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

49.2 g/mol

Step-by-step explanation:

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

Volume= 236 mL x (
`(1 L)/(1000 mL)`) = .236 L

Pressure= 740 mm Hg x (
`(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=
`(mass)/(moles)` or MM=
`(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=
`(PV)/(RT)`, where R (constant)= 0.082 L atm mol-1 K-1

Let's plug in what we know.

n=
`((0.97 atm)(0.236 L))/((0.082)(295K))`

n= 0.009 mol

Let's look back at MM=
`(m)/(n)` and plug in what we know.

MM=
`(0.443 g)/(0.009 mol)`

MM= 49.2 g/mol