In a compound `C, H, N` atoms are present in `9:1:3.5` by weight. Molecular weight of compound is `108`. Its molecular formula is:

Options

A. (a)`C_(2)H_(6)N_(2)`
B. (b)`C_(3)H_(4)N`
C. (c )`C_(6)H_(8)N_(2)`
D. (d)`C_(9)H_(12)N_(3)`

Explanation

To find the molecular formula of the compound with the given weight ratio of carbon, hydrogen, and nitrogen, we can follow these steps:

### Step 1: Set Up the Weight Ratios
Given the weight ratios of C:H:N = 9:1:3.5, we can express the weights of each element in terms of a variable \( x \):
- Weight of Carbon (C) = \( 9x \)
- Weight of Hydrogen (H) = \( x \)
- Weight of Nitrogen (N) = \( 3.5x \)

### Step 2: Calculate Total Weight
The total weight of the compound can be expressed as:
\[ \text{Total weight} = 9x + x + 3.5x = 13.5x \]
We know that the total weight of the compound is 108 grams, so we can set up the equation:
\[ 13.5x = 108 \]

### Step 3: Solve for \( x \)
To find \( x \), we divide both sides by 13.5:
\[ x = \frac{108}{13.5} = 8 \]

### Step 4: Calculate the Weights of Each Element
Now we can find the actual weights of each element:
- Weight of Carbon = \( 9x = 9 \times 8 = 72 \) grams
- Weight of Hydrogen = \( x = 8 \) grams
- Weight of Nitrogen = \( 3.5x = 3.5 \times 8 = 28 \) grams

### Step 5: Calculate Moles of Each Element
Next, we convert these weights into moles using the atomic weights:
- Atomic weight of Carbon (C) = 12 g/mol
- Atomic weight of Hydrogen (H) = 1 g/mol
- Atomic weight of Nitrogen (N) = 14 g/mol

Calculating the moles:
- Moles of Carbon = \( \frac{72 \text{ g}}{12 \text{ g/mol}} = 6 \) moles
- Moles of Hydrogen = \( \frac{8 \text{ g}}{1 \text{ g/mol}} = 8 \) moles
- Moles of Nitrogen = \( \frac{28 \text{ g}}{14 \text{ g/mol}} = 2 \) moles

### Step 6: Write the Molecular Formula
From the moles calculated, we can write the molecular formula:
\[ \text{Molecular Formula} = C_6H_8N_2 \]

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

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