The chemical reaction  $P+Q\to \mathrm{Pr}oduct$. The order of reaction with respect to P and Q

Rate =$K{\left[P\right]}^x{\left[Q\right]}^y$  what is the sum of values of  x and y?

$$\begin{gathered} \text{P}+\text{Q}\to \text{ Product } \\ \text{Rate }=K{\left[P\right]}^{\text{'}}{\left[Q\right]}^{\text{'}} \\ {r}_1=0.1\left[\text{P}\right]=20\left[\text{Q}\right]=0.5 \\ {r}_2=0.4\left[\text{P}\right]=80\left[Q\right]=0.5 \\ {r}_3=0.8\left[\text{P}\right]=40\left[Q\right]=2 \\ \frac{r_1}{r_2}=\frac{K{\left[P\right]}^x{\left[Q\right]}^{y^{\text{'}}}}{K{\left[P\right]}^x{\left[Q\right]}^y} \frac{r_3}{r_1}=\frac{K{\left[P\right]}^x{\left[Q\right]}^y}{K{\left[P\right]}^x{\left[Q\right]}^y} \\ \frac{0.4}{0.1}=\frac{80\times 0.5}{20\times 0.5} \frac{0.8}{0.1}=\frac{2\times 40}{20\times 0.5} \\ x=1 y=1 \end{gathered}$$

$\text{Rate }=K{\left[P\right]}^x{\left[Q\right]}^y\text{x}+\text{y}=1+1=2$