0.01 mole of an organic compound (X) containing 10% hydrogen, on complete combustion, produced 0.9 g H₂O. Molar mass of (X) is ___________g mol\(^{-1}\).
0.01 mole of an organic compound (X) containing 10% hydrogen, on complete combustion, produced 0.9 g H₂O. Molar mass of (X) is ___________g mol\(^{-1}\).
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Correct Answer: 100
Approach Solution - 1
To find the molar mass of the organic compound (X), we begin by determining the number of moles of hydrogen in 0.9 g of H₂O.
Step 1: Calculate moles of H₂O.
The molar mass of H₂O = 18 g/mol.
Number of moles = Mass / Molar mass = 0.9 g / 18 g/mol = 0.05 moles.
Step 2: Calculate moles of hydrogen in H₂O.
Each mole of H₂O contains 2 moles of hydrogen, so 0.05 moles of H₂O contain 0.1 moles of H.
Step 3: Relate moles of hydrogen to the compound (X).
The given organic compound (X) contains 10% hydrogen by mass. Thus, in 0.01 moles of (X), the moles of hydrogen = 0.1 moles (from combustion data).
Step 4: Calculate the molar mass of (X).
Since 10% of the molar mass is due to hydrogen: 0.1 M (where M = molar mass of X) = 0.01 moles of H, leading to M = 0.01 moles of H * 100 / 10% mol fraction of H = 0.1 moles / 0.01 * 100 = 100 g/mol.
Step 5: Verify the result.
The calculated molar mass of (X) = 100 g/mol, which is within the provided range of 100 to 100.
Approach Solution -2
Problem:
0.01 mole of an organic compound (X) containing 10% hydrogen, on complete combustion, produced 0.9 g of H2O. Find the molar mass of compound (X).
Given:
Moles of compound \( X = 0.01 \, \text{mol} \)
Hydrogen content = 10% by mass
Mass of water produced = \( 0.9 \, \text{g} \)
Step 1: Moles of Water Produced
Molar mass of water \( H_2O = 18 \, \text{g/mol} \)
\[ \text{Moles of } H_2O = \frac{0.9}{18} = 0.05 \, \text{mol} \]
Step 2: Mass of Hydrogen in Water
Each mole of water contains 2 grams of hydrogen.
\[ \text{Mass of hydrogen} = 0.05 \times 2 = 0.1 \, \text{g} \]
Step 3: Use Percentage to Find Molar Mass
If 0.1 g of hydrogen is 10% of the mass of 0.01 mol of X:
\[ \frac{0.1}{0.01 \times M} = 0.10 \]
Solving:
\[ 0.1 = \frac{0.1}{0.01M} \Rightarrow 0.01M = \frac{0.1}{0.1} = 1 \Rightarrow M = \frac{1}{0.01} = 100 \]
Final Answer:
\[ \boxed{\text{Molar mass of } X = 100 \, \text{g/mol}} \]
Approach Solution -3
Given that the compound contains 10% hydrogen, we can assume the molar mass of the compound is \( M_X \). - Mass of hydrogen in 0.01 mole of X = \( 0.01 \times 10 = 0.1 \text{g} \).
- In the complete combustion of X, the hydrogen reacts with oxygen to form H₂O.
- The number of moles of water formed is \( \frac{0.9}{18} = 0.05 \text{moles} \).
- In 1 mole of H₂O, there are 2 moles of hydrogen atoms. So, the moles of hydrogen atoms that reacted are \( 2 \times 0.05 = 0.1 \text{moles} \). The number of moles of hydrogen in 0.01 mole of X is 0.1 g, which gives the molar mass of X as: \[ \text{Molar Mass of X} = \frac{\text{Mass of X}}{\text{Number of moles of X}} = \frac{0.01}{0.01} = 100 \text{ g/mol}. \] Thus, the molar mass of X is 100 g/mol.
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