Question

A 248 mL gas sample has a mass of 0.433 g at a pressure of 745 mmHg and a temperature of 28°C. What is the molar mass of the gas?

Answer 1

The molar mass of the gas is 44.0 g/mol.

Explanation:

We can use the Ideal Gas Law to solve this problem.

`color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "`

Since `n = "mass"/"molar mass" = m/M`,

we can write the Ideal Gas Law as

`color(blue)(bar(ul(|color(white)(a/a) PV = m/MRTcolor(white)(a/a)|)))" "`

We can rearrange this to get

`M = (mRT)/(PV)`

In your problem,

`m = "0.433 g"`
`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`
`T = "28 °C" = "301.15 K"`
`P = 745 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg"))))= "0.9803 atm"`
`V = "248 mL" = "0.248 L"`

∴ `M = ("0.433 g"× "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 301.15 color(red)(cancel(color(black)("K"))))/(0.9803 color(red)(cancel(color(black)("atm")))× 0.248 color(red)(cancel(color(black)("L")))) = "44.0 g/mol"`