If the volume of #"2.05 g"# of gas is #"2.55 L"# at #65^@ "C"# and #"1 atm"#, what is its molar mass, assuming it is an ideal gas?
1 Answer
Nov 20, 2017
It doesn't matter what identity it is. At
#PV = nRT# where:
#P# is the pressure in#"atm"# .#V# is the volume in#"L"# .#n# is the mols of ideal gas.#R = "0.082057 L"cdot"atm/mol"cdot"K"# is the universal gas constant.#T# is the temperature in#"K"# .
One can immediately evaluate the density from the given data:
#color(blue)(D) = "2.05 g"/"2.55 L" = color(blue)("0.804 g/L")#
As a result, one can then determine the molar mass simply by knowing how many mols there are of the gas.
#n = (PV)/(RT)#
#= (1.00 cancel"atm" cdot 2.55 cancel"L")/(0.082057 cancel"L"cdotcancel"atm""/mol"cdotcancel"K" cdot (65 + 273.15 cancel"K"))#
#=# #"0.0919 mols ideal gas"#
Therefore, the molar mass is:
#color(blue)(M) = "2.05 g"/"0.0919 mol" = color(blue)("22.3 g/mol")#
