Question

The composition of a compound used to make polyvinyl chloride (PVC) is 38.4% C, 4.8% H and 56.8% Cl by mass. It took 7.73 min for a given volume of the compound to effuse through a porous plug, but it took only 6.18 min for the same amount of Ar to diffuse at the same temperature and pressure. What is the molecular formula of the compound?

Answer 1

C₂H₃Cl

Step-by-step explanation:

We can calculate the compound's molar mass using the data given by the problem and Graham's law:

Rate₁/Rate₂ =
`\sqrt{(M_(2))/(M_(1)) }`

In this case the subscript 1 refers to the compound and 2 refers to Ar.

Keeping in mind that Rate = volume/time, and that the volume is the same for both compounds, we can rewrite the equation as:

Time₂/Time₁ =
`\sqrt{(M_(2))/(M_(1)) }`

6.18/7.73 =
`\sqrt{(39.95)/(M_(1)) }`

M₁ = 62.5 g/mol

Now we determine the molecular formula by using the elemental % analysis:

Assuming we have 1 mol of the compound:

C ⇒ 62.5 g * 38.4/100 = 24 g C = 2 mol C

H ⇒ 62.5 g * 4.8/100 = 3 g H = 3 mol H

C ⇒ 62.5 g * 56.8/100 = 35.5 g Cl = 1 mol Cl

Thus the molecular formula is C₂H₃Cl