Question

.Chloroethane decomposes at elevated temperatures according to the reaction .${\text{C}}_2{\text{H}}_5\text{Cl}\to {\text{C}}_2{\text{H}}_4+\text{HCl}$

This reaction obeys first-order kinetics. After 340 s at 800 K, a measurement shows that the concentration of C₂H₅Cl has decreased from 0.0098 mol L^-1to 0.0016 mol L^-1 . Calculate the rate constant k at 800 K.

Short answer

The rate constant k value at 800 K is 0.0053s^-1

Step-by-step solution

Rate expression:

The eqaution for the firat order reaction when initail and final concendration are given as

$$\begin{gathered} \ln \left(\frac{C_o}{C_t}\right)=kt.........\left(1\right) \\ or \\ 2.303\ln \left(\frac{C_0}{C_t}\right)=kt.......\left(2\right) \end{gathered}$$

Calculation of rate constant K value:

Substituting all the values such as initial,final concendration,time in the given above equation

$$\begin{gathered} C_0=0.0098\text{molL}-1 \\ {C}_t=0.0016\text{molL}-1 \\ \text{Timeinseaconds}=240s \\ \text{Substitutingalltheseinequation}2 \\ 2.303\log \left(\frac{0.0098}{0.0016}\right)=k\times 340s \\ \text{K}\hspace{0.17em}=\frac{2.303}{340}\log \left(6.125\right)s^{-1} \\ k=0.0053s^{-1} \end{gathered}$$

Therefore the rate constant k value at 800 K is 0.0053s^-1