A solid catalyst adsorbs of gas (reduced to S.T.P.) per gram to form a tightly packed monolayer. If — Surface Chemistry Chemistry Question
Question
A solid catalyst adsorbs $1000\text{ cm}^3$ of $N_2$ gas (reduced to S.T.P.) per gram to form a tightly packed monolayer. If the effective area occupied by a single $N_2$ molecule on the surface is $1.62 \times 10^{-15}\text{ cm}^2$, calculate the surface area of the catalyst in $\text{m}^2\text{ g}^{-1}$. (Use $N_A = 6.022 \times 10^{23}\text{ mol}^{-1}$ and molar volume at S.T.P. $= 22400\text{ cm}^3$)
💡 Solution & Explanation
Moles of $N_2$ adsorbed $= 1000 / 22400 = 0.04464\text{ mol}$. Total molecules $= 0.04464 \times 6.022 \times 10^{23} = 2.688 \times 10^{22}$. Total surface area $= \text{Number of molecules} \times \text{Area per molecule} = 2.688 \times 10^{22} \times 1.62 \times 10^{-15}\text{ cm}^2 = 4.354 \times 10^7\text{ cm}^2 = 4354\text{ m}^2\text{ g}^{-1}$.