Question

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?

Answer 1

The molar mass of the gas is `"126 g/mol"`.

Explanation:

First calculate the moles of the gas using the gas law, `PV=nRT`, 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

`"mass":` `"0.950 g"`

`"pressure":` `P="0.985 atm"`

`"volume":` `V=232 cancel"mL"xx(1"L")/(1000cancel"mL")="0.232 L"`

`"gas constant":` `R="0.082057338 L atm K"^(-1) "mol"^(-1)`

`"temperature":` `T=95^"o""C"+273.15="368 K"`

Unknown

`n`

Equation

`PV=nRT`

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

`n=(PV)/(RT)`

`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`=` `("grams")/("mol")`

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