An organic compound of carbon, hydrogen and nitrogen contains these elements having mass percentage `66.67%`,` 7.41%` and` 25.92%` respectively. Calculate empirical formula

Options

A. `C_3H_4N`
B. `C_2H_6N`
C. `C_4H_4N`
D. `C_4H_9N`

Answer

To calculate the empirical formula of the organic compound containing carbon, hydrogen, and nitrogen with the given mass percentages, follow these steps:

### Step 1: Convert mass percentages to grams
Assume we have 100 grams of the compound. This means:
- Mass of Carbon (C) = 66.67 g
- Mass of Hydrogen (H) = 7.41 g
- Mass of Nitrogen (N) = 25.92 g

### Step 2: Calculate the number of moles of each element
Using the 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 = 66.67 g / 12 g/mol = 5.56 moles
- Moles of Hydrogen = Mass of H / Molar mass of H = 7.41 g / 1 g/mol = 7.41 moles
- Moles of Nitrogen = Mass of N / Molar mass of N = 25.92 g / 14 g/mol = 1.85 moles

### Step 3: Determine the simplest mole ratio
Next, we need to find the simplest ratio of moles by dividing each by the smallest number of moles calculated:
- Smallest number of moles = 1.85 (for Nitrogen)

Now divide each mole value by 1.85:
- Ratio of Carbon = 5.56 / 1.85 = 3.00
- Ratio of Hydrogen = 7.41 / 1.85 = 4.00
- Ratio of Nitrogen = 1.85 / 1.85 = 1.00

### Step 4: Write the empirical formula
From the ratios calculated:
- Carbon = 3
- Hydrogen = 4
- Nitrogen = 1

Thus, the empirical formula is C₃H₄N.

### Final Answer:
The empirical formula of the compound is **C₃H₄N**.

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