Question

The specific reaction rate constant for a first order reaction is $1\times {10}^{-2}{s}^{-1}$. If the initial concentration is $1M$, find the initial rate. What is the reaction rate after two minutes?

Answer 1

$K=1\times {10}^{-2}{s}^{-1}$

$A_o=1M$

$\Rightarrow R=K[A_o{]}^1$

$\Rightarrow R=1\times {10}^{-2}{s}^{-1}\times 1M$

$\Rightarrow R={10}^{-2}M{s}^{-1}\Rightarrow$ Initial rate

After two minutes,

$K=\frac{2.303}{t}\log \frac{A_o}{A}$

$\Rightarrow A=A_o{e}^{-kt}$

$\Rightarrow A=1e^{-({10}^{-2}\times 2)}$

$\Rightarrow A=0.98M$

Thus, Rate= $K[A{]}^1$

$=1\times {10}^{-2}\times 0.98M$

Rate= $9.8\times {10}^{-3}M{s}^{-1}$ $\Rightarrow$ Rate of reaction after two minute