One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is __________.

For an alkane having the general formula $$C_nH_{2n+2}$$, the balanced combustion reaction is

$$C_nH_{2n+2} + \left(n + \frac{2n+2}{4}\right)O_2 \rightarrow nCO_2 + (n+1)H_2O$$

The number of $$O_2$$ molecules needed equals the sum of:

• $$n$$ (for converting $$n$$ carbon atoms to $$nCO_2$$)
• $$\dfrac{n+1}{2}$$ (because each mole of $$H_2O$$ needs one atom of oxygen, and each mole of $$O_2$$ supplies two atoms)

Hence, moles of $$O_2$$ required per mole of alkane $$=$$

$$n + \frac{n+1}{2} = \frac{2n + n + 1}{2} = \frac{3n+1}{2}$$

The problem states that 1 mole of the alkane requires 8 moles of $$O_2$$:

$$\frac{3n+1}{2} = 8 \quad \Longrightarrow \quad 3n+1 = 16 \quad \Longrightarrow \quad 3n = 15 \quad \Longrightarrow \quad n = 5$$

So the alkane is $$C_5H_{2(5)+2} = C_5H_{12}$$.

The sum of the number of carbon and hydrogen atoms in one molecule is

$$5 + 12 = 17$$

Therefore, the required sum is 17.