For the reaction `SO_(2)CL_(2)(g) to SO_(2)(g) +Cl_(2)(g)` , it is found that a plot f 1n `[SO_(2)Cl_(2)]` versus time is linear , and the that in 240 seconds the `[SO_(2)Cl_(2)]` decreases from `0.4` M to `0.28` M . What is the rate constant ?

Explanation

To find the rate constant \( k \) for the reaction \( SO_2Cl_2(g) \rightarrow SO_2(g) + Cl_2(g) \), we can follow these steps:

### Step 1: Identify the order of the reaction
Since the problem states that a plot of \( \ln [SO_2Cl_2] \) versus time is linear, we can conclude that the reaction is first order with respect to \( SO_2Cl_2 \).

**Hint:** A linear plot of \( \ln [A] \) versus time indicates a first-order reaction.

### Step 2: Use the first-order rate equation
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