A 0.500 g sample of an unknown gas occupies 0.250 L at 27°C and 1.00 atm. What is the molar mass of the gas? (R = 0.0821 L·atm·mol⁻¹·K⁻¹)

Correct answer

A. 49.2 g/mol

Principle or equation

The ideal gas law is PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature in kelvin. Molar mass (M) is mass divided by moles, so M = mRT / (PV).

Why this answer is correct

Convert temperature to kelvin: 27°C + 273 = 300 K. Use the ideal gas law to find moles: n = PV / RT = (1.00 atm × 0.250 L) / (0.0821 L·atm·mol⁻¹·K⁻¹ × 300 K) = 0.01015 mol. Molar mass = mass / moles = 0.500 g / 0.01015 mol = 49.3 g/mol, which rounds to 49.2 g/mol.

Example

For a gas with mass 1.00 g, volume 0.500 L, pressure 1.00 atm, and temperature 273 K, n = (1.00 × 0.500) / (0.0821 × 273) = 0.0223 mol, so M = 1.00 / 0.0223 = 44.8 g/mol.