Question 1

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 CH₃NC, we can use the equation: ln([CH₃NC]t/[CH₃NC]0) = -kt 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 the time. If it takes 10.3 minutes for exactly one quarter of the initial amount of CH₃NC to react, that means [CH₃NC]t/[CH₃NC]0 = 0.75. Thus, we can rewrite the equation as: ln(0.75) = -k(10.3 min) Solving for k, we get: k = (ln(0.75))/(-10.3 min) = 0.0279 min ⁻¹

Question 2

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 3

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

Accepted Answer

We can use the Arrhenius equation:

$k = Ae^{-\frac{E_a}{RT}}$

Taking the natural logarithm of both sides:

$\ln k = \ln A - \frac{E_a}{RT}$

We can then use the two given values of k and temperature to create two equations:

$\ln (2.5 	imes 10^{13}) = \ln A - \frac{E_a}{R(-5+273)}$

$\ln (3.5 	imes 10^{14}) = \ln A - \frac{E_a}{R(25+273)}$

Simplifying:

$\ln A = \ln (2.5 	imes 10^{13}) + \frac{E_a}{R(278)}$

$\ln A = \ln (3.5 	imes 10^{14}) + \frac{E_a}{R(298)}$

Subtracting the second equation from the first:

$0.73 = \frac{E_a}{R}(\frac{1}{278} - \frac{1}{298})$

Solving for $E_a$:

$E_a = 58$ kJ/mol

Question 4

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 decay of tritium follows first-order kinetics, described by the equation $N_t = N_0 e^{-kt}$, where $N_t$ is the amount of substance at time $t$, $N_0$ is the initial amount, $k$ is the rate constant, and $t$ is the time. Given $k = 0.056 \, \text{year}^{-1}$ and $t = 30 \, \text{years}$, we can calculate the fraction remaining as $e^{-0.056 \times 30} \approx 0.19$.

Question 5

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

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

Question 6

If the activation energy of a reaction decreases by 10.0 kJ/mol, from 100.0 to 90.0 kJ/mol, what effect will this have on the rate of reaction at 298K?

Accepted Answer

Lowering the activation energy increases the rate of reaction. According to the Arrhenius equation, a decrease in activation energy at a constant temperature significantly increases the reaction rate, often by a factor greater than what might be intuitively expected, such as 50 in this context.

Question 7

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]₀e^(-kt). Substituting the given values: [A] = 0.150e^(-5.4 × 10^−2 × 22.0) = 0.0457 M.

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

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 first-order rate constant is given by the formula k = 0.693/t1/2, where t1/2 is the half-life. 
Substituting t1/2 = 5730 years, we get k = 0.693/5730 = 1.21 × 10-4 years-1, which is closest to option B.

Question 10

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...

Question 11

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⁻¹and the rate constant k = 1.08 × 10⁻⁶ s⁻¹, what concentration of R remains after 25 days?

Accepted Answer

The answer of A gas-phase decomposition is first-order with respect...

Question 12

Ammonia will react with oxygen in the presence of a copper catalyst to form nitrogen and water. From 164.5°C to 179.0°C, the rate constant increases by a factor of 4.27. What is the activation energy of this oxidation reaction?

Accepted Answer

The increase in the rate constant with temperature can be analyzed using the Arrhenius equation. The factor increase and temperature change can be used to calculate the activation energy, which is approximately 165 kJ/mol.

Question 13

The rate law for the reaction 3A → C is Rate = 4.36 × 10⁻² L mol⁻¹hr⁻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 14

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 (t1/2) for a first-order reaction can be calculated using the equation: t1/2 = ln(2) / k where k is the rate constant. From the rate law given, we can see that the reaction is first-order with respect to [CH₃NC]. Therefore, we can write: k = (1300 s⁻¹) Plugging this value of k into the equation for t1/2: t1/2 = ln(2) / (1300 s⁻¹) Calculating this value gives us: t1/2 = 5.3 × 10 ⁻⁴s Therefore, the best answer choice is B.

Question 15

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

Question 16

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 SOCl₂to drop from 0.36 M to 0.045 M?

Accepted Answer

For a first-order reaction, the time taken for the concentration to drop to a certain level can be calculated using the formula t = (t₁/₂ / 0.693) * ln([A]₀/[A]). Given the half-life (t₁/₂) is 4.1 hr, [A]₀ = 0.36 M, and [A] = 0.045 M, the time t is approximately 12 hours.

Question 17

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 18

A boiled egg can be cooked at 100.0°C in exactly 5 minutes. At an altitude of around 2000 m where the boiling point of water is 93.0°C, it takes exactly 7.5 minutes to cook the egg to the same amount. What is the activation energy for the reaction involved when an egg is boiled?

Accepted Answer

The problem involves the Arrhenius equation for temperature dependence of reaction rates:

k = Ae^(-Ea/RT)

Where k is the reaction rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

We can write the ratio of two reaction rates at two different temperatures as:

k1/k2 = (A1/A2) * exp[(Ea/R) * (1/T2 - 1/T1)]

We can use this equation to solve for the activation energy for the boiling of an egg. Let's assume that the reaction rate for boiling an egg is proportional to the rate at which heat is transferred to the egg from the boiling water. Then we can write:

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

where T1 is the boiling point of water at sea level (100.0°C), T2 is the boiling point of water at an altitude of 2000 m (93.0°C), and k1/k2 is the ratio of the reaction rates at these two temperatures.

Plugging in the values given, we get:

k1/k2 = (100.0/93.0) * exp[(Ea/R) * (1/366.85 - 1/278.15)]

Solving for Ea, we get:

Ea = -ln(k1/k2) * R * (1/366.85 - 1/278.15)

Ea = -ln(5/7.5) * 8.314 J/(mol*K) * (1/366.85 - 1/278.15)

Ea = 66.3 kJ/mol

Therefore, the answer is D: 66 kJ/mol.

Question 19

In going from room temperature (25.0°C) to 10°C above room temperature, the rate of a reaction doubles. Calculate the activation energy for the reaction.

Accepted Answer

The rate of a reaction doubling with a 10°C increase in temperature suggests a moderate activation energy. Using the Arrhenius equation and the rule of thumb that a 10°C increase doubles the rate, the activation energy is approximately 52.9 kJ/mol.

Question 20

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 given rate law, we can set up a differential equation: $\frac{d[C₄H₆]}{dt} = k[C₄H₆][C₈H₁₂]$ Where k = 0.014 L/(mol·s). Separating variables and integrating, we get: $\int_{[C₄H₆]0}^[C₄H₆]t \frac{d[C₄H₆]}{[C₄H₆]}$ = $\int_0^t k[C₈H₁₂]dt$ After solving the above equation, we'll get concentration of C₄H₆ after 3 hours equal to 0.0052 M. Hence the answer is choice A.

Quiz 16: Kinetics: Rates and Mechanisms of Chemical Reactions

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?

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?

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

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 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?

If the activation energy of a reaction decreases by 10.0 kJ/mol, from 100.0 to 90.0 kJ/mol, what effect will this have on the rate of reaction at 298K?

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 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?

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 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?

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⁻¹and the rate constant k = 1.08 × 10⁻⁶ s⁻¹, what concentration of R remains after 25 days?

Ammonia will react with oxygen in the presence of a copper catalyst to form nitrogen and water. From 164.5°C to 179.0°C, the rate constant increases by a factor of 4.27. What is the activation energy of this oxidation reaction?

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

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?

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 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 SOCl₂to drop from 0.36 M to 0.045 M?

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 boiled egg can be cooked at 100.0°C in exactly 5 minutes. At an altitude of around 2000 m where the boiling point of water is 93.0°C, it takes exactly 7.5 minutes to cook the egg to the same amount. What is the activation energy for the reaction involved when an egg is boiled?

In going from room temperature (25.0°C) to 10°C above room temperature, the rate of a reaction doubles. Calculate the activation energy for the reaction.

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?

Quiz 16: Kinetics: Rates and Mechanisms of Chemical Reactions

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?

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?

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?

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 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?

If the activation energy of a reaction decreases by 10.0 kJ/mol, from 100.0 to 90.0 kJ/mol, what effect will this have on the rate of reaction at 298K?

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 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?

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 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?

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−1and the rate constant k = 1.08 × 10−6 s−1, what concentration of R remains after 25 days?

Ammonia will react with oxygen in the presence of a copper catalyst to form nitrogen and water. From 164.5°C to 179.0°C, the rate constant increases by a factor of 4.27. What is the activation energy of this oxidation 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 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?

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 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?

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 boiled egg can be cooked at 100.0°C in exactly 5 minutes. At an altitude of around 2000 m where the boiling point of water is 93.0°C, it takes exactly 7.5 minutes to cook the egg to the same amount. What is the activation energy for the reaction involved when an egg is boiled?

In going from room temperature (25.0°C) to 10°C above room temperature, the rate of a reaction doubles. Calculate the activation energy for the reaction.

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 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?

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?

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

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 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?

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 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?

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 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?

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⁻¹and the rate constant k = 1.08 × 10⁻⁶ s⁻¹, what concentration of R remains after 25 days?

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

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?

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 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 SOCl₂to drop from 0.36 M to 0.045 M?

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?