Question

Which function of $\left[X\right]$, plotted against time, will give a straight line for a second order reaction, $X⟶$ Product?

• A. $\left[X\right]$
• B. ${\left[X\right]}^2$
• C. $\ln \left[X\right]$
• D. $\frac{1}{\left[X\right]}$

Answer 1

Answer: (D)

$\frac{1}{\left[X\right]}$

For second order reaction, $-\frac{dx}{dt}=k[X{]}^2$

${\int }_{x_0}^x-\frac{dx}{[X{]}^2}={\int }_0^{t}kdt$

$=>\frac{1}{\left[X\right]}-\frac{1}{\left[X_0\right]}=kt$

or $\frac{1}{\left[X\right]}=kt+\frac{1}{\left[X_0\right]}$

Hence plot of $\frac{1}{\left[X\right]}$ against time will be a straight line