Question

$2X\left(g\right)+3Y\left(g\right)+Z\left(g\right)\to P\left(g\right)+Q\left(g\right)$
The order of the given reaction is $\frac{3}{4}$ and the experimental rate law of the given reaction is $K\left[X{]}^{\frac{1}{2}}\right[Y{]}^{\frac{3}{4}}[Z{]}^a$. Find the order of reaction with respect to Z.

• A. $0$
• B. $\frac{1}{2}$
• C. $1$
• D. $\frac{-1}{2}$

Answer 1

The correct option is D $\frac{-1}{2}$

Order of a reaction:
For a given reaction:
$aA+bB+cC\to \text{Products}$
If,
$\text{Rate}\propto \left[A{]}^p\right[B{]}^q[C{]}^r$
Overall order of the reaction is :
$(p+q+r)$

So, for
$2X\left(g\right)+3Y\left(g\right)+Z\left(g\right)\to P\left(g\right)+Q\left(g\right)$

The experimental rate law is,
$R=K\left[X{]}^{\frac{1}{2}}\right[Y{]}^{\frac{3}{4}}[Z{]}^a$.

Thus, the overall order of the reaction is
$(\frac{1}{2}+\frac{3}{4}+a)$

Order of given reaction is $\frac{3}{4}$
$\therefore$
$\Rightarrow \frac{1}{2}+\frac{3}{4}+a=\frac{3}{4}$

$a=\frac{-1}{2}$
Thr order of reaction with respect to Z is $\frac{-1}{2}$