Initial conc of reactant in a first order reaction is 10M . The half life period of reaction is 10 sec . The rate of reaction after 20 sec

Dear Student,

To solve this, first we need to find the concentration of the reactant at time=20s.
Let the reactant be A.
So, [A_o] = 10 M, t_1/2 = 10 s, t = 20 s
Now,
$$\begin{gathered} t_{\frac{1}{2}}=\frac{0.693}{\lambda }, \lambda =rate cons\tan t \\ \lambda =\frac{0.693}{10}=0.0693 \\ Now, \\ \ln \frac{\left[A\right]}{\left[A_o\right]}=-kt \\ \ln \left[A\right]=\ln \left[A_o\right]-kt=\ln \left[10\right]-(0.0693)\left(20\right) \\ \ln \left[A\right]=2.303-1.386=0.917 \\ \left[A\right]=anti\ln (0.917)=2.502 M \\ Rate of reaction = k\left[A\right]=0.0693 \times 2.502 = 0.1734 M s^{-1} \end{gathered}$$

Hope it helps.

Regards