Question 1

The first-order decay of radon has a half-life of 3.823 days. How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

Accepted Answer

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Question 2

The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams?

Accepted Answer

The decay of radon follows first-order kinetics, and the formula for the remaining amount after time t is N(t) = N0 * (1/2)^(t/T), where N0 is the initial amount, t is the time elapsed, and T is the half-life. After 5.55 days, the remaining radon is 100 * (1/2)^(5.55/3.823) ≈ 36.6 g. Therefore, the decomposed amount is 100 - 36.6 = 63.4 g.

Question 3

The rate constant for a first-order reaction is 0.54 L mol^-1s^-1. What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

Accepted Answer

For a first-order reaction, the half-life is calculated using the formula t₁/₂ = 0.693/k. Substituting the given rate constant (k = 0.54 s⁻¹), the half-life is approximately 1.3 s.

Question 4

How many half-lives are required for the concentration of reactant to decrease to 12.5% of its original value?

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Question 5

The rate constant for the first-order decomposition of N₂O is 3.40 s^-1. What is the half-life of the decomposition?

Accepted Answer

The formula for calculating half-life (t1/2) of a first-order reaction is:

t1/2 = 0.693/k

where k is the rate constant.

Plugging in the given rate constant, we get:

t1/2 = 0.693/3.40 s-1

t1/2 = 0.204 s

Therefore, the answer is choice B.

Question 6

The first-order decomposition of N₂O at 1000 K has a rate constant of 0.76 s^-1. If the initial concentration of N₂O is 10.9 mol L^-1, what is the concentration of N₂O after 9.6 s?

Accepted Answer

The integrated rate law for a first-order reaction is:ln[A]t = -kt + ln[A]0where [A]t is the concentration of the reactant at time t, k is the rate constant, and [A]0 is the initial concentration of the reactant.Substituting the given values into the integrated rate law, we get:ln[N2O]t = -(0.76 s-1)(9.6 s) + ln(10.9 mol L-1)ln[N2O]t = -7.344 + 2.415ln[N2O]t = -4.929[N2O]t = e-4.929 = 7.4 × 10-3 mol L-1Therefore, the concentration of N2O after 9.6 s is 7.4 × 10-3 mol L-1.

Question 7

Derive an expression for a "1/4-life" for a first-order reaction.

Accepted Answer

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Question 8

The rate constant for a zero-order reaction is 0.54 L mol^-1s^-1. What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

Accepted Answer

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Question 9

The rate constant for a second-order reaction is 0.54 L mol^-1s^-1. What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

Accepted Answer

The half-life of a second-order reaction is given by the equation t_1/2 = 1/(k[A]₀), where k is the rate constant and [A]₀ is the initial concentration. Substituting the given values into this equation, we get t_1/2 = 1/(0.54 L mol^-1s^-1 x 0.27 mol L^-1) = 6.9 s.

Question 10

Which of the following represents the equation for a zero-order half-life?

Accepted Answer

The equation for zero-order half-life is t1/2 = [Ao]/2k where [Ao] is the initial concentration and k is the rate constant. Rearranging this equation, we get t = [Ao]/2k = (1/2)t1/2. Therefore, the equation for zero-order half-life is t = (1/2)t1/2. Looking at the options, only option C has this exact form where t_1/2 represents t1/2 and is multiplied by (1/2) to give the value of t.

Question 11

The first-order decomposition of N₂O₅ at 328 K has a rate constant of 1.70 × 10^-3 s^-1. If the initial concentration of N₂O₅ is 2.88 mol L^-1, what is the concentration of N₂O₅ after 12.5 minutes?

Accepted Answer

The concentration of N₂O₅ after time t can be calculated using the first-order kinetics formula: [A] = [A]₀ * e^(-kt). Substituting the given values: [A] = 2.88 * e^(-1.70 × 10⁻³ * 750) = 0.805 mol L⁻¹.

Question 12

How many half-lives are required for the concentration of reactant to decrease to 1.56% of its original value?

Accepted Answer

The concentration of reactant decreases to 1/2 of its original value after each half-life. So, to decrease to 1.56% of its original value, it requires 6 half-lives.

Question 13

Derive an expression for a "1/3-life" for a first-order reaction.

Accepted Answer

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Question 14

The first-order decomposition of cyclopropane has a rate constant of 6.7 × 10^-4 s^-1. If the initial concentration of cyclopropane is 1.33 mol L^-1, what is the concentration of cyclopropane after 644 s?

Accepted Answer

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Question 15

The half-life for the decay of radium is 1620 years. What is the rate constant for this first-order process?

Accepted Answer

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Question 16

Which of the following statements is FALSE?

Accepted Answer

The half-life of a first-order reaction is independent of the initial concentration of the reactant.

Question 17

If the concentration of a reactant is 6.25%, how many half-lives has it gone through?

Accepted Answer

To determine the number of half-lives, we need to use the formula:

concentration final = concentration initial x (1/2)^(number of half-lives)

Rearranging the formula, we get:

number of half-lives = log (concentration final / concentration initial) / log (1/2)

Plugging in the values, we get:

number of half-lives = log (0.0625/1) / log (1/2) = 4

Therefore, the answer is D, which corresponds to 4 half-lives.

Question 18

How many half-lives are required for the concentration of reactant to decrease to 25% of its original value?

Accepted Answer

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Question 19

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 mol L^-1. What is the rate constant for this reaction?

Accepted Answer

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Question 20

The second-order decomposition of HI has a rate constant of 1.80 × 10^-3 L mol^-1s^-1. How much HI remains after 27.3 s if the initial concentration of HI is 4.78 mol L^-1?

Accepted Answer

For a second-order reaction, the integrated rate law is 1/[A] = kt + 1/[A]₀. Plugging in the values: 1/[A] = (1.80 × 10⁻³ L mol⁻¹ s⁻¹)(27.3 s) + 1/4.78 mol L⁻¹. Solving for [A] gives approximately 3.87 mol L⁻¹.

Quiz 13: Chemical Kinetics

The first-order decay of radon has a half-life of 3.823 days. How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams?

The rate constant for a first-order reaction is 0.54 L mol-1 s-1. What is the half-life of this reaction if the initial concentration is 0.27 mol L-1?

How many half-lives are required for the concentration of reactant to decrease to 12.5% of its original value?

The rate constant for the first-order decomposition of N2O is 3.40 s-1. What is the half-life of the decomposition?

The first-order decomposition of N2O at 1000 K has a rate constant of 0.76 s-1. If the initial concentration of N2O is 10.9 mol L-1, what is the concentration of N2O after 9.6 s?