can you help with 7b **Sulfuryl Chloride Decomposition: Kinetics and Calculations**Sulfuryl chloride, \( \mathrm{SO_2Cl_2} \), is a colorless, corrosive liquid known to decompose through a first-order reaction to form sulfur dioxide and chlorine. At a temperature of \( 320 \, ^\circ \mathrm{C} \), the reaction follows this rate equation with a rate constant \( k = 2.20 \times 10^{-5} \, \mathrm{s^{-1}} \).The decomposition reaction is represented as:\[ \mathrm{SO_2Cl_2 \rightarrow SO_2 + Cl_2} \]### Questions:**a. What is the half-life of \( \mathrm{SO_2Cl_2} \) at this temperature?****b. How long would it take for 30.0% of the \( \mathrm{SO_2Cl_2} \) to decompose?**### Explanation:#### Part (a): Calculation of Half-lifeFor a first-order reaction, the half-life (\( t_{1/2} \)) can be calculated using the formula:\[ t_{1/2} = \frac{0.693}{k} \]Given:\[ k = 2.20 \times 10^{-5} \, \mathrm{s^{-1}} \]Substitute the value of \( k \):\[ t_{1/2} = \frac{0.693}{2.20 \times 10^{-5} \, \mathrm{s^{-1}}} \]Perform the calculation to find the half-life.#### Part (b): Time for 30.0% DecompositionTo determine the time required for 30% decomposition, we utilize the first-order decay formula given by:\[ \ln \left( \frac{[A]_0}{[A]} \right) = kt \]Where:- \( [A]_0 \) is the initial concentration.- \( [A] \) is the concentration after time \( t \).- \( k \) is the rate constant.- \( t \) is the time.Given that 30% of \( \mathrm{SO_2Cl_2} \) decomposes, 70% (\( [A]/[A]_0 = 0.70 \)) of it remains. Thus,\[

Given, SO2Cl2 ➝ SO2 + Cl2 Rate constant (k) = 2.20 × 10-5 s-1 Reaction follows first order…

7. Sulfuryl chloride, SO₂Cl2, is a colorless, corrosive liquid whose vapor decomposes in a first-order reaction to sulfur dioxide and chlorine. At 320 °C, the rate constant is 2.20 x 10-5 s¹. SO₂Cl2 → SO₂ + Cl₂ a. What is the half-life of SO₂Cl2 at this temperature? b. How long would it take for 30.0% of the SO₂Cl2 to decompose?

7. Sulfuryl chloride, SO₂Cl2, is a colorless, corrosive liquid whose vapor decomposes in a first-order reaction to sulfur dioxide and chlorine. At 320 °C, the rate constant is 2.20 x 10-5 s¹. SO₂Cl2 → SO₂ + Cl₂ a. What is the half-life of SO₂Cl2 at this temperature? b. How long would it take for 30.0% of the SO₂Cl2 to decompose?

Chemistry: The Molecular Science

5th Edition

ISBN:9781285199047

Author:John W. Moore, Conrad L. Stanitski

Publisher:John W. Moore, Conrad L. Stanitski

Chapter11: Chemical Kinetics: Rates Of Reactions

Section: Chapter Questions

Problem 112QRT

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