Question

A 5 ml of hydrocarbon ' X ' on complete combustion produces 30 ml of \( CO _{2} \) and 25 ml of \( H _{2} O \) at same temperature and pressure. The formula of the hydrocarbon is

(1) \( C _{6} H _{12} \)

(2) \( C _{6} H _{10} \)

(3) \( C _{6} H _{14} \)

(4) \( C _{6} H _{6} \)

Answer 1

Correct option is (2) C₆H₁₀

The complete combustion of a hydrocarbon (C_x H_y) produces carbon dioxide (CO₂) and water (H₂O). 

The general reaction can be represented as: \(C_xH_y + O_2 → CO_2 + H_2O\)

From the combustion reaction:

Each mole of CO₂ produced corresponds to one mole of carbon in the hydrocarbon.

Each mole of H₂O produced corresponds to half a mole of hydrogen in the hydrocarbon.

Given,

30 ml of CO₂

25 ml of H₂O

Assuming the gases are at the same temperature and pressure, we can directly relate the volumes to moles:

Moles of CO₂ = 30 ml

Moles of H₂O = 25 ml

From the combustion:

Moles of carbon (C) = Moles of CO₂ = 30 ml

Moles of hydrogen (H) = 2 x Moles of H₂O = 2 x 25 ml = 50 ml

From the moles calculated:

C : 30

H : 50

The ratio of C to H is : C : H = 30 : 50 = 3 : 5

To find the molecular formula, we need to scale the empirical formula (C₃H₅) to match the options given. The molecular formula can be derived by multiplying the empirical formula by a factor that gives us a hydrocarbon with 6 carbons.

C₆H₁₀ is obtained by multiplying C₃H₅ by 2.

The formula of the hydrocarbon is C₆H₁₀.