What is the molar mass of a gas if #"96 g"# of it exists in a #"52 L"# container at #"700 mm Hg"# pressure and #25^@ "C"#?

I got about #"50 g/mol"# to one significant figure.

Well, we don't know what the gas is, but we naively assume it is ideal, i.e. that its pressure and volume are given by...

#PV = nRT#

with

• #P# the pressure in #"atm"#.
• #V# the volume in #"L"#.
• #n# the mols of the ideal gas.
• #R = "0.082057 L"cdot"atm/mol"cdot"K"# the universal gas constant.
• #T# the temperature in #"K"#.

Knowing that molar mass must be in units of #"mass/mol"#, one can solve for the mols first.

#n = (PV)/(RT)#

The pressure and temperature must be in units that match #R#.

#P = 700 cancel"mm Hg" xx "1 atm"/(760 cancel"torr")#

#=# #"0.921 atm"#

#T = 25^@ "C" -> 25 + "273.15 K"#

#=# #"298.15 K"#

Therefore, the mols of gas are:

#n = (0.921 cancel"atm" cdot 52 cancel"L")/(0.082057 cancel"L"cdotcancel"atm""/""mol"cdotcancel"K" cdot 298.15 cancel"K")#

#=# #"1.96 mols ideal gas"#

As a result, the molar mass is approximately:

#color(blue)(M) = "96 g"/"1.96 mols"#

#=# #color(blue)ul("50 g/mol")#

to one significant figure, what you have given for the pressure.