Question

Calculate the molar mass of a gas at 388 torr and 45°c if 206 ng of gas occupies 0.206 ul. (

Answer 1

To make our solution more systematic, let's convert all units that is consistent with the units of R which is 0.0821 L-atm/mol-K.

For pressure: 760 torr = 1 atm
388 torr * 1 atm/760 torr = 0.5105 atm

For volume, 1 μL = 10⁻⁶ L
0.206 μL * 10⁻⁶ L/1 μL = 2.06×10⁻⁷ L

For temperature,
T = 45 + 273 = 318 K

For mass, 1 ng = 10⁻⁹ g
206 ng * 10⁻⁹ g/1 ng = 2.06×10⁻⁷ g

Assuming ideal gas,

PV=nRT
(0.5105 atm)(2.06×10⁻⁷ L) = n(0.0821 L-atm/mol-K)(318 K)
n = 4×10⁻⁹ mol

Molar mass = Mass/n = 2.06×10⁻⁷ g/4×10⁻⁹ mol
Molar mass = 51.14 g/mol