JEE Chemistry 2023 Question with Solution

Given: Hydrocarbon A has $85.8\%$ carbon and molar mass $84 \, \text{g/mol}$.

Find: Number of hydrogen atoms per molecule of A.

From percentage composition:

$$\frac{85.8}{12}=7.5$$

for carbon, and

$$\frac{14.2}{1}=14.2$$

for hydrogen.

Taking the mole ratio:

$$\text{C} : \text{H} = 1 : 2$$

So, the empirical formula is $CH_2$.

Empirical formula mass:

$$12 + 2 = 14$$

Given molecular mass is $84$, so

$$14 \times n = 84$$ $$n=6$$

Therefore, molecular formula is

$$(CH_2)_6 = C_6H_{12}$$

Hence, the number of hydrogen atoms per molecule is $12$.

Given: Percentage of carbon is $85.8\%$, so percentage of hydrogen is $14.2\%$. Molar mass = $84 \, \text{g/mol}$.

Find: Hydrogen atoms in one molecule.

1. Calculate moles of each element from percentage composition.

$$\text{Moles of C} = \frac{85.8}{12}$$ $$\text{Moles of H} = \frac{14.2}{1} = 14.2$$

2. Divide by the smaller value to get the simplest ratio.

$$\text{C} = 1, \quad \text{H} \approx 2$$

So the empirical formula is $CH_2$.

3. Compute empirical formula mass.

$$(1 \times 12) + (2 \times 1) = 14 \, \text{g/mol}$$

4. Find the multiplying factor.

$$\frac{84}{14} = 6$$

5. Molecular formula:

$$(CH_2)_6 = C_6H_{12}$$

So each molecule contains $12$ hydrogen atoms.

The numerical answer is 12.