Gas mixtures — Equal masses of methane (CH4) and hydrogen (H2) are mixed in an empty container. What fraction of the total pressure is contributed by hydrogen (its partial pressure/total pressure)?

Introduction / Context:
Dalton’s law of partial pressures states that, for ideal gases, each species’ partial pressure is proportional to its mole fraction in the mixture at a given temperature and total pressure. When mixing equal masses of gases with different molar masses, the lighter gas will contribute more moles—and hence a larger share of the total pressure. This question quantifies that share for H2 and CH4.

Given Data / Assumptions:

• Equal masses of CH4 and H2 are mixed.
• Ideal-gas behavior; same temperature and total pressure.
• Molar masses: M_CH4 = 16 g/mol; M_H2 = 2 g/mol.

Concept / Approach:

Partial pressure fraction = mole fraction for ideal gases. With equal masses, moles are inversely proportional to molar mass. Because hydrogen is eight times lighter than methane, equal masses contain eight times more moles of H2 than CH4, so H2 dominates the mole fraction and therefore the partial pressure.

Step-by-Step Solution:

Verification / Alternative check:

Dalton’s law: p_i = y_i * P_total. The computed mole fraction 8/9 directly sets the partial pressure fraction.

Why Other Options Are Wrong:

1/2 suggests equal moles (not the case). 1/9 would correspond to methane’s share. 5/9 or 7/9 are arbitrary and not supported by stoichiometry.

Common Pitfalls:

Confusing equal masses with equal moles; ignoring the large molar-mass difference which skews mole fractions heavily toward the lighter gas.

Final Answer:

8/9