For the adsorption of hydrogen on platinum, the activation energy is $30 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and for the adsorption of hydrogen on nickel, the activation energy is $41.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at 300 K is (Nearest integer) Given: $\ln 10=2.3 \quad \mathrm{R}=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Surface Chemistry

For the adsorption of hydrogen on platinum, the activation energy is

30 kJ mol^{- 1}

and for the adsorption of hydrogen on nickel, the activation energy is

41.4 kJ mol^{- 1}

. The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at 300 K is (Nearest integer)
Given:

ln 10 = 2.3 R = 8.3 JK^{- 1} mol^{- 1}

Answer: 2

By the Arrhenius expression

k = A e^{- E_{a} / R T}

, with equal pre-exponential factors the ratio of chemisorption rates on platinum and nickel is

\frac{k _{Pt}}{k _{Ni}} = e^{(E_{a, Ni} - E_{a, Pt}) / R T}

. Taking logarithms to base ten,

lo g \frac{k _{Pt}}{k _{Ni}} = \frac{E _{a, Ni} - E _{a, Pt}}{2.303 R T} = \frac{( 41.4 - 30 ) \times 1 0 ^{3}}{2.3 \times 8.3 \times 300} = \frac{11400}{5727} \approx 1.99

. The nearest integer value of the logarithm of the rate ratio is 2.

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Integer answer