The decomposition of `N_(2)O_(5)` in a carbon tetrachloride solution has been investigated.
`N_(2)O_(5)("solution") to 2NO_(3)` (solution) +`1//2O_(2)(g)` . The reaction has been found to be of the first order in `N_(2)O_(5)` with a first order rate-constant = `6.2 xx 10^(-4)s^(-1)`. Calculate the rate of the reaction when (a) `[N_(2)O_(5)]` = 1.25 mol `L^(-1)` and b) `[N_(2)O_(5)]` = 0.25 mol `L^(-1)`. b) What concentration of `N_(2)O_(5)` would give a rate of `2.4 xx 10^(-3) mol L^(-1)s^(-1)` ?

Explanation

To solve the problem step by step, we will follow the given information about the decomposition of \( N_2O_5 \) and the first-order kinetics of the reaction.

### Step 1: Write the Rate Law Expression
The rate of a first-order reaction is given by the equation:
\[ \text{Rate} = k \cdot [N_2O_5] \]
where \( k \) is the rate constant and \([N_2O_5]\) is the concentration of \( N_2O_5 \).
...