In an organic compound of molar mass `108 gm mol^-1 C, H and N` atoms are presents in `9 : 1 : 3.5` by mass. Molecular formula can be

Options

A. `C_6H_8N_2`
B. `C_7H_10N`
C. `C_5H_6N_3`
D. `C_4H_18N_3`

Answer

To find the molecular formula of the organic compound with a molar mass of 108 g/mol and the mass ratio of C, H, and N as 9:1:3.5, we will follow these steps:

### Step 1: Determine the mass of each element
Given the ratio of the elements:
- Carbon (C): 9 parts
- Hydrogen (H): 1 part
- Nitrogen (N): 3.5 parts

### Step 2: Convert the mass ratio to moles
To find the number of moles of each element, we will divide the mass of each by its atomic mass:
- Moles of Carbon = \( \frac{9 \text{ g}}{12 \text{ g/mol}} = 0.75 \text{ mol} \)
- Moles of Hydrogen = \( \frac{1 \text{ g}}{1 \text{ g/mol}} = 1 \text{ mol} \)
- Moles of Nitrogen = \( \frac{3.5 \text{ g}}{14 \text{ g/mol}} = 0.25 \text{ mol} \)

### Step 3: Find the simplest mole ratio
Now we will find the simplest whole number ratio by dividing each by the smallest number of moles (0.25):
- Ratio of C = \( \frac{0.75}{0.25} = 3 \)
- Ratio of H = \( \frac{1}{0.25} = 4 \)
- Ratio of N = \( \frac{0.25}{0.25} = 1 \)

Thus, the empirical formula is \( C_3H_4N \).

### Step 4: Calculate the empirical formula mass
Now we will calculate the molar mass of the empirical formula \( C_3H_4N \):
- Molar mass = \( (3 \times 12) + (4 \times 1) + (1 \times 14) \)
- Molar mass = \( 36 + 4 + 14 = 54 \text{ g/mol} \)

### Step 5: Determine the molecular formula
We know the molar mass of the compound is 108 g/mol. To find the molecular formula, we will divide the molar mass of the compound by the empirical formula mass:
- \( \frac{108 \text{ g/mol}}{54 \text{ g/mol}} = 2 \)

This means the molecular formula is \( (C_3H_4N)_2 = C_6H_8N_2 \).

### Final Answer
The molecular formula of the organic compound is \( C_6H_8N_2 \).

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