**Chlorine Monoxide and Its Role in Ozone Depletion****Introduction**Chlorine monoxide (ClO) accumulates in the stratosphere above Antarctica each winter and plays a key role in the formation of the ozone hole above the South Pole each spring. This occurs through a decomposition reaction.**Decomposition Reaction**The decomposition of ClO in the stratosphere is represented by the following chemical equation:\[ 2 \text{ClO}(g) \rightarrow \text{Cl}_2(g) + \text{O}_2(g) \]**Rate of Decomposition**The rate at which this decomposition occurs can be quantified through a second-order rate constant. The given second-order rate constant for the decomposition of ClO is:\[ k = 6.48 \times 10^9 \, \text{M}^{-1}\text{s}^{-1} \]**Problem Statement**Determine the half-life of ClO when its initial concentration is:\[ [\text{ClO}]_0 = 1.76 \times 10^{-8} \, \text{M} \]**Solution**To compute the half-life (\( t_{1/2} \)) for a second-order reaction, the formula is:\[ t_{1/2} = \frac{1}{k [\text{ClO}]_0} \]Given:- \( k = 6.48 \times 10^9 \, \text{M}^{-1}\text{s}^{-1} \)- \( [\text{ClO}]_0 = 1.76 \times 10^{-8} \, \text{M} \)Substitute these values into the formula:\[ t_{1/2} = \frac{1}{(6.48 \times 10^9 \, \text{M}^{-1}\text{s}^{-1})(1.76 \times 10^{-8} \, \text{M})} \]Calculate \( t_{1/2} \):\[ t_{1/2} = \frac{1}{1.14048 \times 10^2 \, \text{s}^{-1}} \]\[ t_{1/2} = 8.76 \times 10^{-3} \, \text{s} \]Thus, the half-life of ClO

Chlorine monoxide accumulates in the stratosphere above Antarctica each winter and plays a key role in the formation of the ozone hole above the South Pole each spring. Eventually, CIO decomposes according to the equation: 2C10 (g) > Cl₂(g) + O₂(g) The second-order rate constant for the decomposition of CIO is 6.48×10⁹ M-¹s-1 at a particular temperature. Determine the half-life of CIO when its initial concentration is 1.76×10-8 M. x 101

Chlorine monoxide accumulates in the stratosphere above Antarctica each winter and plays a key role in the formation of the ozone hole above the South Pole each spring. Eventually, CIO decomposes according to the equation: 2C10 (g) > Cl₂(g) + O₂(g) The second-order rate constant for the decomposition of CIO is 6.48×10⁹ M-¹s-1 at a particular temperature. Determine the half-life of CIO when its initial concentration is 1.76×10-8 M. x 101

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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