**Q1:** A very unstable molecule, ‘XYZ’, decomposes via the following set of first-order reactions:\[ \text{XY + Z} \xleftrightarrow[k_2]{k_1} \text{XYZ} \xrightarrow{k_3} \text{X + Y + Z} \]If the initial concentration of XYZ is $[XYZ]_0$, show that the decomposition of XYZ follows:\[ [XYZ] = [XYZ]_0 \exp[-(k_1 + k_2 + k_3)t] \]**Q2:** Radioactive decay is a first-order kinetic process. A convenient source of gamma rays for radiation chemistry research is $^{60}\text{Co}$, which decays to give a beta particle, gamma rays, and $^{60}\text{Ni}$. The half-life for the decay is 5.27 years. What is the rate constant for the decay process? How many days will it take for a sample of $^{60}\text{Co}$ to decay to $ \frac{1}{8} $th of its original amount?**Q3:** Hydrogen peroxide, $ \text{H}_2\text{O}_2 $, decomposes in water by a first-order kinetic process. A solution of 0.156 mol/L $ \text{H}_2\text{O}_2 $ in water has an initial decomposition rate of $ 1.14 \times 10^{-5} \text{ mol}\cdot\text{L}^{-1}\cdot\text{s}^{-1} $. Calculate the rate constant for the decomposition reaction and the half-life of the reaction.**Q4:** The equilibrium constant for the reaction $ \text{H}^+ (\text{aq}) + \text{OH}^- (\text{aq}) \rightleftharpoons \text{H}_2\text{O} (\ell) $ at 25 °C is $ 5.49 \times 10^{15} \text{ L mol}^{-1} $. The time-dependent conductivity of the solution following a temperature jump to a final temperature of 25 °C shows a relaxation time of $ \tau = 3.7 \times 10^{-5} $ s. Determine the values of the rate constant $ k_1 $ and \( k

Answered: Q1: A very unstable molecule, 'XYZ',…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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**Q1:** A very unstable molecule, ‘XYZ’, decomposes via the following set of first-order reactions:

\[ \text{XY + Z} \xleftrightarrow[k_2]{k_1} \text{XYZ} \xrightarrow{k_3} \text{X + Y + Z} \]

If the initial concentration of XYZ is $[XYZ]_0$, show that the decomposition of XYZ follows:

\[ [XYZ] = [XYZ]_0 \exp[-(k_1 + k_2 + k_3)t] \]

**Q2:** Radioactive decay is a first-order kinetic process. A convenient source of gamma rays for radiation chemistry research is $^{60}\text{Co}$, which decays to give a beta particle, gamma rays, and $^{60}\text{Ni}$. The half-life for the decay is 5.27 years. What is the rate constant for the decay process? How many days will it take for a sample of $^{60}\text{Co}$ to decay to $ \frac{1}{8} $th of its original amount?

**Q3:** Hydrogen peroxide, $ \text{H}_2\text{O}_2 $, decomposes in water by a first-order kinetic process. A solution of 0.156 mol/L $ \text{H}_2\text{O}_2 $ in water has an initial decomposition rate of $ 1.14 \times 10^{-5} \text{ mol}\cdot\text{L}^{-1}\cdot\text{s}^{-1} $. Calculate the rate constant for the decomposition reaction and the half-life of the reaction.

**Q4:** The equilibrium constant for the reaction $ \text{H}^+ (\text{aq}) + \text{OH}^- (\text{aq}) \rightleftharpoons \text{H}_2\text{O} (\ell) $ at 25 °C is $ 5.49 \times 10^{15} \text{ L mol}^{-1} $. The time-dependent conductivity of the solution following a temperature jump to a final temperature of 25 °C shows a relaxation time of $ \tau = 3.7 \times 10^{-5} $ s. Determine the values of the rate constant $ k_1 $ and \( k

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$XYZ space rightwards arrow space straight X plus space YZ space left parenthesis Rate space constant colon space straight k subscript 1 right parenthesis XYZ space space rightwards arrow space XY plus straight Z space left parenthesis Rate space constant colon space straight k subscript 2 right parenthesis space XYZ space rightwards arrow space straight X space plus space straight Y space plus space straight Z space left parenthesis Rate space constant colon space straight k subscript 3 right parenthesis$

The order of a chemical reaction is a way to describe how the rate of the reaction depends on the concentration of reactants. There are three main types of reaction orders: zero order, first order, and second order.In a first-order reaction, the rate of the reaction is directly proportional to the concentration of one reactant.

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