Question 1

Dinitrogen tetraoxide, N₂O₄, decomposes to nitrogen dioxide, NO₂, in a first-order process. If k = 2.5 × 10³ s^-1 at -5°C and k = 3.5 × 10⁴ s^-1 at 25°C, what is the activation energy for the decomposition?

Accepted Answer

The Arrhenius equation can be used to relate the rate constant (k) to the temperature (T) and the activation energy (Ea):

k = A e^(-Ea/RT)

where A is a pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin.

Taking the natural logarithm of both sides yields:

ln(k) = ln(A) - Ea/RT

This form of the equation can be used to determine the activation energy from two sets of experimental data at different temperatures. Taking the ratio of the two equations gives:

ln(k2/k1) = Ea/R [(1/T1) - (1/T2)]

where k1 and k2 are the rate constants at temperatures T1 and T2, respectively.

Substituting the given values, we have:

ln(3.5 × 10^14/2.5 × 10^13) = Ea/8.314 [(1/268) - (1/298)]

solving for Ea gives:

Ea = -ln(3.5 × 10^14/2.5 × 10^13) × 8.314 [(1/268) - (1/298)]

Ea ≈ 58 kJ/mol

Question 2

Butadiene, C₄H₆ (used to make synthetic rubber and latex paints) reacts to C₈H₁₂ with a rate law of rate = 0.014 L/(mol·s) [C₄H₆]². What will be the concentration of C₄H₆ after 3.0 hours if the initial concentration is 0.025 M?

Accepted Answer

Using the rate law, we can set up a differential equation: $\frac{d[C₄H₆]}{dt} = k[C₄H₆][C₈H₁₂]$ Plugging in values: $\frac{d[C₄H₆]}{dt} = (0.014 L/(mol·s))(0.025 M)[C₈H₁₂]$ Integrating with initial condition [C₄H₆] = 0.025 M at t = 0: $\int_{0.025}^{[C₄H₆]_t} \frac{d[C₄H₆]}{[C₄H₆]} = (0.014 L/(mol·s))(0.025 M) \int_0^{3 ext{ hours}} dt$ $\ln\frac{[C₄H₆]_t}{0.025} = 0.042$ $[C₄H₆]_t = 0.0052$ M Therefore, the answer is A, 0.0052 M.

Question 3

The rate law for the reaction 3A → 2B is rate = k[A] with a rate constant of 0.0447 hr^-1. What is the half-life of the reaction?

Accepted Answer

The reaction is first-order because the rate law is rate = k[A]. The half-life for a first-order reaction is given by t₁/₂ = 0.693/k. Substituting k = 0.0447 hr⁻¹, we get t₁/₂ = 0.693/0.0447 ≈ 15.5 hr.

Question 4

The rate law for the rearrangement of CH₃NC to CH₃CN at 800 K is Rate = (1300 s^-1)[CH₃NC]. What is the half-life for this reaction?

Accepted Answer

The half-life of a first-order reaction can be calculated using the equation: t1/2 = ln(2)/k where k is the rate constant. In this case, the rate law is: Rate = k[CH₃NC] Comparing this with the standard form of the rate law, we can see that the rate constant is: k = 1300 s^-1 Substituting this into the equation for half-life, we get: t1/2 = ln(2)/k = ln(2)/(1300 s^-1) ≈ 5.3 × 10^-4 s Therefore, the correct answer is B.

Question 5

Cyclopropane is converted to propene in a first-order process. The rate constant is 5.4 × 10^-2 hr^-1. If the initial concentration of cyclopropane is 0.150 M, what will its concentration be after 22.0 hours?

Accepted Answer

The concentration of cyclopropane after 22.0 hours can be calculated using the first-order kinetics formula: [A] = [A]₀ * e^(-kt). Substituting the given values: [A] = 0.150 * e^(-5.4 × 10^-2 * 22) = 0.0457 M.

Question 6

The decomposition of SOCl₂ is first-order in SOCl₂. If the half-life for the reaction is 4.1 hr, how long would it take for the concentration of SOCl₂ to drop from 0.36 M to 0.045 M?

Accepted Answer

The answer of The decomposition of SOCl₂ is first-order in...

Question 7

Carbon-14 is a radioactive isotope which decays with a half-life of 5730 years. What is the first-order rate constant for its decay, in units of years-1?

Accepted Answer

The answer of Carbon-14 is a radioactive isotope which decays...

Question 8

The decomposition of hydrogen peroxide is a first-order process with a rate constant of 1.06 × 10^-3 min^-1. How long will it take for the concentration of H₂O₂ to drop from 0.0200 M to 0.0120 M?

Accepted Answer

The answer of The decomposition of hydrogen peroxide is a...

Question 9

The reaction CH₃NC(g) → CH₃CN(g) is first-order with respect to methyl isocyanide, CH₃NC. If it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react, what is the rate constant in units of min^-1 ?

Accepted Answer

Since the reaction is first-order with respect to methyl isocyanide, we can use the first-order integrated rate law: [CH₃NC]t = [CH₃NC]0 e-k t, where [CH₃NC]t is the concentration of CH₃NC at time t, [CH₃NC]0 is the initial concentration of CH₃NC, k is the rate constant, and t is time. Let's consider the given information, "it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react". That means, at t=10.3 min, [CH₃NC]t = 0.75 [CH₃NC]0 Substituting these values in the first-order integrated rate law, we get: 0.75 [CH₃NC]0 = [CH₃NC]0 e-k (10.3 min) Simplifying, we get: k = ln(4/3)/10.3 min ≈ 0.0279 min^-1 Therefore, the answer is B, 0.0279 min^-1.

Question 10

The rate constant for the reaction 3A → 4B is 6.00 × 10^-3 L mol^-1min^-1. How long will it take the concentration of A to drop from 0.75 M to 0.25 M?

Accepted Answer

We will use the integrated rate law for a first-order reaction, which is: ln([A]t/[A]0) = -kt where [A]t is the concentration of A at time t, [A]0 is the initial concentration of A, k is the rate constant, and t is the time. We rearrange this equation to solve for t: t = (ln([A]0/[A]t))/k Substituting the given values: t = (ln(0.75/0.25))/(6.00 × 10^-3 L mol^-1min^-1) t = 440 min Therefore, it will take 440 min for the concentration of A to drop from 0.75 M to 0.25 M.

Question 11

The reaction X → Y is first-order overall and first-order with respect to the reactant X. The result of doubling the initial concentration of X will be to

Accepted Answer

According to the first-order reaction kinetics, the rate of the reaction is proportional to the concentration of the reactant raised to the power of 1. Therefore, if the concentration of X is doubled, the initial rate will also be doubled.

Question 12

A gas-phase decomposition is first-order with respect to the reactant, R. If the initial concentration of R is 1.0 × 10^-4 mol L^-1 and the rate constant k = 1.08 × 10^-6 s^-1, what concentration of R remains after 25 days?

Accepted Answer

The integrated rate law for a first-order reaction is:ln[R]t = -kt + ln[R]0where [R]t is the concentration of R at time t, k is the rate constant, and [R]0 is the initial concentration of R.We can use this equation to calculate the concentration of R remaining after 25 days:ln[R]t = -(1.08 × 10^-6 s^-1)(25 days)(86400 s/day) + ln(1.0 × 10^-4 mol L^-1)ln[R]t = -2.30[R]t = 9.7 × 10^-6 mol L^-1

Question 13

A first-order reaction has a half-life of 20.0 minutes. Starting with 1.00 × 10²⁰ molecules of reactant at time t = 0, how many molecules remain unreacted after 100.0 minutes?

Accepted Answer

For a first-order reaction, the number of molecules remaining after a certain time can be calculated using the formula $N = N_0 \times (1/2)^{(t/t_{1/2})}$, where $N_0$ is the initial number of molecules, $t$ is the time elapsed, and $t_{1/2}$ is the half-life of the reaction. Given a half-life of 20.0 minutes and a time of 100.0 minutes, the number of half-lives is $100.0 / 20.0 = 5$. Therefore, the fraction of molecules remaining is $(1/2)^5 = 1/32$. Starting with $1.00 \times 10^{20}$ molecules, the number remaining after 100.0 minutes is $1.00 \times 10^{20} / 32$, which does not match any of the provided options exactly, indicating that the correct answer is "None of these choices are correct."

Question 14

A reaction is first-order with respect to the reactant R. Which of the following plots will produce a straight line?

Accepted Answer

A first-order reaction follows the rate law of rate=k[R]. Taking the natural logarithm of both sides gives us ln(rate) = ln(k) + ln[R]. This is in the form of y = mx + b, where ln(rate) is the y-axis, ln(k) is the y-intercept (b), ln[R] is the x-axis, and the slope (m) is equal to the rate constant, k. Therefore, plotting ln[R] vs. time will produce a straight line.

Question 15

Tetrafluoroethylene, C₂F₄, can be converted to octafluorocyclobutane which can be used as a refrigerant or an aerosol propellant. A plot of 1/[C₂F₄] vs. time gives a straight line with a slope of 0.0448 L mol^-1s^-1. What is the rate law for this reaction?

Accepted Answer

The plot of 1/[C2F4] vs. time being a straight line indicates a second-order reaction. The slope of this line is the rate constant (k) for a second-order reaction, so the rate law is Rate = k[C2F4]^2 with k = 0.0448 L mol^-1 s^-1.

Question 16

A reactant R is being consumed in a first-order reaction. What fraction of the initial R is consumed in 4.0 half-lives?

Accepted Answer

In a first-order reaction, the amount of reactant remaining after n half-lives is given by the formula (1/2)^n. After 4 half-lives, the fraction of the initial reactant remaining is (1/2)^4 = 1/16. Therefore, the fraction consumed is 1 - 1/16 = 15/16 = 0.9375, which rounds to 0.94.

Question 17

A reaction is second-order with respect to the reactant R. Which of the following plots will produce a straight line?

Accepted Answer

A second-order reaction has a rate equation of the form: rate=k[R]^2. Taking the reciprocal of both sides gives: 1/rate = 1/k[R]^2 which can be rearranged to give: 1/[R] = kt + 1/[R]0. This is the equation of a straight line with a slope of k and an intercept of 1/[R]0. Therefore, plotting 1/[R] vs. time will produce a straight line for a second-order reaction.

Question 18

The rate law for the reaction 3A → C is Rate = 4.36 × 10^-2 L mol^-1 hr^-1 [A]² What is the half-life for the reaction if the initial concentration of A is 0.250 M?

Accepted Answer

The answer of The rate law for the reaction 3A...

Question 19

The radioactive isotope tritium decays with a first-order rate constant k of 0.056 year^-1. What fraction of the tritium initially in a sample is still present 30 years later?

Accepted Answer

The fraction remaining can be calculated using the first-order decay formula: N/N0 = e^(-kt). Substituting k = 0.056 year^-1 and t = 30 years, we get N/N0 = e^(-0.056*30) ≈ 0.19.

Question 20

The active ingredient in an over the counter pain killer analgesic decomposes with a rate constant, k = 9.05 × 10^-4 day^-¹. How many days does it take for 15% of the original ingredient to decompose?

Accepted Answer

The answer of The active ingredient in an over the...

Quiz 16: Kinetics Rates and Mechanisms of Chemical Reactions

Dinitrogen tetraoxide, N₂O₄, decomposes to nitrogen dioxide, NO₂, in a first-order process. If k = 2.5 × 10³ s^-1 at -5°C and k = 3.5 × 10⁴ s^-1 at 25°C, what is the activation energy for the decomposition?

Butadiene, C₄H₆ (used to make synthetic rubber and latex paints) reacts to C₈H₁₂ with a rate law of rate = 0.014 L/(mol·s) [C₄H₆]². What will be the concentration of C₄H₆ after 3.0 hours if the initial concentration is 0.025 M?

The rate law for the reaction 3A → 2B is rate = k[A] with a rate constant of 0.0447 hr^-1. What is the half-life of the reaction?

The rate law for the rearrangement of CH₃NC to CH₃CN at 800 K is Rate = (1300 s^-1) [CH₃NC]. What is the half-life for this reaction?

Cyclopropane is converted to propene in a first-order process. The rate constant is 5.4 × 10^-2 hr^-1. If the initial concentration of cyclopropane is 0.150 M, what will its concentration be after 22.0 hours?

The decomposition of SOCl₂ is first-order in SOCl₂. If the half-life for the reaction is 4.1 hr, how long would it take for the concentration of SOCl₂ to drop from 0.36 M to 0.045 M?

Carbon-14 is a radioactive isotope which decays with a half-life of 5730 years. What is the first-order rate constant for its decay, in units of years-1?

The decomposition of hydrogen peroxide is a first-order process with a rate constant of 1.06 × 10^-3 min^-1. How long will it take for the concentration of H₂O₂ to drop from 0.0200 M to 0.0120 M?

The reaction CH₃NC(g) → CH₃CN(g) is first-order with respect to methyl isocyanide, CH₃NC. If it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react, what is the rate constant in units of min^-1 ?

The rate constant for the reaction 3A → 4B is 6.00 × 10^-3 L mol^-1min^-1. How long will it take the concentration of A to drop from 0.75 M to 0.25 M?

The reaction X → Y is first-order overall and first-order with respect to the reactant X. The result of doubling the initial concentration of X will be to

A gas-phase decomposition is first-order with respect to the reactant, R. If the initial concentration of R is 1.0 × 10^-4 mol L^-1 and the rate constant k = 1.08 × 10^-6 s^-1, what concentration of R remains after 25 days?

A first-order reaction has a half-life of 20.0 minutes. Starting with 1.00 × 10²⁰ molecules of reactant at time t = 0, how many molecules remain unreacted after 100.0 minutes?

A reaction is first-order with respect to the reactant R. Which of the following plots will produce a straight line?

Tetrafluoroethylene, C₂F₄, can be converted to octafluorocyclobutane which can be used as a refrigerant or an aerosol propellant. A plot of 1/[C₂F₄] vs. time gives a straight line with a slope of 0.0448 L mol^-1s^-1. What is the rate law for this reaction?

A reactant R is being consumed in a first-order reaction. What fraction of the initial R is consumed in 4.0 half-lives?

A reaction is second-order with respect to the reactant R. Which of the following plots will produce a straight line?

The rate law for the reaction 3A → C is Rate = 4.36 × 10^-2 L mol^-1 hr^-1 [A]² What is the half-life for the reaction if the initial concentration of A is 0.250 M?

The radioactive isotope tritium decays with a first-order rate constant k of 0.056 year^-1. What fraction of the tritium initially in a sample is still present 30 years later?

The active ingredient in an over the counter pain killer analgesic decomposes with a rate constant, k = 9.05 × 10^-4 day^-¹. How many days does it take for 15% of the original ingredient to decompose?

Quiz 16: Kinetics Rates and Mechanisms of Chemical Reactions

Dinitrogen tetraoxide, N2O4, decomposes to nitrogen dioxide, NO2, in a first-order process. If k = 2.5 × 103 s-1 at -5°C and k = 3.5 × 104 s-1 at 25°C, what is the activation energy for the decomposition?

Butadiene, C4H6 (used to make synthetic rubber and latex paints) reacts to C8H12 with a rate law of rate = 0.014 L/(mol·s) [C4H6]2. What will be the concentration of C4H6 after 3.0 hours if the initial concentration is 0.025 M?

The rate law for the reaction 3A → 2B is rate = k[A] with a rate constant of 0.0447 hr-1. What is the half-life of the reaction?

The rate law for the rearrangement of CH3NC to CH3CN at 800 K is Rate = (1300 s-1) [CH3NC]. What is the half-life for this reaction?

Cyclopropane is converted to propene in a first-order process. The rate constant is 5.4 × 10-2 hr-1. If the initial concentration of cyclopropane is 0.150 M, what will its concentration be after 22.0 hours?

The decomposition of SOCl2 is first-order in SOCl2. If the half-life for the reaction is 4.1 hr, how long would it take for the concentration of SOCl2 to drop from 0.36 M to 0.045 M?

Carbon-14 is a radioactive isotope which decays with a half-life of 5730 years. What is the first-order rate constant for its decay, in units of years-1?

The decomposition of hydrogen peroxide is a first-order process with a rate constant of 1.06 × 10-3 min-1. How long will it take for the concentration of H2O2 to drop from 0.0200 M to 0.0120 M?

The reaction CH3NC(g) → CH3CN(g) is first-order with respect to methyl isocyanide, CH3NC. If it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react, what is the rate constant in units of min-1 ?

The rate constant for the reaction 3A → 4B is 6.00 × 10-3 L mol-1min-1. How long will it take the concentration of A to drop from 0.75 M to 0.25 M?

The reaction X → Y is first-order overall and first-order with respect to the reactant X. The result of doubling the initial concentration of X will be to

A gas-phase decomposition is first-order with respect to the reactant, R. If the initial concentration of R is 1.0 × 10-4 mol L-1 and the rate constant k = 1.08 × 10-6 s-1, what concentration of R remains after 25 days?

A first-order reaction has a half-life of 20.0 minutes. Starting with 1.00 × 1020 molecules of reactant at time t = 0, how many molecules remain unreacted after 100.0 minutes?

A reaction is first-order with respect to the reactant R. Which of the following plots will produce a straight line?

Tetrafluoroethylene, C2F4, can be converted to octafluorocyclobutane which can be used as a refrigerant or an aerosol propellant. A plot of 1/[C2F4] vs. time gives a straight line with a slope of 0.0448 L mol-1s-1. What is the rate law for this reaction?

A reactant R is being consumed in a first-order reaction. What fraction of the initial R is consumed in 4.0 half-lives?

A reaction is second-order with respect to the reactant R. Which of the following plots will produce a straight line?

The rate law for the reaction 3A → C is Rate = 4.36 × 10-2 L mol-1 hr-1 [A]2 What is the half-life for the reaction if the initial concentration of A is 0.250 M?

The radioactive isotope tritium decays with a first-order rate constant k of 0.056 year-1. What fraction of the tritium initially in a sample is still present 30 years later?

The active ingredient in an over the counter pain killer analgesic decomposes with a rate constant, k = 9.05 × 10-4 day-1. How many days does it take for 15% of the original ingredient to decompose?

Dinitrogen tetraoxide, N₂O₄, decomposes to nitrogen dioxide, NO₂, in a first-order process. If k = 2.5 × 10³ s^-1 at -5°C and k = 3.5 × 10⁴ s^-1 at 25°C, what is the activation energy for the decomposition?

Butadiene, C₄H₆ (used to make synthetic rubber and latex paints) reacts to C₈H₁₂ with a rate law of rate = 0.014 L/(mol·s) [C₄H₆]². What will be the concentration of C₄H₆ after 3.0 hours if the initial concentration is 0.025 M?

The rate law for the reaction 3A → 2B is rate = k[A] with a rate constant of 0.0447 hr^-1. What is the half-life of the reaction?

The rate law for the rearrangement of CH₃NC to CH₃CN at 800 K is Rate = (1300 s^-1) [CH₃NC]. What is the half-life for this reaction?

Cyclopropane is converted to propene in a first-order process. The rate constant is 5.4 × 10^-2 hr^-1. If the initial concentration of cyclopropane is 0.150 M, what will its concentration be after 22.0 hours?

The decomposition of SOCl₂ is first-order in SOCl₂. If the half-life for the reaction is 4.1 hr, how long would it take for the concentration of SOCl₂ to drop from 0.36 M to 0.045 M?

The decomposition of hydrogen peroxide is a first-order process with a rate constant of 1.06 × 10^-3 min^-1. How long will it take for the concentration of H₂O₂ to drop from 0.0200 M to 0.0120 M?

The reaction CH₃NC(g) → CH₃CN(g) is first-order with respect to methyl isocyanide, CH₃NC. If it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react, what is the rate constant in units of min^-1 ?

The rate constant for the reaction 3A → 4B is 6.00 × 10^-3 L mol^-1min^-1. How long will it take the concentration of A to drop from 0.75 M to 0.25 M?

A gas-phase decomposition is first-order with respect to the reactant, R. If the initial concentration of R is 1.0 × 10^-4 mol L^-1 and the rate constant k = 1.08 × 10^-6 s^-1, what concentration of R remains after 25 days?

A first-order reaction has a half-life of 20.0 minutes. Starting with 1.00 × 10²⁰ molecules of reactant at time t = 0, how many molecules remain unreacted after 100.0 minutes?

Tetrafluoroethylene, C₂F₄, can be converted to octafluorocyclobutane which can be used as a refrigerant or an aerosol propellant. A plot of 1/[C₂F₄] vs. time gives a straight line with a slope of 0.0448 L mol^-1s^-1. What is the rate law for this reaction?

The rate law for the reaction 3A → C is Rate = 4.36 × 10^-2 L mol^-1 hr^-1 [A]² What is the half-life for the reaction if the initial concentration of A is 0.250 M?

The radioactive isotope tritium decays with a first-order rate constant k of 0.056 year^-1. What fraction of the tritium initially in a sample is still present 30 years later?

The active ingredient in an over the counter pain killer analgesic decomposes with a rate constant, k = 9.05 × 10^-4 day^-¹. How many days does it take for 15% of the original ingredient to decompose?