Question

If 28.0 g of methane gas (`CH_4`) are introduced into an evacuated 2.00-L gas cylinder at a temperature of 35°C, what is the pressure inside the cylinder?

Answer 1

The pressure of the methane gas will be 22.2 atm.

Explanation:

Use the ideal gas law with the formula `PV=nRT`, where `n` is moles, `R` is the gas constant, and `T` is temperature in Kelvins.

Determine the mole of `"CH"_4"` by dividing the given mass by its molar mass, `"16.04246 g/mol"` https://pubchem.ncbi.nlm.nih.gov/compound/297

`28.0cancel"g CH"_4xx(1"mol CH"_4)/(16.04246cancel"g CH"_4)="1.7454 mol CH"_4"`

Ideal Gas Law

Given/Known
`V="2.00 L"`
`n="1.7454 mol"`
`R="0.082057338 L atm K"^(-1) "mol"^(-1)`
`T="35"^@"C"+273.15="308 K"`

Unknown
Pressure, `P`

Solution
Rearrange the formula to isolate `P`. Substitute the given values into the formula and solve.

`PV=nRT`

`P=(nRT)/V`

`P=((1.7454"mol") xx (0.082057338"L atm K"^(-1) "mol"^(-1)) xx (308"K"))/(2.00"L")="22.2 atm"` rounded to three significant figures