-order Reaction: Rate ∝ [A]
- For Second-order Reaction: Rate ∝ [A]2
Where [A] is the concentration of the reactant.
3. What are Common Forms of Integrated Rate Equations?
The common form for integrated rate Equation for various differnt order reactions as follows:
- For Zero-order reaction: [A] = [A₀] – kt
- For First-order reaction: ln[A] = ln[A₀] – kt
- For Second-order reaction: 1/[A] = 1/[A₀] + kt
Where,
- k is the rate constant,
- [A₀] is the inital concentration of the reactant,
- [A] is the required concentration after time t, and
- ln represents the natural logarithm.
4. Can Integrated Rate Laws be Used for All Types of Reactions?
Integrated rate laws are typically derived for elementary reactions (reactions that occur in a single step) and reactions with simple rate expressions. They may not be directly applicable to complex reaction mechanisms involving multiple steps or reactions with non-elementary rate laws. In such cases, alternative mathematical approaches or computational methods may be required to analyze the reaction kinetics.
5. What are Units for Rate Constant in Integrated Rate Laws?
The units of the rate constant (k) in integrated rate laws depend on the order of the reaction, and given as follows:
- For zero-order reactions, the units of k are concentration/time (e.g., M/s).
- For first-order reactions, the units of k are 1/time (e.g., 1/s).
- For second-order reactions, the units of k are 1/(concentration·time) (e.g., 1/(M·s)).
6. Can Integrated Rate Laws be Applied to Reversible Reactions?
Integrated rate laws can be used for reversible reactions if the reaction is in a steady state or if the forward and backward reactions have reached equilibrium. In such cases, the concentrations of reactants or products can be treated as constant, allowing for the application of integrated rate laws. However, for reversible reactions that are not at equilibrium, integrated rate laws may not accurately describe the kinetics, and more complex mathematical models are necessary.
Collision Theory
Collision Theory says that when particles collide (strike) each other, a chemical reaction occurs. However, this is necessary but may not be a sufficient condition for the chemical reaction. The collision of molecules must be sufficient to produce the desired products following the chemical reaction. The effective collision process, on the other hand, will determine the qualities and properties of the resulting product. As a result, understanding the collision theory is required in order to understand and determine the resulting products.
Max Trautz and William Lewis created the Collision Theory of Chemical Reactions in 1916-1918, which was based on the kinetic theory of gases. The kinetic Theory of Gases explains the behavior of gases by imagining them as a swarm of particles, molecules, or atoms moving in random directions.
Theory of Collision
According to the Theory of Collision, the collision of molecules is a pre-requisite condition for a chemical reaction to occur. It is a simple rule that more molecules lead to more collisions. As a result, the fraction of collision is determined by the number of particles involved in the collision. Collisions should have enough energy called Activation Energy to start a reaction. Since a chemical reaction involves bond breaking and bond formation, hence, bond disruption will occur only if the collision strength is strong.
Collisions are temperature-dependent—the higher the temperature, the more collisions. Collisions become more violent at higher temperatures. Because neutral molecules have a lower energy level, they cannot break bonds or participate in the collision process, whereas molecules with sufficient energy will. Bending, stretching, and twisting the bond are all part of the reaction process. As a result, the process requires energetic molecules.
Collision of Molecules gives an idea about energy and the mechanism of a chemical reaction.
Collision Theory of Chemical Reactions
According to the Collision Theory of Chemical Reactions, “The molecules of reactants are assumed to be hard spheres, and the reactions are assumed to occur only when these spheres (molecules) clash with each other”. Hence, it became necessary to quantify the number of collisions that occurred in a chemical reaction to produce products in order to have a clear image of the reaction. Hence, the term collision frequency was coined.
Molecular Collisions
Collision theory of chemical reactions and their kinetics has made significant advances that are critical in today’s fast-paced world. Be it packaged drinking water, water bottles, steel production plants, the fastest motor vehicles, or synthetically engineered biological implants, they all involve a chemical reaction in some form. In order to gain a better understanding of these chemical events,
The basic postulates of Molecular Collisions are,
- More molecules result in more molecular collisions.
- In the reaction, various molecules collide to perform the collision.
- The increase in the temperature results in more molecular collisions.
Collision Frequency
Collision Frequency is the number of collisions per second per unit volume of the reacting mixture. It is commonly represented by the letter Z.
We already know that the rate of a chemical reaction is affected by Activation Energy, hence, we will establish a relation between the Rate of Reaction, Collision Frequency, and the Activation Energy of a chemical reaction. Consider the following reaction:
P + Q → Product
According to Collision Theory, the Rate of the above reaction is given by:
Rate = ZPQe−Ea/RT
Where,
- ZPQ is collision frequency of reactants P and Q
- Ea is Activation Energy
- R is Universal Gas Constant
- T is Temperature in absolute scale
If we compare the above equation with Arrhenius’s Equation k = A -Ea/RT we find that A which is the Pre-Exponential Factor in Arrhenius’s equation is similar to ZPQ i.e. Collision Frequency.
Effective Collision
In real scenario especially in the case of complex reaction, not all collision leads to the formation of a product. In order to form a product the collision of molecules must have minimum or sufficient kinetic energy and should also have proper orientation. Such a collision of molecules in which there is minimum energy and proper orientation that leads to the breaking and formation of a bond is called an Effective Collision.
To take account of effective collisions out of total collisions we have a factor ρ which is called the steric factor or the probability factor. Hence, the above equation for the Rate of Reaction can be rewritten as
Rate = ρZPQe−Ea/RT
Thus, we can say that Activation Energy and Proper Orientation are the two most important factors in determining Effective Collision and hence, the Rate of Reaction.
Apart from the above two mentioned factors, the surface area also impacts collision and rate of reaction. We will see its mechanism below:
Collision Theory: Surface Area
When the surface area is large, more molecules are present, and more molecules can react with each other, resulting in a higher collision or reaction rate. As a result, the larger the surface area, the faster the response. Furthermore, according to the collision hypothesis, if the surface area of molecules is greater, it has more energy and boosts the reaction rates.
Since not all collisions lead to the formation of new products based on this collision is classified into two categories. We will learn those types below.
Types of Collision
The types of collision are classified on the basis of the formation of products. Basically, there are two types of collision
- Elastic Collision
- Inelastic Collision
Elastic Collision
In Elastic Collision, the system’s kinetic and momentum energy are both conserved. It means the total Kinetic Energy of the two bodies before and after the collision remains the same. The collision of distinct subatomic particles is primarily elastic in this case. The impact of two glass or steel balls, for example, is often elastic. The forces involved in elastic collisions are conservative in nature.
Pictorial Representation of Elastic Collision is given below:
Inelastic Collision
An inelastic collision is one in which kinetic energy is not conserved and only momentum is conserved. The Kinetic Energy gets transformed into other forms of energy say Thermal Energy, Sound Energy, etc. Every day, we encounter numerous collisions that are mostly inelastic. For Example, a ball hitting the ground from a height. Some of the kinetic energy gets transformed into thermal and sound energy.
Pictorial Representation of Inelastic Collision is given below:
The activation energy is another quantity that has a substantial impact on the speeds of chemical processes (Ea). Arrhenius used the term activation energy to describe the least amount of energy that reactants must have in order to generate a product during a chemical reaction.
Activation Energy
Activation Energy is the minimum amount of energy required by the reacting particles in any given reaction for that reaction to occur. Particles do not react unless they collide with enough energy to produce the Activation Energy. Before a reaction may occur, Activation Energy must be given. To begin a chemical reaction, chemical bonds in the reactants must be broken, which takes energy. The energy required to initiate the reaction is referred to as activation energy. When the Activation Energy is low enough, the reaction can begin at ambient temperature without being heated. When the Activation Energy gap is large enough, then the reaction occurs at elevated temperature i.e. external energy is provided to break the barrier of Activation Energy.
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FAQs on Collision Theory
Q 1: What is the Collision Theory of Chemical Reactions?
Answer:
Collision Theory of Molecule states that for a chemical reaction to happen molecules of reactant must collide effectively and in a proper orientation.
Q2: What is Collision Frequency?
Answer:
Collision Frequency is the number of collision per second per unit volume of reaction mixture.
Q3: What is the relation between Rate of Reaction and Collision Frequency?
Answer:
The relation between Rate of Reaction and Collision Frequency is given by
Rate = ρZPQe−Ea/RT
where,
- ZPQ is the collision frequency of reactants P and Q
- Ea is the Activation Energy
- R is the Universal Gas Constant
- T is the Temperature in absolute scale
- ρ is the Steric Factor
Q4: What is Activation Energy?
Answer:
Activation energy is defined as the minium energy required to initiate a chemical recation.
Q5: What is Effective Collision?
Answer:
Effective Collision refers to the collision in which reactant molecule collide with a minimum threshold energy and in proper orientation so as there is breaking and formation of bond among the atoms of the molecule.
Activation Energy Formula
Activation energy of a chemical reaction is defined as the least amount of energy necessary to initiate the reaction. It can be interpreted as the differential in energy content between molecules and atoms that causes it to be in an activation or transition-state configuration while the associated atoms and molecules stay in their initial configuration. It is known that to initiate a reaction, molecules must collide with other molecules and exchange kinetic energy or velocity. There will be no response if the collision does not occur or if the molecules do not have enough kinetic energy. This forms the basis for the concept of activation energy. Its standard unit of measurement is kilojoules per mole (kJ/mol).
Formula
Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]
where,
Ea is the activation energy of the reaction,
R is the ideal gas constant with the value of 8.3145 J/K mol,
k1,k2 are the rates of reaction constant at initial and final temperature,
T1 is the initial temperature,
T2 is the final temperature.
This is also known as the Arrhenius equation.
Derivation
Suppose a reaction takes place between two reactants P and Q to give a product R. The completion of a reaction is ensured and denoted by its rate constant.
We know the formula for rate constant is given by,
k = Ae−EaRT
Taking log on both sides we get,
ln k = −EaRT + ln A
For initial temperature T1 and rate of constant k1, the equation is written as,
ln k1 = −Ea/RT1 + ln A …….. (1)
For final temperature T2 and rate of constant k2, the equation is written as,
ln k2 = −Ea/RT2 + ln A …….. (2)
Subtracting (2) from (1) we get,
ln k2 – ln k1 = −Ea/RT2 + ln A − (− Ea/RT1 + ln A)
ln (k2/k1) = EaR (1/T1 − 1/T2)
2.303 log (k2/k1) = EaR (1/T1 − 1/T2)
Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]
This derives the formula for activation energy.
Sample Problems
Problem 1. Calculate the activation energy of a reaction if its rate doubles when there is a temperature change from 200K to 400K.
Solution:
We have,
k2 = 2k1,
T1 = 200
T2 = 400
Using the formula we get,
Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]
= 2.303 (8.3145) (log 2) (80000/200)
= 461090.907/200
= 2305.45 KJ/mol
Problem 2. Calculate the activation energy of a reaction if its rate triples when there is a temperature change from 100K to 300K.
Solution:
We have,
k2 = 3k1,
T1 = 100
T2 = 300
Using the formula we get,
Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]
= 2.303 (8.3145) (log 3) (30000/200)
= 274012.079/200
= 1370.060 KJ/mol
Problem 3. Calculate the activation energy of a reaction if its rate quadruples when there is a temperature change from 150K to 400K.
Solution:
We have,
k2 = 4k1,
T1 = 150
T2 = 400
Using the formula we get,
Ea = 2.303 (8.3145) (log 4) (60000/250)
= 691636.36/250
= 2766.55 KJ/mol
Problem 4. Calculate the activation energy of a reaction if its rate becomes five times when there is a temperature change from 300K to 600K.
Solution:
We have,
k2 = 5k1,
T1 = 300
T2 = 600
Using the formula we get,
Ea = 2.303 (8.3145) (log 5) (180000/300)
= 2405791.59/300
= 8019.30 KJ/mol
Problem 5. Calculate the change in the rate of reaction if the activation energy of a reaction is 500 KJ/mol when there is a temperature change from 120K to 360K.
Solution:
We have,
Ea = 500
T1 = 120
T2 = 360
Using the formula we get,
=> 3000 = 2.303 (log k2/k1) [43200/240]
=> log (k2/k1) = (500/2.303) (240/43200)
=> log (k2/k1) = 7.23
=> k2/k1 = 16
=> k2 = 16 k1
Problem 6. Calculate the change in the rate of reaction if the activation energy of a reaction is 200 KJ/mol when there is a temperature change from 50K to 100K.
Solution:
We have,
Ea = 200
T1 = 50
T2 = 100
Using the formula we get,
=> 200 = 2.303 (log k2/k1) [5000/50]
=> log (k2/k1) = (200/2.303) (50/5000)
=> log (k2/k1) = 0.86
=> k2/k1 = 7.37
=> k2 = 7.37 k1
Problem 7. Calculate the change in the rate of reaction if the activation energy of a reaction is 450 KJ/mol when there is a temperature change from 100K to 200K.
Solution:
We have,
Ea = 450
T1 = 100
T2 = 200
Using the formula we get,
=> 450 = 2.303 (log k2/k1) [20000/100]
=> log (k2/k1) = (450/2.303) (100/20000)
=> log (k2/k1) = 0.97
=> k2/k1 = 9.33
=> k2 = 9.33 k1
Temperature Dependence of the Rate of a Reaction
The meal cooks slowly if the gas is kept at a low temperature while cooking. When we raise the temperature to its highest setting, however, the food cooks quickly. As a result, increasing the temperature increases the rate of a reaction. The Arrhenius equation helps explain this rate-temperature relationship. Let’s have a look at this equation and see how it works.
Temperature dependence of the rate of a reaction
Activation energy comes into play. A reaction occurs when the reactant molecules clash with each other, according to collision theory. The threshold energy is the smallest amount of energy that colliding molecules must have in order for their collision to be effective.
The activation energy is the lowest additional amount of energy absorbed by the reactant molecules in order for their energy to equal the threshold value.
Threshold energy = Activation energy + Energy possessed.
The lower the activation energy, the faster the reaction. The reactants must overcome an energy barrier in order to transform into products. Reactant molecules absorb energy and create an intermediate called an activated complex, which dissociates into the products almost instantly.
From left to right, the diagram is viewed. At first, the system contains solely reactants (A + B). When sufficient energy reactant molecules collide, they generate a high-energy activated complex or transition state. After that, the unstable transition state decays to produce stable products (C + D).
The activation energy of the reaction, Ea, is shown as the energy difference between the reactants and the transition state in the diagram. The enthalpy change of the reaction (H) is equal to the energy difference between the reactants and products. The reaction is exothermic (H<0) in this example because it results in a drop in the system enthalpy.
Temperature Dependence of the rate of a reaction
The rate constant approximately doubles for a chemical process when the temperature rises by ten degrees.
Temperature coefficient = Rate constant at T + 10° / Rate constant at T°
Explanation
If fractions of molecules are plotted against corresponding kinetic energies at a specific temperature, a graph similar to the one depicted is created. The most probable kinetic energy is represented by the peak of the curve, which indicates the kinetic energy possessed by the largest fraction of molecules.
With the increase in temperature
- The maximum of the curve shifts to a higher energy value, indicating that the most likely kinetic energy increases.
- The curve shifts to the right, indicating that there are more molecules with very high energies.
Since total probability must always be one, the area under the curve remains constant. At (t + 10), the region depicting the fraction of molecules with energy equal to or greater than activation energy doubles, resulting in a reaction rate doubled.
Effect of temperature
Temperature is one of the variables that have a significant impact on the rate of a chemical reaction. Milk has frequently been spotted boiling on a gas stove. The rate at which a certain amount of milk boils is determined by the stove’s flame. The milk boils faster if the flame height is set to maximum, while it takes longer if the flame height is set to minimum. The height of the flame here corresponds to the temperature.
When the temperature is high, the milk boils faster, and when the temperature is low, the milk takes longer to boil. The temperature has an impact on many reactions, including the boiling of milk. The reaction rate of the majority of chemical reactions changes as the temperature changes.
For every 10 degrees Celsius increase in temperature, the rate constant for a chemical reaction doubles. There were no definite means to physically measure the temperature dependency of a chemical reaction’s pace until 1889. Svante Arrhenius improved J.H van’t Hoff’s work in 1889 by proposing an equation that quantitatively connected temperature and the rate constant for a process. Arrhenius Equation was the name given to the proposed equation.
Arrhenius equation
The Arrhenius equation can quantitatively explain the temperature dependency of the rate of a chemical process.
k = Ae-Ea/RT
The Arrhenius factor, also known as the frequency factor or pre-exponential factor, is represented by A. Ea is the activation energy in joules/mole, and R is the gas constant.
The fraction of molecules with kinetic energy larger than Ea is represented by the factor e-Ea/RT.
As a result of the Arrhenius equation, it has been discovered that increasing the temperature or decreasing the activation energy causes an increase in the reaction rate and an exponential increase in the rate constant.
Taking both sides of the equation’s natural logarithm
ln k = -(Ea/RT) + ln A
A straight line with slope is drawn when ln k vs 1/T is plotted = -(Ea/R) and intercept = ln A
At temperature T1, equation
ln k1 = Ea/RT1 + ln A
At temperature T2, equation
ln k2 = Ea/RT2 + ln A
For a given reaction, A is constant.
The values of rate constants for temperatures T1 and T2 are k1 and k2, respectively.
Subtracting equation form,
ln k2 – ln k1 = (Ea/RT1) – (Ea/RT2)
ln (k2/k1) = Ea/R ((1/T1)-(1/T2))
log k2/k1 = (Ea/2.303R) × ((1/T1)-(1/T2))
log k2/k1 = (Ea/2.303R) × ((T2-T1)/(T1T2))
Graphical description of effect of temperature
The average kinetic energy of molecules is proportional to temperature, it has been discovered. A bimolecular reaction, according to the collision theory, occurs only when the reacting molecules collide with adequate kinetic energy and suitable orientation.
The fraction of molecules with kinetic energy equal to or greater than Ea at a given temperature may lead to the product. As the temperature rises, the proportion of molecules with energies equal to or greater than (>= Ea) increases. As a result, the reaction rate would increase. Plotting a fraction of molecules with particular kinetic energy versus kinetic energy for two distinct temperatures T1 and T2 illustrates this.
The number of molecules having those levels of kinetic energy is proportional to the area under the curve. At T1 and T2, the entire area is the same. The fraction of molecules with kinetic energy greater than Ea at T1 and T2 are represented by the areas (a) and (b). This means that when the temperature rises, the percentage of molecules having energies greater than Ea rises. As a result, the velocity of the reaction quickens.
Effect of Catalyst
A catalyst is a material that enhances the rate of a reaction while not undergoing any lasting chemical changes. Intermediate Complex Idea: A catalyst makes transient bonds with reactants to produce an intermediate complex, according to this theory. This complex decomposes over time, releasing products and the catalyst.
A catalyst decreases the potential energy barrier by lowering the activation energy. As a result, the catalyst gives an alternative reaction pathway. Catalyze a large number of reactants with a minimal amount of catalyst. Gibbs’ energy is not changed by a catalyst. A catalyst can only catalyze spontaneous reactions and not non-spontaneous reactions. Furthermore, a catalyst does not alter the equilibrium constant; rather, it aids in the speedier attainment of equilibrium.
Sample Problems
Question 1: In chemicals, what is the reaction rate?
Answer:
The frequency with which a chemical reaction occurs is referred to as reaction rate in chemistry. It can also be described in terms of the concentration of a material generated in a time unit (amount per unit volume) or the concentration of a reactant absorbed in a time unit.
Question 2: How does an enzyme speed up a reaction?
Answer:
Enzymes are enzymes that act as biochemical catalysts. Catalysts reduce the amount of energy required to initiate reactions. The activation energy of a reaction decreases as the rate of the reaction increases. Enzymes also accelerate processes by lowering the activation energy.
Question 3: Explain Temperature Dependence of the rate of a reaction.
Answer:
The rate constant approximately doubles for a chemical process when the temperature rises by ten degrees.
Temperature coefficient = Rate constant at T + 10° / Rate constant at T°
Explanation:
If fractions of molecules are plotted against corresponding kinetic energies at a specific temperature, a graph similar to the one depicted is created. The most probable kinetic energy is represented by the peak of the curve, which indicates the kinetic energy possessed by the largest fraction of molecules.
With increase in temperature:
The maximum of the curve shifts to a higher energy value, indicating that the most likely kinetic energy increases. The curve shifts to the right, indicating that there are more molecules with very high energies.
Since total probability must always be one, the area under the curve remains constant. At (t +10), the region depicting the fraction of molecules with energy equal to or greater than activation energy doubles, resulting in a reaction rate doubled.
Question 4: Define the Effect of temperature.
Answer:
Temperature is one of the variables that has a significant impact on the rate of a chemical reaction. Milk has frequently been spotted boiling on a gas stove. The rate at which a certain amount of milk boils is determined by the stove’s flame. The milk boils faster if the flame height is set to maximum, while it takes longer if the flame height is set to minimum. The height of the flame here corresponds to the temperature.
When the temperature is high, the milk boils faster, and when the temperature is low, the milk takes longer to boil. Temperature has an impact on many reactions, including the boiling of milk. The reaction rate of the majority of chemical reactions changes as the temperature changes.
For every 10° Celsius increase in temperature, the rate constant for a chemical reaction doubles. There was no definite means to physically measure the temperature dependency of a chemical reaction’s pace until 1889. Svante Arrhenius improved J.H van’t Hoff’s work in 1889 by proposing an equation that quantitatively connected temperature and the rate constant for a process. Arrhenius Equation was the name given to the proposed equation.
Question 5: What role does pH play in reaction rate?
Answer:
Chemical reactions can be speed up or slowed down by changing the pH, temperature, or concentration of the substratum. The enzyme complex to which it interacts is referred to as the substrate. The enzyme’s reaction rate increases at appropriate pH, but decreases at less than optimal pH. It is eventually harmed when an enzyme is denatured.
Question 6: Explain the Effect of the Catalyst in brief.
Answer:
A catalyst is a material that enhances the rate of a reaction while not undergoing any lasting chemical changes. Intermediate Complex Idea: A catalyst makes transient bonds with reactants to produce an intermediate complex, according to this theory. This complex decomposes over time, releasing products and the catalyst.
A catalyst decreases the potential energy barrier by lowering the activation energy. As a result, the catalyst gives an alternative reaction pathway. Catalyze a large number of reactants with a minimal amount of catalyst. Gibbs energy is not changed by a catalyst. A catalyst can only catalyze spontaneous reactions and not non-spontaneous reactions. Furthermore, a catalyst does not alter the equilibrium constant; rather, it aids in the speedier attainment of equilibrium.
Question 7: Write the Arrhenius equation and explain the terms involved in it.
Answer :
k = Ae-Ea/RT
Where,
k = rate constant of the reaction
A = Arrhenius Constant
Ea = Activation Energy for the reaction (in Joules mol-1)
R = Universal Gas Constant
T = Temperature in absolute scale (in kelvins)
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