A compound has 62 % carbon, 10.4% hydrogen and 27.5% oxygen. If molar mass of compound is 58, find number of H-atom per molecule of the compound.

Answer

To solve the problem step by step, we will follow these procedures:

### Step 1: Determine the Molar Masses of the Elements
We know the atomic masses of the elements involved:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol
- Oxygen (O) = 16 g/mol

### Step 2: Convert Percentage Composition to Mass
Assuming we have 100 g of the compound, the masses of each element will be:
- Mass of Carbon = 62 g
- Mass of Hydrogen = 10.4 g
- Mass of Oxygen = 27.5 g

### Step 3: Calculate the Number of Moles of Each Element
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
We calculate the moles of each element:
- Moles of Carbon = \(\frac{62 \text{ g}}{12 \text{ g/mol}} = 5.17 \text{ moles}\)
- Moles of Hydrogen = \(\frac{10.4 \text{ g}}{1 \text{ g/mol}} = 10.4 \text{ moles}\)
- Moles of Oxygen = \(\frac{27.5 \text{ g}}{16 \text{ g/mol}} = 1.71 \text{ moles}\)

### Step 4: Find the Simplest Mole Ratio
To find the simplest ratio, we divide the number of moles of each element by the smallest number of moles calculated:
- Ratio of Carbon = \(\frac{5.17}{1.71} \approx 3\)
- Ratio of Hydrogen = \(\frac{10.4}{1.71} \approx 6\)
- Ratio of Oxygen = \(\frac{1.71}{1.71} = 1\)

### Step 5: Write the Empirical Formula
From the simplest mole ratio, we can write the empirical formula:
- Empirical formula = \(C_3H_6O\)

### Step 6: Determine the Molar Mass of the Empirical Formula
Calculate the molar mass of the empirical formula:
\[ \text{Molar mass of } C_3H_6O = (3 \times 12) + (6 \times 1) + (1 \times 16) = 36 + 6 + 16 = 58 \text{ g/mol} \]

### Step 7: Determine the Number of Hydrogen Atoms in the Molecular Formula
Since the molar mass of the empirical formula (58 g/mol) is equal to the molar mass of the compound (58 g/mol), the molecular formula is the same as the empirical formula. Thus, the number of hydrogen atoms in the molecular formula is 6.

### Final Answer
The number of hydrogen atoms per molecule of the compound is **6**.

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