What is the molar mass of a gas if 2.50 g occupies 0.875 L at 685 torr and 35 ° C?

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Quizplus · Accepted Answer

To find the molar mass of the gas, we can use the ideal gas law equation rearranged to solve for molar mass (M):$$ M = \frac{mRT}{PV} $$where $ m $ is the mass of the gas in grams, $ R $ is the ideal gas constant, $ P $ is the pressure, $ V $ is the volume, and $ T $ is the temperature in Kelvin.Given:- $ m = 2.50 $ g- $ V = 0.875 $ L- $ P = 685 $ torr (1 atm = 760 torr, so $ P = 685 $ torr $ \times \frac{1 \text{ atm}}{760 \text{ torr}} $)- $ T = 35 $ °C (To convert to Kelvin, $ T = 35 + 273.15 = 308.15 $ K)- $ R = 0.0821 $ L·atm/(K·mol) (ideal gas constant)First, convert pressure from torr to atm:$$ P = 685 \text{ torr} \times \frac{1 \text{ atm}}{760 \text{ torr}} = 0.9013 \text{ atm} $$Now, plug the values into the rearranged ideal gas law equation:$$ M = \frac{(2.50 \text{ g}) \times (0.0821 \text{ L·atm/K·mol}) \times (308.15 \text{ K})}{(0.9013 \text{ atm}) \times (0.875 \text{ L})} $$$$ M = \frac{63.2 \text{ g·K/mol}}{0.7886 \text{ L·atm}} $$$$ M \approx 80.2 \text{ g/mol} $$Therefore, the molar mass of the gas is approximately 80.2 g/mol.

What Is the Molar Mass of a Gas If 2