# At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of O2 for complete combustion, and 40 mL of CO2 is formed. The formula of t

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At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of O2 for complete combustion, and 40 mL of CO2 is formed. The formula of the hydrocarbon is:
1. C4 H10
2. C4 H6
3. C4 H7 Cl
4. C4 H8

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Correct Answer - Option 2 : C4 H6

Concept:

Let, the hydrocarbon be CxHy

The general equation for hydrocarbon combustion be

${C_x}{H_y} + \left( {x\, + \frac{y}{4}} \right){O_2}{\rm{\;}} \to xC{O_2}{\rm{\;}} + {\rm{\;}}\frac{y}{2}{H_2}0$

Here the carbon has x number of moles and hydrogen has y number of moles in LHS.

So, x is placed before carbon dioxide, and $\frac{y}{2}$ is placed before water and $\left( {x\, + \frac{y}{4}} \right)$ by adding the RHS.

For 1 ml of hydrocarbon, the general equation will be written as,

$1\;ml\; + \;\left( {x\, + \frac{y}{4}} \right)ml{\rm{\;}} \to x\;ml + {\rm{\;}}\frac{y}{2}{\rm{\;ml}}$

Similarly, for 10 ml of hydrocarbon the general equation will be written as,

$10\;ml\; + \;10\left( {x\, + \frac{y}{4}} \right)ml{\rm{\;}} \to 10x\;ml + 10.{\rm{\;}}\frac{y}{2}{\rm{\;ml}}$

Calculation:

From the question, 10 mL of a hydrocarbon releases 40 mL of CO2

⇒ 10x = 40

⇒ x = 4

Similarly, from the question, oxygen produced is 55 ml, thus from the general equation given above,

$10\left( {x + \frac{y}{4}} \right) = 55$

$\Rightarrow 10\left( {4 + \frac{y}{4}} \right) = 55$

$4 + \frac{y}{4} = \frac{{55}}{{10}}$

$\frac{y}{4} = 5.5 - 4$

y = 1.5 × 4 = 6

∴ The required formula for Hydrocarbon is C4 H6