Textbook Question
This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms. b. Write the rate law for the reaction.
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Ch.14 - Chemical Kinetics
Chapter 14, Problem 55
a. What is the half-life for the first-order decomposition of SO2Cl2 with a rate constant of 1.42 x 10^-4 s^-1? b. How long will it take for the concentration of SO2Cl2 to decrease to 25% of its initial concentration? c. If the initial concentration of SO2Cl2 is 1.00 M, how long will it take for the concentration to decrease to 0.78 M? d. If the initial concentration of SO2Cl2 is 0.150 M, what is the concentration of SO2Cl2 after 2.00 x 10^2 s? After 5.00 x 10^2 s?
Verified step by step guidance1
Step 1: For part (a), use the formula for the half-life of a first-order reaction: \( t_{1/2} = \frac{0.693}{k} \), where \( k \) is the rate constant.
Step 2: For part (b), use the first-order integrated rate law: \( \ln \left( \frac{[A]_t}{[A]_0} \right) = -kt \). Set \( [A]_t = 0.25[A]_0 \) and solve for \( t \).
Step 3: For part (c), use the same first-order integrated rate law: \( \ln \left( \frac{[A]_t}{[A]_0} \right) = -kt \). Set \( [A]_0 = 1.00 \text{ M} \) and \( [A]_t = 0.78 \text{ M} \), then solve for \( t \).
Step 4: For part (d), use the first-order integrated rate law again: \( \ln \left( \frac{[A]_t}{[A]_0} \right) = -kt \). First, calculate \( [A]_t \) after \( 2.00 \times 10^2 \text{ s} \) with \( [A]_0 = 0.150 \text{ M} \).
Step 5: Repeat the calculation from Step 4 for \( 5.00 \times 10^2 \text{ s} \) to find the concentration \( [A]_t \) after this time period.
Related Practice
Textbook Question
This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms. c. What is the half-life when the initial concentration is 0.55 M?
Textbook Question
This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms.
d. If the initial concentration of AB is 0.250 M, and the reaction mixture initially contains no products, what are the concentrations of A and B after 75 s?
Open Question
The decomposition of XY is second order in XY and has a rate constant of 7.02 * 10^-3 M^-1 s^-1 at a certain temperature. b. How long will it take for the concentration of XY to decrease to 12.5% of its initial concentration when the initial concentration is 0.100 M? When the initial concentration is 0.200 M? c. If the initial concentration of XY is 0.150 M, how long will it take for the concentration to decrease to 0.062 M? d. If the initial concentration of XY is 0.050 M, what is the concentration of XY after 5.0 * 10^1 s? After 5.50 * 10^2 s?
Textbook Question
The decomposition of XY is second order in XY and has a rate constant of 7.02⨉10-3 M-1• s-1 at a certain temperature. a. What is the half-life for this reaction at an initial concentration of 0.100 M?
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Textbook Question
The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. How long will it take for 10% of the U-238 atoms in a sample of U-238 to decay?
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