help me!!! guessing formula of hydrocarbon with data from comubstion

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universalcj
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10 cm3
of a gaseous hydrocarbon was mixed with excess oxygen and ignited. The
gas volumes were measured at room temperature and pressure before and after
combustion and it was found that the total gas volume had contracted by 20 cm3
.
Given that combustion was complete, the formula of the hydrocarbon was

A C4H4
B C4H6
C C4H8
D C4H10

the answer is A according to mark scheme why????
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charco
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(Original post by universalcj)
10 cm3
of a gaseous hydrocarbon was mixed with excess oxygen and ignited. The
gas volumes were measured at room temperature and pressure before and after
combustion and it was found that the total gas volume had contracted by 20 cm3
.
Given that combustion was complete, the formula of the hydrocarbon was

A C4H4
B C4H6
C C4H8
D C4H10

the answer is A according to mark scheme why????
These are fun questions. Until you get the trick, they seem very complicated. Let's look at the facts:

(1) All hydrocarbons can be represented by the formula CaHb.
(2) When a hydrocarbon burns completely all of the carbon becomes carbon dioxide and all of the hydrogen becomes water
(3) Water is a liquid at room temperature and so has negligible volume (i.e. we can ignore it in the volume calculations).
(4) Avogadro's law tells us that for ALL gases the moles are directly proportional to the volume (at const T and P)

So according to (1) and (2) when the hydrocarbon burns in excess air or oxygen 1 mol of CaHb produces 'a' mol of carbon dioxide and 'b/2' mol of water.
Combining this with (4)

A volume of Vcm3 hydrocarbon must produce a volume of (V x a) cm3 of carbon dioxide

Are you with me so far?

Now lets consider the oxygen.

In order to produce 'a' mol of carbon dioxide and 'b/2' mol of water you need (a + b/4) mol of oxygen.

So we can write a general equation that appies to ALL hydrocarbons:

CaHb + (a + b/4)O2 ==> aCO2 + (b/2)H2O

So if the initial volume is known, and the final volume is also known it is possible to work out the formula of the hydrocarbon.
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