Question

The rate constant for a first order reaction is $4.606\times {10}^{-3}{s}^{-1}$. The time required to reduce $2.0g$ of the reactant to $0.2g$ is :

• A. 1000 s
• B. 200 s
• C. 500 s
• D. 100 s

Answer 1

The correct option is C 500 s

For first order reaction,
$Kt=2.303log\frac{\left[A_0\right]}{\left[A_t\right]}$
$\left[A_0\right]$ is initial concentration of reactant
$\left[A_t\right]$ is concentration of reactant at time 't'
$t=\frac{2.303}{K}log\frac{\left[A_0\right]}{\left[A_t\right]}$

$t=\frac{2.303}{4.606\times {10}^{-3}}log\frac{\left[2\right]}{\left[0.2\right]}$

$t=500s$