An organic compound containing C,H and N gave the following analysis
C=40 %,H=13.33 %,N=46.67 %
What would be its empirical formula ?

Options

A. `CH_(4)N`
B. `CH_(5)N`
C. `C_(2)H_(7)N_(2)`
D. `C_(2)H_(7)N`

Answer

To find the empirical formula of the organic compound containing carbon (C), hydrogen (H), and nitrogen (N) based on the given percentage composition, we can follow these steps:

### Step 1: Write down the percentages of each element.
- Carbon (C) = 40%
- Hydrogen (H) = 13.33%
- Nitrogen (N) = 46.67%

### Step 2: Convert the percentages to grams.
Assuming we have 100 grams of the compound, the mass of each element will be:
- Mass of C = 40 g
- Mass of H = 13.33 g
- Mass of N = 46.67 g

### Step 3: Convert the masses to moles.
To find the number of moles, we divide the mass of each element by its molar mass (atomic weight):
- Moles of C = \( \frac{40 \text{ g}}{12 \text{ g/mol}} \) = 3.33 moles
- Moles of H = \( \frac{13.33 \text{ g}}{1 \text{ g/mol}} \) = 13.33 moles
- Moles of N = \( \frac{46.67 \text{ g}}{14 \text{ g/mol}} \) = 3.33 moles

### Step 4: Determine the simplest mole ratio.
Next, we divide the number of moles of each element by the smallest number of moles calculated:
- Ratio of C = \( \frac{3.33}{3.33} \) = 1
- Ratio of H = \( \frac{13.33}{3.33} \) = 4
- Ratio of N = \( \frac{3.33}{3.33} \) = 1

### Step 5: Write the empirical formula.
From the ratios calculated, we can write the empirical formula:
- Empirical formula = C₁H₄N₁ or simply CH₄N

### Conclusion:
The empirical formula of the compound is **CH₄N**.

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