Question

For the reaction 2A + B $\to$ C, the values of initial rate at different reactant concentrations are given in the table below. The rate law for the reaction is :

$ [A] (mol L^{-1})$	$ [B] (mol L^{-1})$	$ Initial \; Rate (mol \; L^{-1} s^{-1})$
0.05	0.05	0.045
0.10	0.05	0.090
0.20	0.10	0.72

• A. Rate = k [A][B]
• B. Rate = $k [A]^2[B]^2$
• C. Rate = $k [A][B]^2$
• D. Rate = $k [A]^2[B]$

Answer 1

Answer: (C)

$r = K [A]^x \; [B]^y$
$0.045 = K (0.05)^x \; (0.05)^y$ ....(1)
$0.090 = K (0.10)^x (0.05)^y $....(2)
$0.72 = K (0.20)^x (0.10)^y$ ....(3)
From $\left(1\right) \div \left(2\right), \frac{0.045}{0.090} = \left(\frac{0.05}{0.10}\right)^{x} \Rightarrow x =1 $
From $ \left(2\right)\div \left(3\right), \frac{0.090}{0.720} =\left(\frac{0.10}{0.20}\right)^{x} .\left(\frac{0.05}{0.10}\right)^{y} \Rightarrow y = 2$
Hence $ r =K \left[A\right]\left[B\right]^{2}$