AS/A-level chemistry. PLEASE HELP ME😭😭

When bromine water was added to a hydrocarbon, X, the bromine was decolourised. Analysis of X showed that it contained 85.7% carbon and 14.3% hydrogen, when 50 cm^3, or gaseous X were burned completely in oxygen, 250 cm^3 of carbon dioxide were formed.

Question: calculate the molecular formula for X.

NB: this is a past paper question but I was not given the code or even year.

No unfortunately I don’t know the answer, we were given this for homework but I can’t get to the rest of the questions (which I can do) without first having this one.

Okay, no worries.

So they gave us percentage by mass of carbon and hydrogen and we know it is a hydrocarbon (by definition, only consisting of hydrogen and carbon).

So hopefully you can work out the empirical formula which should be CH2.

They then tell us this hydrocarbon when burned COMPLETELY in oxygen. This means a complete combustion reaction took place. So only CO2 and H20 will be produced.

Write a general reaction equation: X(g) + O2(g) ---> CO2(g) + H2O(g)

Here I make a key assumption, I assume that all of these gases are at the same temperature and pressure, because this will allow us to use avagadro's law which states "gases at the same temperature and pressure can have their volumes worked out via molar ratio (stoichiometry)"

They tell you that 50cm3 of X produced 250cm3 of CO2 can you see that 1 mole of X (50 cm3) produces 5 moles of CO2 (250 cm3) as per Avagadro's Law.

Can you see this means that X originally had 5 carbons? to produce 5 moles of co2?

As such you do 5(CH2) = C5H10. You can check that this follows the general formula for an alkene (CnH2n) which concurrs with what the question has said that bromine water decolourises it.

And the fact they've told us it is a hydrocarbon means only C and H atoms are there - no other functional groups apart from a C=C - which opens up and bonds to bromine causing the decolourisation.

Edit: In all honesty, the question should really say that the combustion of X was done at constant pressure and temperature - but I guess unless they say otherwise you can assume.