Question

What is the molar mass of a gas if a 40.0-gram sample of the gas occupies 11.2 liters of space at STP?

Answer 1

`M = 80.0 g/(mol)`

Explanation:

For this solution one would use the variation of the Ideal Gas Law
`PM = dRT`
`P = Pressure` in `atm`
`M = Molar Mass` in `g/(mol)`
`d = Density` in `g/L`
`R = 0.0821 (atmL)/(molK)` the gas law constant
`T = Temperature` `K`

The density can be found by dividing the mass by the volume.

`d = (mass)/(volume) = g/L`

`mass = 40.0 g`
`volume = 11.2 L`

`d = (40.0g)/(11.2 L)`
`d = 3.57 g/L`

The STP values (standard temperature and pressure) are 1 atm and 273 K.

`P = 1 atm`
`M = ?`
`d = 3.57 g/L`
`R = 0.0821 (atmL)/(molK)`
`T = 273K`

`PM=dRT`
`(1 atm)(M)=(3.57g/L)(0.0821 (atmL)/(molK))(273K)`
`(M)=((3.57g/cancel(L))(0.0821 (cancel(atm)cancel(L))/(molcancel(K))(273cancelK)))/(1 cancel(atm))`
`M = 80.0 g/(mol)`