Question

For a reaction between $A$ and $B$, the initial rate of reaction is measured for various initial concentrations of $A$ and $B$. The data provided are

	$\left[A\right]$	$\left[B\right]$	Initial reaction rate
(a)	$0.20M$	$0.30M$	$5\times {10}^{-5}$
(b)	$0.20M$	$0.10M$	$5\times {10}^{-5}$
(c)	$0.40M$	$0.05M$	$7.5\times {10}^{-5}$

The overall order of the reaction is

• A. One (1)
• B. Two (2)
• C. Two and a half (2.5)
• D. Three (3)
• E. None of the above

Answer 1

The correct option is E None of the above

Suppose order with respect to $A$ is $x$ and with respect to $B$ is $y$:

From (a),

${\left[0.20\right]}^x{\left[0.30\right]}^{y}K=5\times {10}^{-5}....\left(i\right)$

From (b),

${\left[0.20\right]}^x{\left[0.10\right]}^{y}K=5\times {10}^{-5}....\left(ii\right)$

Dividing (i) by (ii), $1={\left[3\right]}^y$ or $y=0$

From (c), $7.5\times {10}^{-5}=K{\left[0.40\right]}^x{\left[0.05\right]}^y...\left(iii\right)$

As $y=0$

Dividing (ii) by (iii),

$0.67=[0.5{]}^x$

Taking log on both sides

$x\log \left(0.5\right)=\log \left[0.67\right]$

$x=0.5$

THe overall order of the reaction is $0.5+0=0.5$

None of the options are correct