In an organic compound of molar mass `108 g mol^(-1)`, H and N atoms are present in `9 : 1 : 3.5` by weight. Molecular formula can be: "1.C_(6)H_(8)N_(2)`" 2.C_(7)H_(10)N` 3.C_(5)H_(6)N_(3)` 4.C_(4)H_(18)N_(3)`

Options

A. `C_(6)H_(8)N_(2)`
B. `C_(7)H_(10)N`
C. `C_(5)H_(6)N_(3)`
D. `C_(4)H_(18)N_(3)`

Answer

To determine the molecular formula of the organic compound with a molar mass of 108 g/mol and a weight ratio of carbon (C), hydrogen (H), and nitrogen (N) of 9:1:3.5, we can follow these steps:

### Step 1: Assign Variables to the Masses
Let the masses of carbon, hydrogen, and nitrogen be represented as follows:
- Mass of Carbon = 9x g
- Mass of Hydrogen = 1x g
- Mass of Nitrogen = 3.5x g

### Step 2: Set Up the Equation for Total Mass
The total mass of the compound is given as 108 g. Therefore, we can write the equation:
\[ 9x + 1x + 3.5x = 108 \]

### Step 3: Solve for x
Combine the terms:
\[ 13.5x = 108 \]
Now, solve for x:
\[ x = \frac{108}{13.5} = 8 \]

### Step 4: Calculate the Mass of Each Element
Now that we have the value of x, we can calculate the mass of each element:
- Mass of Carbon = \( 9x = 9 \times 8 = 72 \) g
- Mass of Hydrogen = \( 1x = 1 \times 8 = 8 \) g
- Mass of Nitrogen = \( 3.5x = 3.5 \times 8 = 28 \) g

### Step 5: Calculate the Number of Moles of Each Element
Using the molar masses (C = 12 g/mol, H = 1 g/mol, N = 14 g/mol), we calculate the number of moles:
- Moles of Carbon = \( \frac{72}{12} = 6 \) moles
- Moles of Hydrogen = \( \frac{8}{1} = 8 \) moles
- Moles of Nitrogen = \( \frac{28}{14} = 2 \) moles

### Step 6: Determine the Empirical Formula
Now, we find the simplest whole number ratio of the moles:
- Ratio of C:H:N = 6:8:2
- Dividing by 2 gives us the ratio: 3:4:1

Thus, the empirical formula is:
\[ \text{Empirical Formula} = C_3H_4N \]

### Step 7: Calculate the Empirical Formula Mass
Now, we calculate the mass of the empirical formula:
- Mass of \( C_3H_4N = (3 \times 12) + (4 \times 1) + (1 \times 14) = 36 + 4 + 14 = 54 \) g/mol

### Step 8: Find the Value of n
To find the molecular formula, we need to determine n:
\[ n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}} = \frac{108}{54} = 2 \]

### Step 9: Determine the Molecular Formula
Now, we can find the molecular formula by multiplying the empirical formula by n:
\[ \text{Molecular Formula} = n \times \text{Empirical Formula} = 2 \times C_3H_4N = C_6H_8N_2 \]

### Conclusion
The molecular formula of the compound is:
\[ C_6H_8N_2 \]

### Answer Options
Among the given options, the correct answer is:
1. \( C_6H_8N_2 \)

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