MHTCET 26 Apr 2025 Shift 1 Paper

Concept:According to Dalton's law of partial pressures, the fraction of total pressure exerted by a gas in a mixture is equal to its mole fraction.Explanation:Let the mass of each gas be $m$ grams.The molar mass of helium is $M_{\mathrm{He}}=4\ \mathrm{g/mol}$, so the number of moles of helium is:$$n_{\mathrm{He}}=\frac{m}{4}$$The molar mass of oxygen is $M_{\mathrm{O_2}}=32\ \mathrm{g/mol}$, so the number of moles of oxygen is:$$n_{\mathrm{O_2}}=\frac{m}{32}$$The mole fraction of helium is:$$x_{\mathrm{He}}=\frac{n_{\mathrm{He}}}{n_{\mathrm{He}}+n_{\mathrm{O_2}}}=\frac{\frac{m}{4}}{\frac{m}{4}+\frac{m}{32}}$$Simplify by cancelling $m$:$$x_{\mathrm{He}}=\frac{\frac{1}{4}}{\frac{1}{4}+\frac{1}{32}}=\frac{\frac{1}{4}}{\frac{8}{32}+\frac{1}{32}}=\frac{\frac{1}{4}}{\frac{9}{32}}=\frac{8}{9}$$Since partial pressure is directly proportional to mole fraction, the fraction of total pressure exerted by helium is $\frac{8}{9}$.Answer:$\frac{8}{9}$, which is option C.