Find the best tutors and institutes for Class 12 Tuition
Q3.7:
What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?
Solution :
1. Effect of Temperature on the Rate Constant
The rate constant ($k$) of a chemical reaction is highly sensitive to changes in temperature. For most chemical reactions, an increase in temperature leads to an exponential increase in the rate constant, typically resulting in a doubling or tripling of the reaction rate for every $10^\circ\text{C}$ rise in temperature.
Qualitative Justification: According to the Maxwell-Boltzmann distribution of molecular energies, an increase in temperature shifts the distribution curve to the right and increases the area under the curve representing molecules with energy equal to or greater than the threshold activation energy ($E_a$). Consequently, the frequency of effective collisions increases, directly elevating the rate constant [$Per\ Arrhenius\ collision\ theory$].
2. Quantitative Representation: The Arrhenius Equation
The quantitative relationship between the rate constant ($k$) and temperature ($T$) is defined by the Arrhenius equation:
$k = A e^{-\frac{E_a}{RT}}$
Where:
- $k$: Rate constant of the reaction.
- $A$: Arrhenius factor or frequency factor (pre-exponential factor).
- $E_a$: Activation energy ($\text{J mol}^{-1}$).
- $R$: Universal gas constant ($8.314 \text{ J K}^{-1} \text{ mol}^{-1}$).
- $T$: Temperature in Kelvin.
3. Mathematical Derivation for Temperature Variation
To evaluate the effect of changing temperature from $T_1$ to $T_2$, we take the natural logarithm ($\ln$) of the Arrhenius equation:
$\ln k = \ln A - \frac{E_a}{RT}$
For two different temperatures $T_1$ and $T_2$ with corresponding rate constants $k_1$ and $k_2$:
$\ln k_1 = \ln A - \frac{E_a}{RT_1}$
$\ln k_2 = \ln A - \frac{E_a}{RT_2}$
Subtracting the first equation from the second yields the linear form used for calculation [$By\ algebraic\ subtraction$]:
$\ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left[ \frac{1}{T_1} - \frac{1}{T_2} \right]$
Converting to base-10 logarithm ($\log$):
$\log \left( \frac{k_2}{k_1} \right) = \frac{E_a}{2.303R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]$
| Parameter | Effect of Increasing Temperature |
|---|---|
| Rate Constant ($k$) | Increases exponentially |
| Fraction of molecules with $E \ge E_a$ | Increases |
| Frequency of collisions | Increases |
Final Solution: The effect of temperature on the rate constant is quantitative expressed via the Arrhenius equation $k = A e^{-E_a/RT}$. This shows that $k$ increases exponentially with temperature because a higher fraction of reactant molecules possess sufficient kinetic energy to overcome the activation energy barrier.
More Questions from Class 12 Chemistry Chemical Kinetics Exercises
- Q3.1 (i): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (i) (3NO(g) \rightarrow N_{2}O (g)) Rate = (k[NO]^{2})
- Q3.1 (ii): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (ii) (H_{2}O_{2} (aq) + 3I^{-} (aq) + 2H^{+} \rightarrow 2H_{2}O (l) + I_{3}^{-}) Rate = (k[H_{2}O_{2}][I^{-}])
- Q3.1 (iii): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (iii) (CH_{3}CHO (g) \rightarrow CH_{4} (g) + CO(g)) Rate = (k [CH_{3}CHO]^{3/2})
- Q3.1 (iv): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (iv) (C_{2}H_{5}Cl (g) \rightarrow C_{2}H_{4} (g) + HCl (g)) Rate = (k [C_{2}H_{5}Cl])
- Q3.1(i): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (i) \(3NO(g) \rightarrow N_{2}O (g)\) Rate = \(k[NO]^{2}\)
- Q3.1(ii): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (ii) \(H_{2}O_{2} (aq) + 3I^{-} (aq) + 2H^{+} \rightarrow 2H_{2}O (l) + I_{3}^{-}\) Rate = \(k[H_{2}O_{2}][I^{-}]\)
- Q3.1(iii): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (iii) \(CH_{3}CHO (g) \rightarrow CH_{4} (g) + CO(g)\) Rate = \(k [CH_{3}CHO]^{\frac{3}{2}}\)
- Q3.1(iv): From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (iv) \(C_{2}H_{5}Cl (g) \rightarrow C_{2}H_{4} (g) + HCl (g)\) Rate = \(k [C_{2}H_{5}Cl]\)
- Q3.10: In a reaction between (A) and (B), the initial rate of reaction ((r_{0})) was measured for different initial concentrations of (A) and (B) as given below: What is the order of the reaction with respect to (A) and (B)?
- Q3.10: In a reaction between \(A\) and \(B\), the initial rate of reaction (\(r_{0}\)) was measured for different initial concentrations of \(A\) and \(B\) as given below: What is the order of the reaction with respect to \(A\) and \(B\)?
- Q3.11: The following results have been obtained during the kinetic studies of the reaction: (2A + B \rightarrow C + D) Determine the rate law and the rate constant for the reaction.
- Q3.11: The following results have been obtained during the kinetic studies of the reaction: \(2A + B \rightarrow C + D\) Determine the rate law and the rate constant for the reaction.
- Q3.12: The reaction between (A) and (B) is first order with respect to (A) and zero order with respect to (B). Fill in the blanks in the following table:
- Q3.12: The reaction between \(A\) and \(B\) is first order with respect to \(A\) and zero order with respect to \(B\). Fill in the blanks in the following table:
- Q3.13 (i): Calculate the half-life of a first order reaction from their rate constants given below: (i) (200 s^{-1})
- Q3.13 (ii): Calculate the half-life of a first order reaction from their rate constants given below: (ii) (2 min^{-1})
- Q3.13 (iii): Calculate the half-life of a first order reaction from their rate constants given below: (iii) (4 years^{-1})
- Q3.13(i): Calculate the half-life of a first order reaction from their rate constants given below: (i) \(200 s^{-1}\)
- Q3.13(ii): Calculate the half-life of a first order reaction from their rate constants given below: (ii) \(2 min^{-1}\)
- Q3.13(iii): Calculate the half-life of a first order reaction from their rate constants given below: (iii) \(4 years^{-1}\)
- Q3.14: The half-life for radioactive decay of (^{14}C) is 5730 years. An archaeological artifact containing wood had only 80% of the (^{14}C) found in a living tree. Estimate the age of the sample.
- Q3.14: The half-life for radioactive decay of \(^{14}C\) is 5730 years. An archaeological artifact containing wood had only 80% of the \(^{14}C\) found in a living tree. Estimate the age of the sample.
- Q3.15 (i): The experimental data for decomposition of (N_{2}O_{5}) [(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2})] in gas phase at 318K are given below: t/s 0 400 800 1200 1600 2000 2400 2800 3200 (10^{2} \times [N_{2}O_{5}])/(mol L^{-1}) 1.63 1.36 1.14 0.93 0.78 0.64 0.53 0.43 0.35 (i) Plot ([N_{2}O_{5}]) against (t).
- Q3.15 (ii): The experimental data for decomposition of (N_{2}O_{5}) [(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2})] in gas phase at 318K are given below: (ii) Find the half-life period for the reaction.
- Q3.15 (iii): The experimental data for decomposition of (N_{2}O_{5}) [(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2})] in gas phase at 318K are given below: (iii) Draw a graph between (\log[N_{2}O_{5}]) and (t).
- Q3.15 (iv): The experimental data for decomposition of (N_{2}O_{5}) [(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2})] in gas phase at 318K are given below: (iv) What is the rate law ?
- Q3.15 (v): The experimental data for decomposition of (N_{2}O_{5}) [(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2})] in gas phase at 318K are given below: (v) Calculate the rate constant.
- Q3.15 (vi): The experimental data for decomposition of (N_{2}O_{5}) [(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2})] in gas phase at 318K are given below: (vi) Calculate the half-life period from (k) and compare it with (ii).
- Q3.15(i): The experimental data for decomposition of \(N_{2}O_{5}\) [\(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2}\)] in gas phase at 318K are given below: (i) Plot \([N_{2}O_{5}]\) against \(t\).
- Q3.15(ii): The experimental data for decomposition of \(N_{2}O_{5}\) [\(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2}\)] in gas phase at 318K are given below: (ii) Find the half-life period for the reaction.
- Q3.15(iii): The experimental data for decomposition of \(N_{2}O_{5}\) [\(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2}\)] in gas phase at 318K are given below: (iii) Draw a graph between \(log[N_{2}O_{5}]\) and \(t\).
- Q3.15(iv): The experimental data for decomposition of \(N_{2}O_{5}\) [\(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2}\)] in gas phase at 318K are given below: (iv) What is the rate law ?
- Q3.15(v): The experimental data for decomposition of \(N_{2}O_{5}\) [\(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2}\)] in gas phase at 318K are given below: (v) Calculate the rate constant.
- Q3.15(vi): The experimental data for decomposition of \(N_{2}O_{5}\) [\(2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2}\)] in gas phase at 318K are given below: (vi) Calculate the half-life period from \(k\) and compare it with (ii).
- Q3.16: The rate constant for a first order reaction is \(60 s^{-1}\). How much time will it take to reduce the initial concentration of the reactant to its \(\frac{1}{16}\)th value?
- Q3.16: The rate constant for a first order reaction is (60 s^{-1}). How much time will it take to reduce the initial concentration of the reactant to its (\frac{1}{16}^{th}) value?
- Q3.17: During nuclear explosion, one of the products is \(^{90}Sr\) with half-life of 28.1 years. If \(1 \mu g\) of \(^{90}Sr\) was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.
- Q3.17: During nuclear explosion, one of the products is (^{90}Sr) with half-life of 28.1 years. If (1\mu g) of (^{90}Sr) was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.
- Q3.18: For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
- Q3.18: For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
- Q3.19: A first order reaction takes 40 min for 30% decomposition. Calculate \(t_{1/2}\).
- Q3.19: A first order reaction takes 40 min for 30% decomposition. Calculate (t_{1/2}).
- Q3.2: For the reaction: (2A + B \rightarrow A_{2}B) the rate = (k[A][B]^{2}) with (k = 2.0 \times 10^{-6} mol^{-2} L^{2} s^{-1}). Calculate the initial rate of the reaction when ([A] = 0.1 mol L^{-1}), ([B] = 0.2 mol L^{-1}). Calculate the rate of reaction after ([A]) is reduced to (0.06 mol L^{-1}).
- Q3.2: For the reaction: \(2A + B \rightarrow A_{2}B\) the rate = \(k[A][B]^{2}\) with \(k = 2.0 \times 10^{-6} mol^{-2} L^{2} s^{-1}\). Calculate the initial rate of the reaction when \([A] = 0.1 \text{ mol } L^{-1}\), \([B] = 0.2 \text{ mol } L^{-1}\). Calculate the rate of reaction after \([A]\) is reduced to \(0.06 \text{ mol } L^{-1}\).
- Q3.20: For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained. Calculate the rate constant.
- Q3.20: For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained. Calculate the rate constant.
- Q3.21: The following data were obtained during the first order thermal decomposition of (SO_{2}Cl_{2}) at a constant volume. ((SO_{2}Cl_{2}(g) \rightarrow SO_{2}(g) + Cl_{2}(g))) Calculate the rate of the reaction when total pressure is 0.65 atm.
- Q3.21: The following data were obtained during the first order thermal decomposition of \(SO_{2}Cl_{2}\) at a constant volume. \(SO_{2}Cl_{2}(g) \rightarrow SO_{2}(g) + Cl_{2}(g)\) Calculate the rate of the reaction when total pressure is 0.65 atm.
- Q3.22: The rate constant for the decomposition of \(N_{2}O_{5}\) at various temperatures is given below: Draw a graph between \(ln k\) and \(1/T\) and calculate the values of \(A\) and \(E_{a}\). Predict the rate constant at 30° and 50°C.
- Q3.22: The rate constant for the decomposition of (N_{2}O_{5}) at various temperatures is given below: Draw a graph between (\ln k) and (1/T) and calculate the values of (A) and (E_{a}). Predict the rate constant at 30° and 50°C.
- Q3.23: The rate constant for the decomposition of hydrocarbons is (2.418 \times 10^{-5}s^{-1}) at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
- Q3.23: The rate constant for the decomposition of hydrocarbons is \(2.418 \times 10^{-5}s^{-1}\) at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
- Q3.24: Consider a certain reaction (A \rightarrow Products) with (k = 2.0 \times 10^{-2}s^{-1}). Calculate the concentration of (A) remaining after 100 s if the initial concentration of (A) is (1.0 mol L^{-1}).
- Q3.24: Consider a certain reaction \(A \rightarrow Products\) with \(k = 2.0 \times 10^{-2}s^{-1}\). Calculate the concentration of \(A\) remaining after 100 s if the initial concentration of \(A\) is \(1.0 mol L^{-1}\).
- Q3.25: Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with \(t_{1/2} = 3.00\) hours. What fraction of sample of sucrose remains after 8 hours ?
- Q3.25: Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with (t_{1/2} = 3.00) hours. What fraction of sample of sucrose remains after 8 hours ?
- Q3.26: The decomposition of hydrocarbon follows the equation \(k = (4.5 \times 10^{11}s^{-1}) e^{-28000K/T}\) Calculate \(E_{a}\).
- Q3.26: The decomposition of hydrocarbon follows the equation (k = (4.5 \times 10^{11}s^{-1}) e^{-28000K/T}) Calculate (E_{a}).
- Q3.27: The rate constant for the first order decomposition of \(H_{2}O_{2}\) is given by the following equation: \(log k = 14.34 – \frac{1.25 \times 10^{4}K}{T}\) Calculate \(E_{a}\) for this reaction and at what temperature will its half-period be 256 minutes?
- Q3.27: The rate constant for the first order decomposition of (H_{2}O_{2}) is given by the following equation: (\log k = 14.34 – 1.25 \times 10^{4}K/T) Calculate (E_{a}) for this reaction and at what temperature will its half-period be 256 minutes?
- Q3.28: The decomposition of (A) into product has value of (k) as (4.5 \times 10^{3} s^{-1}) at 10°C and energy of activation (60 kJ mol^{-1}). At what temperature would (k) be (1.5 \times 10^{4}s^{-1})?
- Q3.28: The decomposition of \(A\) into product has value of \(k\) as \(4.5 \times 10^{3} s^{-1}\) at 10°C and energy of activation \(60 kJ mol^{-1}\). At what temperature would \(k\) be \(1.5 \times 10^{4}s^{-1}\)?
- Q3.29: The time required for 10% completion of a first order reaction at 298K is equal to that required for its 25% completion at 308K. If the value of \(A\) is \(4 \times 10^{10}s^{-1}\). Calculate \(k\) at 318K and \(E_{a}\).
- Q3.29: The time required for 10% completion of a first order reaction at 298K is equal to that required for its 25% completion at 308K. If the value of (A) is (4 \times 10^{10}s^{-1}). Calculate (k) at 318K and (E_{a}).
- Q3.3: The decomposition of \(NH_{3}\) on platinum surface is zero order reaction. What are the rates of production of \(N_{2}\) and \(H_{2}\) if \(k = 2.5 \times 10^{-4} mol^{-1} L s^{-1}\)?
- Q3.3: The decomposition of (NH_{3}) on platinum surface is zero order reaction. What are the rates of production of (N_{2}) and (H_{2}) if (k = 2.5 \times 10^{-4} mol^{-1} L s^{-1})?
- Q3.30: The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.
- Q3.30: The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.
- Q3.4: The decomposition of dimethyl ether leads to the formation of (CH_{4}), (H_{2}) and (CO) and the reaction rate is given by Rate = (k [CH_{3}OCH_{3}]^{3/2}) The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e., (Rate = p_{CH_{3}OCH_{3}}^{3/2}) If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?
- Q3.4: The decomposition of dimethyl ether leads to the formation of \(CH_{4}\), \(H_{2}\) and \(CO\) and the reaction rate is given by Rate = \(k [CH_{3}OCH_{3}]^{\frac{3}{2}} The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e., Rate = \(k(p_{CH_{3}OCH_{3}})^{\frac{3}{2}} If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?
- Q3.5: Mention the factors that affect the rate of a chemical reaction.
- Q3.5: Mention the factors that affect the rate of a chemical reaction.
- Q3.6 (i): A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is (i) doubled
- Q3.6 (ii): A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is (ii) reduced to half ?
- Q3.6(i): A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is (i) doubled
- Q3.6(ii): A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is (ii) reduced to half ?
- Q3.7: What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?
- Q3.8: In a pseudo first order reaction in water, the following results were obtained: Calculate the average rate of reaction between the time interval 30 to 60 seconds.
- Q3.8: In a pseudo first order reaction in water, the following results were obtained: Calculate the average rate of reaction between the time interval 30 to 60 seconds.
- Q3.9 (i): A reaction is first order in (A) and second order in (B). (i) Write the differential rate equation.
- Q3.9 (ii): A reaction is first order in (A) and second order in (B). (ii) How is the rate affected on increasing the concentration of (B) three times?
- Q3.9 (iii): A reaction is first order in (A) and second order in (B). (iii) How is the rate affected when the concentrations of both (A) and (B) are doubled?
- Q3.9(i): A reaction is first order in \(A\) and second order in \(B\). (i) Write the differential rate equation.
- Q3.9(ii): A reaction is first order in \(A\) and second order in \(B\). (ii) How is the rate affected on increasing the concentration of \(B\) three times?
- Q3.9(iii): A reaction is first order in \(A\) and second order in \(B\). (iii) How is the rate affected when the concentrations of both \(A\) and \(B\) are doubled?
CBSE Solutions for Class 12 Chemistry Chemical Kinetics
Chapters in CBSE - Class 12 Chemistry
Top Tutors who teach Chemical Kinetics
Top Tutor
Mahipalpur, Delhi
14 yrs of
Exp
2 hrs of classes completed
Student's Home
As an experienced teacher for 12 years, I have been teaching to make students interested in the subjects of Maths. My attitude is to help children improve in studies in the best possible way.
Top Tutor
Rajouri Garden, Delhi
10 yrs of
Exp
1 student
8 hrs of classes completed
1200
per hour
Online Classes
Student's Home
Tutor's home
I believe in delivering concepts and knowledge from the scratch so as to make the subject easy and relatable. My target is not only marks but rather developing an interest in the students for the subjects so as to have a better understanding and a good prospect for the future.
Top Tutor
Rajarajeshwari Nagar, Bangalore
12 yrs of
Exp
51 students
1960 hrs of classes completed
500
per hour
Online Classes
Student's Home
I have been training students for 12th Board examinations for more than a decade now.
He is outstanding as a teacher, knowledgeable and dedicated. He has helped my daughter so much with his knowledge, that the girl who was just running away from accounts is getting more than 90 percent
Top Tutor
Naskar Bagan, Kolkata
1 yrs of
Exp
3 students
202 hrs of classes completed
400
per hour
Online Classes
Student's Home
🚀 High-Impact Computer Science & IP Tutoring for CBSE& CISCE Class 10, 11 & 12 Hi! I’m a B.C.A. graduate and experienced online educator dedicated to helping students build genuine logical thinking and ace their board examinations. Having scored 94/100 in my own Class 12 Computer Science boards using highly efficient study strategies, I know exactly how to simplify the syllabus for maximum understanding and top marks. I bridge the gap between memorizing syntax and actually understanding how to code. 🌟 Why Choose My Classes? 1. Targeted Expertise: Specialized coaching for CBSE & CISCE Class 10 ,11 & 12 Computer Science, Informatics Practices (IP), and Information Technology (including Java, Python programming and database management). 2. Proven Resources: Standard reference alignment, custom study notes, topic-wise assignments, and rigorous mock tests. 3. Interactive Learning: 100% online sessions utilizing dynamic PPTs and live whiteboards—no boring lectures, just hands-on, practical coding. 4. Track Record: Successfully coached students from top schools to become confident, independent problem solvers. 5. My Approach: I don't just teach you how to write code; I teach you how to think like a programmer so you can approach any exam question with confidence. Let’s turn coding anxiety into board exam success.
Great thought Shares real-life experiences Great mentor Includes most of the important topics in the demo session.
Super Tutor
Katira Maharaja Hata, Arrah
4 yrs of
Exp
16 students
5807 hrs of classes completed
600
per hour
Online Classes
Tutor's home
I have successfully taught hundreds of Class 12 students across multiple boards, including CBSE, ICSE, IGCSE, International Curricula, and State Boards. My expertise spans Mathematics & Physics for students from science, commerce, and arts streams, with a strong focus on clarity and conceptual understanding. Alongside my individual teaching, I manage a coaching institute dedicated to preparing students from Class 10 to 12 and guiding IIT JEE aspirants with personalized strategies for success. Please note: The fees displayed on my profile apply to one-on-one personalized sessions. For details on group or batch classes, please refer to my monthly fee structure or contact me directly.
Shiwam is a good guide for my son. I love the tips and tricks he teaches in Maths so that it becomes easy for my son.
