What is the molar mass of a gas if a 0.950 gram sample of it occupies 232 mL at 95 °C and 0.985 atm?

Nov 26, 2015

The molar mass of the gas is $\text{126 g/mol}$.

Explanation:

First calculate the moles of the gas using the gas law, $P V = n R T$, where $n$ is the moles and $R$ is the gas constant. Then divide the given mass by the number of moles to get molar mass.

Calculate Moles

Given/Known

$\text{mass} :$$\text{0.950 g}$

$\text{pressure} :$$P = \text{0.985 atm}$

$\text{volume} :$$V = 232 \cancel{\text{mL"xx(1"L")/(1000cancel"mL")="0.232 L}}$

$\text{gas constant} :$$R = {\text{0.082057338 L atm K"^(-1) "mol}}^{- 1}$

$\text{temperature} :$$T = {95}^{\text{o""C"+273.15="368 K}}$

Unknown

$n$

Equation

$P V = n R T$

Solution
Rearrange the equation to isolate $n$ and solve.

$n = \frac{P V}{R T}$

n=(0.985cancel"atm"xx0.232cancel"L")/(0.082057338 cancel"L "cancel"atm"cancel"K"^(-1)cancel"mol"^(-1)xx368cancel"K")="0.007568 mol"

(I'm keeping a couple of guard digits to reduce rounding errors. I'll round to three significant figures at the end.)

Molar Mass of Gas

Molar mass$=$$\left(\text{grams")/("mol}\right)$

Molar mass$=$(0.950"g")/(0.007568"mol")="126 g/mol"