Number of hydrogen atoms per molecule of a hydrocarbon A having `85.8%` carbon is (Given: Molar mass of `A=84gmol^(-1)` )

Answer

To solve the problem of determining the number of hydrogen atoms per molecule of a hydrocarbon A with 85.8% carbon and a molar mass of 84 g/mol, we can follow these steps:

### Step 1: Determine the percentage of hydrogen
Given that the hydrocarbon is composed of carbon and hydrogen, we can find the percentage of hydrogen by subtracting the percentage of carbon from 100%.

\[ \text{Percentage of Hydrogen} = 100\% - 85.8\% = 14.2\% \]

### Step 2: Calculate the moles of carbon and hydrogen
Next, we convert the percentages of carbon and hydrogen to moles. We use the molar mass of carbon (12 g/mol) and hydrogen (1 g/mol) for this calculation.

- Moles of Carbon:
\[ \text{Moles of Carbon} = \frac{85.8 \, \text{g}}{12 \, \text{g/mol}} \approx 7.15 \, \text{mol} \]

- Moles of Hydrogen:
\[ \text{Moles of Hydrogen} = \frac{14.2 \, \text{g}}{1 \, \text{g/mol}} = 14.2 \, \text{mol} \]

### Step 3: Find the simplest mole ratio
To find the simplest ratio of carbon to hydrogen, we divide the number of moles of each element by the smaller number of moles.

\[ \text{Ratio of C to H} = \frac{7.15}{7.15} : \frac{14.2}{7.15} \approx 1 : 2 \]

This gives us the empirical formula \( \text{CH}_2 \).

### Step 4: Calculate the empirical formula mass
Next, we calculate the molar mass of the empirical formula \( \text{CH}_2 \):

\[ \text{Empirical formula mass} = 12 \, \text{g/mol (C)} + 2 \times 1 \, \text{g/mol (H)} = 14 \, \text{g/mol} \]

### Step 5: Determine the molecular formula
Now we can find the molecular formula using the molar mass of the hydrocarbon (84 g/mol). We divide the molar mass by the empirical formula mass:

\[ N = \frac{\text{Molar mass}}{\text{Empirical formula mass}} = \frac{84 \, \text{g/mol}}{14 \, \text{g/mol}} = 6 \]

Thus, the molecular formula is:

\[ \text{C}_6\text{H}_{12} \]

### Step 6: Determine the number of hydrogen atoms
Finally, we can find the number of hydrogen atoms in the molecular formula:

\[ \text{Number of Hydrogen atoms} = 12 \]

### Final Answer
The number of hydrogen atoms per molecule of hydrocarbon A is **12**.

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