Correct Answer - Option 1 : 166
Concept:
Arrhenius equation:
Arrhenius equation gives the dependence of the rate constant of a chemical reaction on the absolute temperature, a pre-exponential factor and other constants of the reaction.
\(k={{e}^{\frac{-{{E}_{a}}}{RT}}}\) ----(1)
Where,
k is the rate constant,
T is the absolute temperature (in Kelvin),
Ea is the activation energy for the reaction (in the same units as RT),
R is the universal gas constant.
Calculation:
We can get the activation energy using Arrhenius equation which is given by the formula:
\(k={{e}^{\frac{-{{E}_{a}}}{RT}}}\)
From the question, the reaction is:
H2 (g) + I2 (g) → 2HI (g)
Now, taking logarithm on both sides on equation (1),
\(\Rightarrow \ln k=-\frac{{{E}_{a}}}{RT}\)
Now, the s for the given reaction is:
\(\log \frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\)
T1 = 327°C + 273 = 600 K
T2 = 527°C + 273 = 800 K
\(\Rightarrow \log \left( \frac{1}{2.5\times {{10}^{-4}}} \right)=\frac{{{E}_{a}}}{2.303\times 8.314}\left[ \frac{1}{600}-\frac{1}{800} \right]\)
\(\Rightarrow \log \left( \frac{1}{2.5\times {{10}^{-4}}} \right)=\frac{{{E}_{a}}}{2.303\times 8.314}\left[ \frac{4-3}{2400} \right]\)
\(\Rightarrow \log \left( \frac{1}{2.5\times {{10}^{-4}}} \right)=\frac{{{E}_{a}}}{2.303\times 8.314}\left[ \frac{1}{2400} \right]\)
\(\Rightarrow 3.602=\frac{{{E}_{a}}}{2.303\times 8.314}\left[ \frac{1}{2400} \right]\)
⇒ Ea = 2.303 × 8.314 × 2400 × 3.602
∴
Ea = 165.5 KJ.mol-1