Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is,
Given : Atomic masses of C, H and N are 12,1 and 14 amu respectively.
The molar mass of the compound A is 162 g `mol^(-1)`.

Options

A. `C_4H_6N_2`
B. `C_2H_3N`
C. `C_5H_7N`
D. `C_(10)H_(14)N_2`

Explanation

To determine the molecular formula of compound A, we will follow these steps:

### Step 1: Convert the percentage composition to grams
Assuming we have 100 g of the compound, we can directly use the percentage values as grams:
- Hydrogen (H): 8.7 g
- Carbon (C): 74 g
- Nitrogen (N): 17.3 g

### Step 2: Calculate the number of moles of each element
Using the atomic masses:
- Hydrogen (H) = 1 g/mol
- Carbon (C) = 12 g/mol
- Nitrogen (N) = 14 g/mol

Now, we calculate the moles:
- Moles of H = mass / molar mass = 8.7 g / 1 g/mol = 8.7 mol
- Moles of C = mass / molar mass = 74 g / 12 g/mol = 6.17 mol
- Moles of N = mass / molar mass = 17.3 g / 14 g/mol = 1.23 mol

### Step 3: Find the simplest mole ratio
To find the simplest ratio, we divide each mole value by the smallest number of moles calculated:
- Smallest number of moles = 1.23 (for N)

Now, we calculate the ratios:
- Ratio of H = 8.7 mol / 1.23 mol ≈ 7.07 (approximately 7)
- Ratio of C = 6.17 mol / 1.23 mol ≈ 5.02 (approximately 5)
- Ratio of N = 1.23 mol / 1.23 mol = 1

Thus, the empirical formula is approximately C5H7N.

### Step 4: Calculate the empirical formula mass
Now we calculate the molar mass of the empirical formula (C5H7N):
- Molar mass = (5 × 12) + (7 × 1) + (1 × 14) = 60 + 7 + 14 = 81 g/mol

### Step 5: Determine the molecular formula
Given that the molar mass of the compound A is 162 g/mol, we can find the ratio of the molecular formula mass to the empirical formula mass:
- Ratio = Molar mass of compound / Empirical formula mass = 162 g/mol / 81 g/mol = 2

### Step 6: Multiply the empirical formula by this ratio
To find the molecular formula, we multiply the subscripts in the empirical formula (C5H7N) by 2:
- Molecular formula = C(5×2)H(7×2)N(1×2) = C10H14N2

### Final Answer
The molecular formula of compound A is C10H14N2.

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