Taking the reaction X+2Y→products to be of second order, which of the following is/are the rate law expression/s for the reaction1)dxdt=KXyII) dxdt=KXy2III)dxdt=KX2IV)dxdt=KX+Ky2Then the correct answers can be

# Taking the reaction $\mathrm{X}+2\mathrm{Y}\to$products to be of second order, which of the following is/are the rate law expression/s for the reaction$1\right)\frac{\mathrm{dx}}{\mathrm{dt}}=K\left[X\right]\left[y\right]$III)$\frac{\mathrm{dx}}{\mathrm{dt}}=K{\left[X\right]}^{\mathit{2}}$IV)$\frac{\mathrm{dx}}{\mathrm{dt}}=K\left[X\right]\mathit{+}K{\left[y\right]}^{\mathit{2}}$Then the correct answers can be

1. A

I only

2. B

I and III only

3. C

I and II only

4. D

I and IV only

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### Solution:

$\mathrm{X}+2\mathrm{Y}\to \mathrm{product}$

According law of mass action (or) rate law expression

$\mathrm{r}=\mathrm{K}{\left[\mathrm{X}\right]}^{1}{\left[\mathrm{Y}\right]}^{2}$

$\frac{\mathrm{dx}}{\mathrm{dt}}=k\left[X\right]{\left[y\right]}^{2}$

According to given ${2}^{\mathrm{nd}}$ order reaction based on this concept

$\mathrm{r}=\mathrm{K}{\left[\mathrm{X}\right]}^{1}{\left[\mathrm{Y}\right]}^{1}$

$\frac{\mathrm{dx}}{\mathrm{dt}}=k{\left[X\right]}^{\mathit{1}}{\left[y\right]}^{1}$  +91

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