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?

1 Answer
Nov 26, 2015

Answer:

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"#