Equal masses of CH₄ and H₂ are mixed in an empty container. The partial pressure of hydrogen in this container expressed as the fraction of total pressure is

ANS:B - 8/9

To find the partial pressure of hydrogen (𝑃H2PH2​​) in the container, we first need to determine the total pressure (𝑃totalPtotal​) in the container. Given:

• Equal masses of CH4 and H2 are mixed.
• The total pressure in the container is the sum of the partial pressures of each gas.

First, let's denote:

• 𝑃CH4PCH4​​ as the partial pressure of methane (CH4)
• 𝑃H2PH2​​ as the partial pressure of hydrogen (H2)

Since equal masses of CH4 and H2 are mixed, the number of moles of each gas will be in the same ratio as their molar masses. The molar mass of CH4 (methane) = 12.01+4×1.01=16.05 g/mol12.01+4×1.01=16.05g/mol The molar mass of H2 (hydrogen) = 2×1.01=2.02 g/mol2×1.01=2.02g/mol Since the number of moles of each gas is directly proportional to its molar mass, the ratio of the number of moles of H2 to CH4 is: moles of H2moles of CH4=molar mass of CH4molar mass of H2=16.052.02=7.941moles of CH4​moles of H2​​=molar mass of H2​molar mass of CH4​​=2.0216.05​=7.941 So, for every 7.941 moles of CH4, there is 1 mole of H2. Now, the total pressure (𝑃totalPtotal​) in the container is the sum of the partial pressures of each gas: 𝑃total=𝑃CH4+𝑃H2Ptotal​=PCH4​​+PH2​​ Since CH4 and H2 are mixed in equal masses, their partial pressures are also in the same ratio. Therefore, the partial pressure of H2 is: 𝑃H2=17.941+1×𝑃total=18.941×𝑃totalPH2​​=7.941+11​×Ptotal​=8.9411​×Ptotal​ Now, the partial pressure of hydrogen (𝑃H2PH2​​) expressed as the fraction of the total pressure (𝑃totalPtotal​) is: 𝑃H2𝑃total=18.941×𝑃total𝑃total=18.941=19Ptotal​PH2​​​=Ptotal​8.9411​×Ptotal​​=8.9411​=91​ Therefore, the partial pressure of hydrogen in the container, expressed as the fraction of the total pressure, is 1991​.