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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})
Solution :
Step 1: Identification of the Rate Law Expression
The rate law for the decomposition of acetaldehyde is given as:
$\text{Rate} = k [CH_{3}CHO]^{3/2}$
[Per the definition of the Rate Law, the rate of a reaction is proportional to the concentration of reactants raised to the power of their respective stoichiometric orders.]
Step 2: Determining the Order of Reaction
The order of reaction ($n$) is defined as the sum of the exponents of the concentration terms in the rate law expression. Given the rate law expression above:
$n = \frac{3}{2} = 1.5$
[By the Law of Mass Action and Rate Law definitions, the order of reaction is the sum of the powers of the concentration terms appearing in the rate equation.]
Step 3: Deriving the Dimensions (Units) of the Rate Constant ($k$)
The general rate equation is expressed as:
$\text{Rate} = k [Concentration]^n$
The units for $\text{Rate}$ are $\text{mol L}^{-1} \text{s}^{-1}$.
The units for $[Concentration]$ are $\text{mol L}^{-1}$.
Therefore, the units for $k$ can be derived using the formula:
$k = \frac{\text{Rate}}{[Concentration]^n} = \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^n}$
Substituting $n = 1.5$ (or $\frac{3}{2}$):
$k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^{3/2}}$
$k = (\text{mol L}^{-1})^{1 - 1.5} \text{s}^{-1}$
$k = (\text{mol L}^{-1})^{-0.5} \text{s}^{-1}$
$k = \text{mol}^{-0.5} \text{L}^{0.5} \text{s}^{-1}$
Visual Representation of Kinetic Order
Summary of Calculated Values
| Parameter | Value |
|---|---|
| Order of Reaction ($n$) | $1.5$ |
| Units of Rate Constant ($k$) | $\text{mol}^{-0.5} \text{L}^{0.5} \text{s}^{-1}$ |
Final Solution: The order of the reaction is 1.5, and the dimensions of the rate constant are $\text{mol}^{-0.5} \text{L}^{0.5} \text{s}^{-1}$.
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 (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?
- Q3.7: 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?
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