Degree of Unsaturation of Hydrocarbon JEE Chemistry Question

 

❓ Question

A hydrocarbon $X$ has a molar mass of 80 g mol⁻¹ and contains 90% carbon by mass. Find the degree of unsaturation of the hydrocarbon.

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✍️ Solution

Mass percentage of carbon:

$$C=90\%$$

Since the compound is a hydrocarbon,

$$H=100-90=10\%$$

Assume 100 g of hydrocarbon.

Moles of carbon:

$$\frac{90}{12}=7.5$$

Moles of hydrogen:

$$\frac{10}{1}=10$$

Therefore,

$$C:H=7.5:10$$
$$C:H=3:4$$

Hence, the empirical formula is

$$\boxed{C_3H_4}$$

Empirical formula mass:

$$=3(12)+4(1)=40\text{ g mol}^{-1}$$

Now,

$$n=\frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$$
$$n=\frac{80}{40}=2$$

Therefore, the molecular formula is

$$(C_3H_4)_2=C_6H_8$$

For a hydrocarbon $C_nH_m$,

$$\text{Degree of Unsaturation}=\frac{2n+2-m}{2}$$

For $C_6H_8$:

$$\text{DoU}=\frac{2(6)+2-8}{2}$$
$$=\frac{6}{2}=3$$

✅ Final Answer

$$\boxed{3}$$