# 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 **STP**, or Standard Temperature and Pressure.

In order to find the gas' molar mass, you need to know two things

the mass of this sample of gasthe 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")#