Question

Complete combustion of 1 mol of hydrocarbon X requires exactly 8.5 mol of oxygen. 

Incomplete combustion of 1 mol of hydrocarbon X, to form carbon monoxide and water requires exactly 5.5 moles of oxygen.

How many hydrogen atoms are in one molecule of hydrocarbon X?

A)6

B)8

C)10

D)12

E)12

The answer is C) 10 but no idea why

Thanks

Answer 1

Complete combustion:

CxHy + 8.5O₂ → xCO₂ + $\frac{y}{2}$ H₂O

O atoms balance:

$8.5 \times 2 = 2x + \frac{y}{2}$

Incomplete combustion:

CxHy + 5.5O₂ → xCO + $\frac{y}{2}$ H₂O

O atoms balance:

$5.5 \times 2 = x + \frac{y}{2}$

System of equations:

$17 = 2x + \frac{y}{2} \\ 11 = x + \frac{y}{2}$

Solution:

$17-11 = 2x-x + \frac{y}{2} - \frac{y}{2} \\ x=6 \\ 11 = 6 + \frac{y}{2} \\ 11 -6 = \frac{y}{2} \\ 5 = \frac{y}{2} \\ y=10$

Answer: C)10