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: ln10 = 2.3, R = 8.3 J K$$^{-1}$$ mol$$^{-1}$$

The rate of a reaction depends on the activation energy through the Arrhenius equation: $$k = A e^{-E_a/RT}$$.

For adsorption on equal areas of Pt and Ni at the same temperature, the ratio of rates is:

$$\frac{r_{Pt}}{r_{Ni}} = \frac{e^{-E_{a,Pt}/RT}}{e^{-E_{a,Ni}/RT}} = e^{(E_{a,Ni} - E_{a,Pt})/RT}$$

We have $$E_{a,Pt} = 30$$ kJ/mol = 30000 J/mol, $$E_{a,Ni} = 41.4$$ kJ/mol = 41400 J/mol, and $$T = 300$$ K. So:

$$\ln\left(\frac{r_{Pt}}{r_{Ni}}\right) = \frac{41400 - 30000}{8.3 \times 300} = \frac{11400}{2490} = 4.578$$

Converting to log base 10:

$$\log\left(\frac{r_{Pt}}{r_{Ni}}\right) = \frac{4.578}{2.3} = 1.99 \approx 2$$

Hence, the answer is $$2$$.