Arsine decomposes on heating according to the equation `2AsH_(3)(g) rarr 2As(s) + 3H_(2)(g)`. The decompoistion was studied at constant temperature and constant volume by measuring the total pressure at various intervals of time.
`|{:("Time (min)",0,5,7.5,10),("Total Pressure (atm)",1,1.09,1.13,1.16):}|`
Assume it to be a first order reaction, calculate the specific rate constant and half life of the reaction.

Explanation

To solve the problem of calculating the specific rate constant and half-life of the decomposition of arsine (AsH₃), we will follow these steps:

### Step 1: Understand the Reaction
The decomposition of arsine is represented by the equation:
\[ 2 \text{AsH}_3(g) \rightarrow 2 \text{As}(s) + 3 \text{H}_2(g) \]

### Step 2: Gather Data
We have the following data for total pressure at different time intervals:
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