The rate constants for decomposition of acetaldehyde have been measured over the temperature range $$700 - 1000$$ K. The data has been analysed by plotting $$\ln k$$ vs $$\frac{10^3}{T}$$ graph. The value of activation energy for the reaction is ______ kJ mol$$^{-1}$$. (Nearest integer) (Given : $$R = 8.31$$ J K$$^{-1}$$ mol$$^{-1}$$)

The Arrhenius equation is:

$$\mathrm{\ln k = \ln A - \frac{E_a}{RT}}$$

The graph is plotted between $$\mathrm{\ln k}$$ and $$\mathrm{\frac{10^3}{T}}$$.

Rewriting the Arrhenius equation according to the given axes:

$$\mathrm{\ln k = -\left(\frac{E_a}{10^3R}\right)\left(\frac{10^3}{T}\right) + \ln A}$$

Comparing with:

$$\mathrm{y = mx + c}$$

Slope of the graph is:

$$\mathrm{-\frac{E_a}{10^3R}}$$

Given slope:

$$\mathrm{-18.5}$$

Thus:

$$\mathrm{-18.5 = -\frac{E_a}{10^3 \times R}}$$

Substituting:

$$\mathrm{R = 8.31\ J\,K^{-1}\,mol^{-1}}$$

$$\mathrm{18.5 = \frac{E_a}{1000 \times 8.31}}$$

$$\mathrm{E_a = 18.5 \times 1000 \times 8.31}$$

$$\mathrm{E_a = 153735\ J\,mol^{-1}}$$

Converting into $$\mathrm{kJ\,mol^{-1}}$$:

$$\mathrm{E_a = 153.735\ kJ\,mol^{-1}}$$

Rounding to nearest integer:

$$\mathrm{154}$$

Correct Answer: $$\mathrm{154}$$