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

1 Answer
Jun 18, 2018

Answer:

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"#