What fraction of the total pressure is exerted by oxygen, if equal weights of oxygen and methane are mixed in an empty vessel at 25°C ?

ANS:B - 1/3

To find the fraction of the total pressure exerted by oxygen in the mixture, we can use Dalton's law of partial pressures. According to Dalton's law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Given that equal weights of oxygen and methane are mixed, the number of moles of each gas is the same. Therefore, the partial pressure of each gas is directly proportional to its molar mass. The molar mass of oxygen (O2) is approximately 32 g/mol, and the molar mass of methane (CH4) is approximately 16 g/mol. Since equal weights are taken, the partial pressure exerted by oxygen will be twice the partial pressure exerted by methane. Let's denote:

• 𝑃totalPtotal​ as the total pressure of the mixture,
• 𝑃oxygenPoxygen​ as the partial pressure exerted by oxygen, and
• 𝑃methanePmethane​ as the partial pressure exerted by methane.

We have: 𝑃oxygen=2×𝑃methanePoxygen​=2×Pmethane​ Therefore, the total pressure 𝑃totalPtotal​ is given by: 𝑃total=𝑃oxygen+𝑃methanePtotal​=Poxygen​+Pmethane​ 𝑃total=2×𝑃methane+𝑃methanePtotal​=2×Pmethane​+Pmethane​ 𝑃total=3×𝑃methanePtotal​=3×Pmethane​ Since the total pressure is proportional to the partial pressure exerted by methane, the fraction of the total pressure exerted by oxygen is: 𝑃oxygen𝑃total=2×𝑃methane3×𝑃methane=23Ptotal​Poxygen​​=3×Pmethane​2×Pmethane​​=32​ Therefore, the fraction of the total pressure exerted by oxygen is 2332​.