Chemistry: Finding Molecular Formula when Volume is given

Question

Question: Complete combustion analysis of a hydrocarbon compound was performed to define its molecular formula.

On complete combustion, the hydrocarbon gave 20 cm^3 of CO2 and 60 cm^3 of water.

The volumes were measured in identical conditions.

Select the option that corresponds to a possible molecular formula for the hydrocarbon.

1. C4H6
2. C3H3
3. C2H4
4. C2H6

(Ans: C4H6)

-----> My question: How do you find the molecular formula when the volume is given?

Answer 1

When the conditions are constant (no change in temperature or pressure, etc.), the volumes can be used just like we use moles. So, the ratio of moles of H₂O to moles CO₂ in this case is 3:1. But since each unit of H₂O has 2 H, that translates to a ratio of H to C of 6:1. Unfortunately, this does not correspond to any of the options. So, either there is an error in the presentation of the problem, or there is something that unusual that is missing.

In fact, if you take the answer given, and look at the combustion of C₄H₆, the ratio of H₂O to CO₂ is NOT 60:20, or 3:1, but is 3:4

C₄H₆ + 51/2 O₂ ==> 4CO₂ + 3H₂O .. balanced equation for combustion of C₄H₆ (note ratio of H₂O:CO₂)