An organic compound containing `C,H` and `N` have the percentage `40,13.33` and `46.67` respectively. Its empirical formula may be`:`

Options

A. `C_3H_13N_3`
B. `CH_2N`
C. `CH_4N`
D. `CH_6N`

Answer

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

### Step 1: Convert Percentages to Masses
Assuming we have 100 grams of the compound, the masses of each element can be directly taken as their percentages:
- Mass of Carbon (C) = 40 g
- Mass of Hydrogen (H) = 13.33 g
- Mass of Nitrogen (N) = 46.67 g

### Step 2: Calculate Moles of Each Element
Next, we will convert the masses of each element to moles using their atomic masses:
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Hydrogen (H) = 1 g/mol
- Atomic mass of Nitrogen (N) = 14 g/mol

Calculating the moles:
- Moles of Carbon (C) = Mass of C / Atomic mass of C = 40 g / 12 g/mol = 3.33 moles
- Moles of Hydrogen (H) = Mass of H / Atomic mass of H = 13.33 g / 1 g/mol = 13.33 moles
- Moles of Nitrogen (N) = Mass of N / Atomic mass of N = 46.67 g / 14 g/mol = 3.33 moles

### Step 3: Determine the Simplest Mole Ratio
Now we need to find the simplest ratio of moles of each element:
- The smallest number of moles among C, H, and N is 3.33 (for both C and N).
- Divide each mole value by the smallest number of moles (3.33):
- Ratio of C = 3.33 / 3.33 = 1
- Ratio of H = 13.33 / 3.33 = 4
- Ratio of N = 3.33 / 3.33 = 1

### Step 4: Write the Empirical Formula
From the ratios calculated, we can write the empirical formula:
- The empirical formula is C₁H₄N₁, which can be simplified to CH₄N.

### Final Answer
The empirical formula of the compound is **CH₄N**.

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