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Ch.14 - Chemical Kinetics
All textbooksBrown 14th EditionCh.14 - Chemical KineticsProblem 97
Chapter 14, Problem 97

A first-order reaction A → B has the rate constant k = 3.2 * 10^-3 s^-1. If the initial concentration of A is 2.5 * 10^-2 M, what is the rate of the reaction at t = 660 s?

Verified step by step guidance
1
Step 1: Understand that for a first-order reaction, the rate of the reaction is given by the formula: rate = k[A], where k is the rate constant and [A] is the concentration of A at time t.
Step 2: Use the integrated rate law for a first-order reaction to find the concentration of A at time t. The integrated rate law is: ln([A]_t/[A]_0) = -kt, where [A]_t is the concentration at time t, [A]_0 is the initial concentration, and t is the time.
Step 3: Substitute the given values into the integrated rate law: ln([A]_t/2.5 \times 10^{-2}) = -(3.2 \times 10^{-3}) \times 660.
Step 4: Solve the equation from Step 3 to find [A]_t, the concentration of A at time t = 660 s.
Step 5: Substitute the value of [A]_t obtained in Step 4 into the rate equation from Step 1 to calculate the rate of the reaction at t = 660 s.
Related Practice
Open Question
The following kinetic data are collected for the initial rates of a reaction 2X + Z → products: Experiment [X] (M) [Z] (M) Rate (M/s) 1 0.25 0.25 4.0 * 10^1 2 0.50 0.50 3.2 * 10^2 3 0.50 0.75 7.2 * 10^2. (c) What is the reaction rate when the initial concentration of X is 0.75 M and that of Z is 1.25 M?
Textbook Question

The reaction 2 NO2¡2 NO + O2 has the rate constant k = 0.63 M- 1s - 1. (b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

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Textbook Question

Consider two reactions. Reaction (1) has a constant halflife, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?

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Open Question
The reaction H₂O₂(aq) → H₂O(l) + 1/2 O₂(g) is first order. At 300 K, the rate constant equals 7.0 * 10⁻⁴ s⁻¹. If the activation energy for this reaction is 75 kJ/mol, at what temperature would the reaction rate be doubled?
Textbook Question

Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (b) Which one decays at a faster rate?

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Textbook Question

Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (c) How much of a 1.00-mg sample of each isotope remains after three half-lives?

1042
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