An imaginary ideal gas has a density of 3 g/L at STP. What is the molar mas of this gas?
1 Answer
Explanation:
You know that you're dealing with a sample of an unknown gas that has a density of
In order to find the gas' molar mass, you need to know two things
- the mass of this sample of gas
- the number of moles of gas present in this sample
Now, STP conditions imply a pressure of
You will have to use the ideal as law
#color(blue)(PV = nRT)#
in order to try to find a relationship between the gas' density and its molar mass.
You know that molar mass is defined as mass per mole, so you can say that
#M_"m" = m/n implies n = m/M_"m"#
Replace the number of moles in the ideal gas law equation to get
#PV = m/M_"m" * RT#
You also know that density is defined as mass per unit of volume
#rho = m/V#
Notice what happens if you divide both sides of the ideal gas law equation by
#(P * color(red)(cancel(color(black)(V))))/color(red)(cancel(color(black)(V))) = m/M_"m" * (RT)/V#
#P = underbrace(m/V)_(color(green)("density")) * (RT)/M_"m" = rho * (RT)/M_"m"#
Finally, isolate the molar mass on one side of the equation to get
#M_"m" = rho * (RT)/P#
Now all you have to do is plug in your values - remember that
#R = 0.082("atm" * "L")/("mol" * "K")#
and that the pressure must be expressed in atm and the temperature in Kelvin!
#M_"m" = 3"g"/color(red)(cancel(color(black)("L"))) * (0.082(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 0)color(red)(cancel(color(black)("K"))))/(100/101.325color(red)(cancel(color(black)("atm"))))#
#M_"m" = "68.085 g/mol"#
SInce you only gave one sig fig for the density of the gas, the answer will be
#M_"m" = color(green)("70 g/mol")#