Question

An experiment shows that a 250 ?ml gas sample has a mass of 0.430 g at a pressure of 736 mmhg and a temperature of 28 ?c.

Answer 1

What we're looking for here is the gas sample's molar mass given its mass, pressure, volume, and temperature. Recalling the gas law, we have


`PV = nRT` or

`n = (PV)/(RT)`

where R is 0.08206 L atm / mol K, P is the given pressure, T is the temperature, and V is the volume.

Before applying the values given, it is important to make sure that they are to be converted to have consistent units with that of R.

Thus, we have

P = 736/ 729 = 0.968 atm
T = 28 + 273.15 = 301.15 K
V = 250/1000 = 0.250 L

Now, applying these converted values into the gas law, we have


`n = ((0.968 atm)(0.250 L))/((0.08206 L.atm/mol.K)(301.15 K))`

`n = 0.00979 moles`

Given that the mass of the sample is 0.430 g, we have


`molar mass = (mass)/(number of moles)`

`molar mass = (0.430)/(0.00979) = 43.9`

Thus, the gas sample has a molar mass of 43.9 g/mol.