Question

$A+B\to C$

From the given reaction determine the order of the reaction with respect to B from the information given below.

Initial $\left[A\right]$	Initial $\left[B\right]$	Initial rate of formation of $\left[C\right]$
1.00	1.00	2.0
1.00	2.00	8.1
2.00	2.00	15.9

• A. Zero-order
• B. First-order
• C. Second-order
• D. Third-order
• E. Fourth-order

Answer 1

The correct option is C Second-order

Let :
Rate $=k\left[A{]}^x\right[B{]}^y$
Here, the rate of formation of $C$ is the rate of reaction.
On taking 1st and 2nd case:-
$2.0=k\left[1.00{]}^x\right[1.00{]}^y$ -------1st
$8.1=k\left[1.00{]}^x\right[2.00{]}^y$--------2nd
On dividing 2nd equation by 1st.
$\frac{8.1}{2.0}=\frac{[1.00{]}^x}{[1.00{]}^x}\times \frac{[2.00{]}^y}{[1.00{]}^y}$
$4=\frac{[2.00{]}^y}{[1.00{]}^y}$
If $y=2$, then this equation is satisfied. Hence $y$ must be 2.
Now on taking 2nd and 3rd case: -
$8.1=k\left[1.00{]}^x\right[2.00{]}^y$ -------2nd
$15.9=k\left[2.00{]}^x\right[2.00{]}^y$--------3rd
On dividing 3rd equation by 2nd.
$\frac{15.9}{8.1}=\frac{[2.00{]}^x}{[1.00{]}^x}\times \frac{[2.00{]}^y}{[2.00{]}^y}$
$2=\frac{[2.00{]}^x}{[1.00{]}^x}$
Here, $x$ must be 1 , only then the above equation will be satisfied.
Hence, we have Rate expression as follows:
Rate $=k\left[A{]}^1\right[B{]}^2$
Hence, order of reaction $=1+2=3$.