An organic compound contains `C = 40%, H = 13.33%`, and `N = 46.67%`. Its empirical formula will be

Options

A. `CHN`
B. `C_(3)H_(7)N`
C. `C_(2)H_(2)N`
D. `CH_(4)N`

Explanation

To determine the empirical formula of the organic compound with the given percentages of carbon, hydrogen, and nitrogen, we can follow these steps:

### Step 1: Assume a Sample Size
Assume the total mass of the organic compound is 100 grams. This makes it easy to convert percentages into grams.

- Mass of Carbon (C) = 40% of 100 g = 40 g
- Mass of Hydrogen (H) = 13.33% of 100 g = 13.33 g
- Mass of Nitrogen (N) = 46.67% of 100 g = 46.67 g

### Step 2: Convert Mass to Moles
Next, we need to convert the mass of each element into moles using their respective molar masses:

- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Hydrogen (H) = 1 g/mol
- Molar mass of Nitrogen (N) = 14 g/mol

Now, calculate the number of moles for each element:

- Moles of Carbon = Mass of C / Molar mass of C = 40 g / 12 g/mol = 3.33 moles
- Moles of Hydrogen = Mass of H / Molar mass of H = 13.33 g / 1 g/mol = 13.33 moles
- Moles of Nitrogen = Mass of N / Molar mass of N = 46.67 g / 14 g/mol = 3.33 moles

### Step 3: Find the Simplest Ratio
To find the empirical formula, we need to determine the simplest whole number ratio of the moles of each element.

- The number of moles calculated is:
- Carbon: 3.33
- Hydrogen: 13.33
- Nitrogen: 3.33

Now, divide each mole value by the smallest number of moles (which is 3.33):

- Ratio of Carbon = 3.33 / 3.33 = 1
- Ratio of Hydrogen = 13.33 / 3.33 = 4
- Ratio of Nitrogen = 3.33 / 3.33 = 1

### Step 4: Write the Empirical Formula
Now that we have the simplest whole number ratio, we can write the empirical formula:

- The empirical formula is C₁H₄N₁, which can be simplified to CH₄N.

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

---