A 0.75 g sample of a gas occupies 0.40 L at 298 K and 1 atm. What is its approximate molar mass?

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Multiple Choice

A 0.75 g sample of a gas occupies 0.40 L at 298 K and 1 atm. What is its approximate molar mass?

Explanation:
Use the ideal gas law to relate pressure, volume, and temperature to the number of moles, then divide the sample’s mass by moles to get the molar mass. Calculate moles: n = PV/RT = (1 atm)(0.40 L) / [(0.0821 L·atm)/(mol·K))(298 K] ≈ 0.40 / 24.5 ≈ 1.63×10^-2 mol. Then determine molar mass: M = mass / n = 0.75 g / 0.0163 mol ≈ 4.6×10^1 g/mol, about 46 g/mol. The closest value is 45.7 g/mol, so that is the best choice.

Use the ideal gas law to relate pressure, volume, and temperature to the number of moles, then divide the sample’s mass by moles to get the molar mass.

Calculate moles: n = PV/RT = (1 atm)(0.40 L) / [(0.0821 L·atm)/(mol·K))(298 K] ≈ 0.40 / 24.5 ≈ 1.63×10^-2 mol.

Then determine molar mass: M = mass / n = 0.75 g / 0.0163 mol ≈ 4.6×10^1 g/mol, about 46 g/mol.

The closest value is 45.7 g/mol, so that is the best choice.

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