At 518 ^ o C, the rate of decomposition of a sample of gaseous...

Rate$∝ {\left(concentration\right)}^{n}$

Let the initial concentration be $1M$.

According to the question,

$\begin{cases}Concentration & Rate \\ 0 . 95M & 1 \\ 0 . 67M & 0 . 5\end{cases}$

Substituting in the general rate expression,

${\left(\dfrac{0 .95}{0 .67}\right)}^{n} = \dfrac{1}{0 .5}$

$⇒ n = 2$