Question #4b1ce
1 Answer
Explanation:
As you know, the density of a substance,
In your case, you know that an unknown gas has a density of
#"pressure" = "100 kPa" = 100/101.325# #"atm"#
#"temperature" = 0^@"C" = "273.15 K"#
This tells you that every
#color(blue)(rho = m/V)#
where
At this point, your tool of choice will be the ideal gas law equation
#color(blue)(ul(color(black)(PV = nRT)))#
Here
#P# is the pressure of the gas#V# is the volume it occupies#n# is the number of moles of gas present in the sample#R# is the universal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is the absolute temperature of the gas
If you use the fact that the number of moles of gas can be expressed as the ratio between the mass of the sample and the molar mass of the gas
#n = m/M_M#
you can rewrite the ideal gas law equation as
#PV = m/M_M * RT#
Rearrange this to isolate
#M_M = color(blue)(m/V) * (RT)/P#
This is equivalent to
#M_M = color(blue)(rho) * (RT)/P#
Plug in the density of the gas and the aforementioned conditions for pressure and temperature to find the molar mass of the gas
#M_M = "1.429 g" color(red)(cancel(color(black)("L"^(-1)))) * (0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * 273.15 color(red)(cancel(color(black)("K"))))/(100/101.325color(red)(cancel(color(black)("atm"))))#
#color(darkgreen)(ul(color(black)(M_M = "32.47 g mol"^(-1))))#
The answer is rounded to four sig figs, the number of sig figs you have for the density of the gas.
SIDE NOTE A lot of sources still use the old definition of STP conditions
#"pressure = 1 atm"# #"temperature" = 0^@"C" = "273.15 K"#
so if this is the definition given to you, redo the calculations using