• # question_answer 27) Select the rate law that corresponds to the data shown for the following reaction $A+B\xrightarrow{{}}C$ Expt. No. (1) (2) Initial Rate 1 $0.012$ $0.035$ $0.10$ 2 $0.024$ $0.070$ $0.80$ 3 $0.024$ $0.035$ $0.10$ 4 $0.012$ $0.070$ $0.80$ A)  Rate $=K{{[B]}^{3}}$                              B)  Rate $=K{{[B]}^{4}}$C)  Rate $=K[A]\,{{[B]}^{3}}$D)  Rate $=K{{[A]}^{2}}{{[B]}^{2}}$

Let the rate law be $r={{[A]}^{x}}{{[B]}^{y}}$ Divide (3) by (1) $\frac{0.10}{0.10}=\frac{{{[0.024]}^{x}}{{[0.035]}^{y}}}{{{[0.012]}^{x}}{{[0.035]}^{y}}}$ $\therefore$ $1={{[2]}^{x}},\,x=0$ Divide (2) by (3) $\frac{0.80}{0.10}=\frac{{{[0.024]}^{x}}{{[0.070]}^{y}}}{{{[0.024]}^{x}}{{[0.035]}^{y}}}$ $\therefore$  $8={{(2)}^{y}},\,\,y=3$ Hence rate equation, $R=K{{[A]}^{0}}{{[B]}^{3}}=K{{[B]}^{3}}$