Question

An experiment shows that a 238 mL gas sample has a mass of 0.425 g at a pressure of 765 mm Hg and a temperature of 32°C. What is the molar mass of the gas?

Answer 1

Before we can start, let us make sure that the given values are in the correct SI units.

V = 238 mL (divide by 1000 to get L) = 0.238 L

m= 0.425 g

P= 765 mmHg

T = 32 C ( C + 273 to get to kelvin) = 305 k

R = 8.314 J/mol = 62.4 mmL/molK

The question wants us to find the molar mass of the gas, we could use this equation n = m/M but we do not have the number of moles.

Lets find the number of moles first using the ideal gas law:

pV = nRT

n = pV/RT

n = (1.006 atm x 0.238 L)/(0.0825L.atm/mol.K x 305 K)

n = 9.515x10^-3 mol

Now we have the number of moles, lets find the molar mass.

n = m/M

Lets re-arrange:

M = m/n

M = 0.425 g/9.515x10^-3 mol

M = 44.66 g/mol