Find the best tutors and institutes for Class 12 Tuition
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 ?
Solution :
Step 1: Defining the Rate Law
For a reaction that is second order with respect to a reactant $A$, the rate of the reaction ($r_1$) is expressed by the rate law equation:
$r_1 = k[A]^2$
[Per the definition of Rate Law, where $k$ is the rate constant and $[A]$ is the molar concentration of the reactant].
Step 2: Defining the New Concentration
The problem states that the concentration of the reactant is reduced to half of its initial value. Let the initial concentration be $[A]_1$ and the new concentration be $[A]_2$.
$[A]_2 = \frac{1}{2}[A]_1$
Step 3: Calculating the New Rate of Reaction
The new rate of reaction ($r_2$) can be calculated by substituting the new concentration into the rate law equation:
$r_2 = k[A]_2^2$
$r_2 = k \left( \frac{1}{2}[A]_1 \right)^2$
[By the Principle of Substitution in algebraic expressions].
Step 4: Algebraic Simplification
Expanding the squared term:
$r_2 = k \left( \frac{1}{4} \right) [A]_1^2$
$r_2 = \frac{1}{4} (k[A]_1^2)$
Since $r_1 = k[A]_1^2$, we can substitute $r_1$ into the equation:
$r_2 = \frac{1}{4} r_1$
Visual Representation of Kinetic Dependency
Analytical Conclusion
By comparing the initial rate ($r_1$) and the new rate ($r_2$), it is evident that the rate of the reaction decreases by a factor of 4.
Final Solution: The rate of reaction becomes one-fourth ($\frac{1}{4}$) of its original value when the concentration of the reactant is reduced to half.
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(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?
- Q3.7: 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
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.
Top Tutor
Sector 33, Gurgaon
18 yrs of
Exp
4 students
780 hrs of classes completed
1200
per hour
Online Classes
Tutor's home
Expert Chemistry Mentor for IIT-JEE | NEET | CBSE – 18+ Years of Experience Hi, I’m Anuranjita. I am a Senior Chemistry Expert with over 18 years of experience at India's leading institutes like Aakash, FIITJEE, and TIME and hold an M.Tech. degree from Anna University, Chennai—one of the top 10 engineering universities in India. I have refined a highly structured, result-oriented teaching methodology designed to crack • IIT-JEE (Main & Advanced) • NEET • Score 100% in CBSE Board exams. (Class 11 & 12 – Chemistry) Over the years, I have trained thousands of students, many of whom have successfully secured admissions into AIIMS, IITs, NITs, and other top medical and engineering colleges across India. Here is what makes my classes uniquely effective: • Interactive and concept-driven teaching • Focus on building strong fundamentals • Personalized learning based on each student’s pace • Regular doubt-clearing sessions & Chapter-wise tests • Exam-oriented tips and problem-solving strategies • The "Exclusive 5" Batch Model (Personalized Attention) Unlike massive online batches with thousands of students where individual voices get lost, my classes are strictly limited to a maximum of 5 students. This ensures that every single student receives 1-on-1 level attention, and I can monitor each student's real-time progress, strengths, and weaknesses. • Rigorous Testing & PYQ Practice: Chapter-wise tests modeled strictly on the latest NTA patterns, alongside exhaustive solving of past years' questions (PYQs). Looking forward to helping you master chemistry! Best Regards Anuranjita
The class was good. The explanation of the concept is clear. All the queries are being addressed to the student accordingly.
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
Yamare Village, Bangalore
8 yrs of
Exp
1 student
8 hrs of classes completed
1500
per hour
Student's Home
Tutor's home
Hello! I’m Anwar, a certified mathematics tutor with over 10 years of experience helping students excel at every stage, from Primary, Middle School to High School and University level. My passion is to make math clear, engaging, and enjoyable for learners worldwide. I specialize in teaching Maths to students from Grade 8 to Grade 12 across multiple curricula including IGCSE/Cambridge, IB (MYP), GCSE, CBSE and ICSE. I focus on concept clarity and exam-oriented preparation, helping students understand not just how to solve questions, but how to approach them logically. My teaching approach is highly interactive and student-centric. Each session begins with clear explanation of concepts, followed by strategies to decode questions and step-by-step solving methods. Students actively participate during the class and solve questions along with me, which allows me to check their understanding in real time. Once the concepts are tested, students solve questions independently while I closely monitor their working and provide instant feedback wherever required. This method helps students strengthen accuracy, speed and confidence, and is especially effective for students who feel weak or anxious in Maths and Science. I offer one-to-one personalized tutoring with a minimum class duration of one hour, ensuring complete attention and customized learning for every student.
Super Tutor
Banjara Hills, Hyderabad
12 yrs of
Exp
37 students
1638 hrs of classes completed
800
per hour
Online Classes
Tutor's home
Although I haven't taught in schools or colleges, I have been invited to deliver guest lectures at reputed universities. These sessions allowed me to share my expertise with advanced learners and contribute to academic discussions. My focus has always been on delivering value through practical insights, making complex topics accessible and engaging for university students.
The experience is very good , give an detailed explanation with real life examples and also makes the concept easy to understand.
