A gas sample has density 1.96 g/L at 298 K and 1 atm. What is its molar mass?

A gas sample has density 1.96 g/L at 298 K and 1 atm. What is its molar mass?

• A. 48.0 g/mol
• B. 40.0 g/mol
• C. 18.0 g/mol
• D. 12.0 g/mol

Answer: (A)

At a given temperature and pressure, the density of an ideal gas is connected to its molar mass by the relation d = (MM · P) / (R · T), which rearranges to MM = d · R · T / P. Here, density is 1.96 g/L, temperature is 298 K, and pressure is 1 atm, with R = 0.082057 L·atm/(mol·K). Plugging in the values: MM = (1.96 g/L) × (0.082057 L·atm/(mol·K)) × (298 K) / (1 atm) ≈ 1.96 × 24.45 ≈ 47.9 g/mol, which rounds to about 48.0 g/mol. This is why the correct choice is the one around 48 g/mol.

At a given temperature and pressure, the density of an ideal gas is connected to its molar mass by the relation d = (MM · P) / (R · T), which rearranges to MM = d · R · T / P. Here, density is 1.96 g/L, temperature is 298 K, and pressure is 1 atm, with R = 0.082057 L·atm/(mol·K).

Plugging in the values: MM = (1.96 g/L) × (0.082057 L·atm/(mol·K)) × (298 K) / (1 atm) ≈ 1.96 × 24.45 ≈ 47.9 g/mol, which rounds to about 48.0 g/mol. This is why the correct choice is the one around 48 g/mol.