Molar Mass from Combustion Data JEE Chemistry Question

 

❓ Question

0.01 mole of an organic compound $X$ containing 10% hydrogen by mass on complete combustion produces 0.9 g of $H_2O$. Find the molar mass of $X$.

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✍️ Solution

Given,

$$\text{Moles of }X=0.01\text{ mol}$$

Mass of water produced:

$$=0.9\text{ g}$$

Moles of water:

$$n(H_2O)=\frac{0.9}{18}=0.05\text{ mol}$$

Each mole of $H_2O$ contains 2 moles of H atoms.

Therefore,

$$\text{Moles of H atoms}=2\times0.05=0.1\text{ mol}$$

Mass of hydrogen:

$$=0.1\times1=0.1\text{ g}$$

Let the molar mass of compound $X$ be $M$ g mol$^{-1}$.

Mass of $0.01$ mol of $X$:

$$=0.01M\text{ g}$$

Given hydrogen constitutes 10% by mass,

$$\frac{\text{Mass of H}}{\text{Mass of }X}\times100=10$$
$$\frac{0.1}{0.01M}\times100=10$$
$$\frac{10}{0.01M}=10$$
$$0.01M=1$$
$$M=100\text{ g mol}^{-1}$$

✅ Final Answer

$$\boxed{100\ \text{g mol}^{-1}}$$