Question

In a first order reaction the concentration of reactant decreases from $800mol/d{m}^3$ to $50mol/d{m}^3$ in $2\times {10}^{4}s$. The rate constant of reaction in $s^{-1}$ is:

• A. $2\times {10}^4$
• B. $3.45\times {10}^{-5}$
• C. $1.386\times {10}^{-4}$
• D. $2\times {10}^{-4}$

Answer 1

The correct option is C

$1.386\times {10}^{-4}$

For a first order reaction,

$kt=ln\frac{[A{]}_0}{\left[A\right]}$

$\Rightarrow k=\frac{1}{t}ln\frac{[A{]}_0}{\left[A\right]}$

$=\frac{1}{2\times {10}^4}ln\frac{800}{50}$

$=\frac{4ln2}{2\times {10}^4}{s}^{-1}$

$=1.386\times {10}^{-4}{s}^{-1}$