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**Problem**: The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2 (g) + Cl2 (g), is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 x 105 s.At 320 oC the rate constant is 2.2 x 10 - 5 s- 1. What is the half-life at this temperature?

###### FREE Expert Solution

We're being asked to determine the half-life of the reaction at 320°C. We’re given the following first-order reaction:

SO_{2}Cl_{2}(g) → SO_{2} (g) + Cl_{2} (g)

Recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half.

The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{k}}}$

**We're given:**

###### Problem Details

The gas-phase decomposition of SO_{2}Cl_{2}, SO_{2}Cl_{2}(g) → SO_{2} (g) + Cl_{2} (g), is first order in SO_{2}Cl_{2}. At 600 K the half-life for this process is 2.3 x 10^{5} s.

At 320 ^{o}C the rate constant is 2.2 x 10^{ - 5 }s^{- 1}. What is the half-life at this temperature?

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Based on our data, we think this problem is relevant for Professor Poler's class at UNC.