Question

An experiment shows that a 236 mL gas sample has a mass of 0.443 g at a pressure of 740 mmHg and a temperature of 22 ∘C. What is the molar mass of the gas?

Answer 1

Answer:

49.2 g/mol

Explanation:

Let's first take account of what we have and convert them into the correct units.

Volume= 236 mL x ($\frac{1 L}{1000 mL}$) = .236 L

Pressure= 740 mm Hg x ($\frac{1 atm}{760 mm Hg}$)= 0.97 atm

Temperature= 22C + 273= 295 K

mass= 0.443 g

Molar mass is in grams per mole, or MM= $\frac{mass}{moles}$ or MM= $\frac{m}{n}$. They're all the same.

We have mass (0.443 g) we just need moles. We can find moles with the ideal gas constant PV=nRT. We want to solve for n, so we'll rearrange it to be

n=$\frac{PV}{RT}$, where R (constant)= 0.082 L atm mol-1 K-1

Let's plug in what we know.

n=$\frac{(0.97 atm)(0.236 L)}{(0.082)(295K)}$

n= 0.009 mol

Let's look back at MM= $\frac{m}{n}$ and plug in what we know.

MM= $\frac{0.443 g}{0.009 mol}$

MM= 49.2 g/mol