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Question 5.8: A sample of gas has a mass of 0.311 g. At 55 °C its volume i...

A sample of gas has a mass of 0.311 g. At 55 °C its volume is 0.225 L and its pressure is 886 mmHg. Find its molar mass.

SORT The problem gives you the mass of a gas sample,along with its volume, temperature, and pressure. You must find the molar mass. GIVEN m = 0.311 g, V = 0.225 L, T(°C) = 55 °C,
P = 886 mmHg
FIND molar mass (g/mol)
STRATEGIZE The conceptual plan has two parts. In the first part, use the ideal gas law to find the number of moles of gas.In the second part, use the definition of molar mass to find the molar mass. CONCEPTUAL PLAN
P, V, T     →      n
.        PV = nRT

n, m     →     molar mass
.     molar mass = \frac{mass (m)}{moles (n)}
RELATIONSHIPS USED
PV = nRT
Molar mass = \frac{mass (m)}{moles (n)}
SOLVE To find the number of moles, first solve the ideal gas law for n.
Before substituting into the equation for n, convert the pressure to atm and the temperature to K.
Substitute into the equation and calculate n, the number of moles.
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PV = nRT
n = \frac{PV}{RT}
P = 886 \cancel{mmHg} \times\frac{1 atm}{760 \cancel{mmHg}} = 1.1\underline{6}58 atm
T(K) = 55 + 273 = 328 K
n = \frac{1.1\underline{6}58 \cancel{atm} \times 0.225 \cancel{L}}{0.08206\frac{\cancel{L} . \cancel{atm}}{mol .\cancel{ K}}\times 328 \cancel{K}}= 9.7\underline{4}54 \times 10^{-3} mol

Finally, use the number of moles (n) and the given mass (m) to find the molar mass. molar mass = \frac{mass (m)}{moles (n)}
= \frac{0.311 g}{9.7\underline{4}54 \times 10^{-3} mol} = 31.9 g/mol
CHECK The units of the answer are correct. The magnitude of the answer (31.9 g/mol) is a reasonable number for a molar mass. If you calculated some very small number (for example, any number smaller than 1) or a very large number, you probably made an error. Most common gases have molar masses between two and several hundred grams per mole.

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