Question

What is the molar mass of a gas if 3.50 grams of the gas occupy 1.35 liters of space at STP?

Answer 1

The molar mass of the gas is `"58.9 g/mol"`.

Explanation:

You will need to use the equation for the ideal gas law:

`PV=nRT`,

where:

`P` is pressure, `V` is volume, `n` is moles, `R` is gas constant, and `T` is temperature.

`"STP"` is `0^@"C"` or `"273.15 K"` (required for gas laws), and `10^5` `"Pa"` or `"100 kPa"`.

Use the equation for the ideal gas law to calculate moles of gas. Then calculate the molar mass by dividing the given mass by the calculated moles.

Known

`P="100 kPa"`

`V="1.35 L"`

`R="8.31446 L kPa K"^(-1) "mol"^(-1)"`

`T="273.15 K"`

Unknown

`n`

Solution

Rearrange the ideal gas law equation to isolate `n`. Plug in the known values and solve.

`n=(PV)/(RT)`

`n=(100color(red)(cancel(color(black)("kPa")))xx1.35color(red)(cancel(color(black)("L"))))/(8.31446 color(red)(cancel(color(black)("L"))) color(red)(cancel(color(black)("kPa"))) color(red)(cancel(color(black)("K")))^(-1) "mol"^(-1)xx273.15color(red)(cancel(color(black)("K"))))="0.0594 mol"` (rounded to three significant figures)

To calculate the molar mass of the gas, divide its given mass in grams by the calculated number of moles.

`"molar mass"=("3.50 g")/("0.0594 mol")="58.9 g/mol"`