a hydrocarbon C10Hx requires 32.5 moles of O2 for the combustion of 2.5 moles calculate the value of x?

Brent started off correctly:

C10Hx + 13 O2 → 10 CO2 + __ H2O

Now there are 26 oxygen atoms on the left and 20 oxygen atoms in the CO2 on the right, so there must be 6 more oxygen atoms in the H2O, so:

C10Hx + 13 O2 → 10 CO2 + 6 H2O

Now to make the hydrogen atoms balance, x must be 12:

C10H12 + 13 O2 → 10 CO2 + 6 H2O

which is a reasonable, balanced equation for the combustion of decane.

Start with the combustion equation:

C10Hx + O2 --> CO2 + H2O

Find the whole number ratio of O2 to C10Hx

32.5 / 2.5 = 13

Balance carbon and oxygen:

C10Hx + 13 O2 --> 10 CO2 + 6 H2O

Now, the value of x to balance the hydrogen atoms is 12.

C10H12 + 13 O2 --> 10 CO2 + 3 H2O

(Corrected)

Thanks guys. That cleared a lot of my doubts.