Question

A first order reaction with respect to the reactant $A$ has a rate constant of $6{\sec }^{-1}$. If we start with $\left[A\right]=0.5mol/litre$, then in what time the concentration of $A$ becomes $0.05mol/litre$?

• A. $0.384sec$
• B. $0.214sec$
• C. $3.84sec$
• D. $0.402sec$

Answer 1

Answer: (A)

$0.384sec$

For the first order reaction $t=\frac{2.303}{K}\log \frac{a}{a-x}$

Given: $a=0.5mol/litre;a-x=0.05,mol/litre$

$K=6{\sec }^{-1}$

$t=\frac{2.303}{6}\log \frac{0.5}{0.05}=\frac{2.303}{6}\log 10=\frac{2.303}{6}=0.384sec.$