Question

What is the pressure in atmospheres of 0.246 gram of hydrogen gas occupying a volume of 0.0500 liters at 21.0°C?

Answer 1

The pressure of `"H"_2"` gas will be 58.9 atm, rounded to three significant figures.

Explanation:

You need the ideal gas law to answer this question.

First convert the mass of hydrogen gas `("H"_2")` to moles by dividing the given mass by its molar mass.

Molar mass `"H"_2"` `=` `(1.008"g/mol"xx2=2.016"g/mol")`.

Moles `"H"_2"`

`(0.246cancel"g H"_2)/(2.016cancel"g/mol H"_2")` `=` `"0.122 mol H"_2"`

Now you need to determine your known and unknown variables.

Known
`V="0.0500 L"`
`n="0.122 mol"`
`R="0.082057338 L atm K"^(-1) "mol"^(-1)"`
`T="21.0"^@"C"+"273.15=294.2K"`

Unknown
`P`

Solution
Rearrange the ideal gas equation to isolate `P` and solve.

`P=(nRT)/V`

`P=((0.122cancel"mol")xx(0.082057338 cancel"L" "atm" cancel"K"^(-1) cancel"mol"^(-1))xx(294.2cancel"K"))/(0.0500cancel"L")="58.9 atm"`
rounded to three significant figures