An organic compound contains 20.0%C, 6.66% H, 47.33% N and the rest was oxygen. Its molar mass is 60 g mol^(-1). The molecular formula of the compound is

Options

A. `CH_4N_2O`
B. `C_2H_4NO_2`
C. `CH_3N_2O`
D. `CH_4N_2O_2`

Answer

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

### Step 1: Convert Percentages to Grams
Assuming we have 100 grams of the compound, we can directly use the percentages as grams:
- Carbon (C): 20.0 g
- Hydrogen (H): 6.66 g
- Nitrogen (N): 47.33 g
- Oxygen (O): 100 g - (20.0 g + 6.66 g + 47.33 g) = 26.01 g

### Step 2: Calculate Moles of Each Element
Next, we will convert the grams of each element to moles using their molar masses:
- Molar mass of C = 12 g/mol
- Molar mass of H = 1 g/mol
- Molar mass of N = 14 g/mol
- Molar mass of O = 16 g/mol

Calculating moles:
- Moles of C = 20.0 g / 12 g/mol = 1.67 mol
- Moles of H = 6.66 g / 1 g/mol = 6.66 mol
- Moles of N = 47.33 g / 14 g/mol = 3.38 mol
- Moles of O = 26.01 g / 16 g/mol = 1.63 mol

### Step 3: Determine the Smallest Number of Moles
Now, we will find the smallest number of moles among the calculated values to normalize them:
- Smallest number of moles = 1.63 mol (for O)

### Step 4: Divide All Moles by the Smallest Number
Now, we will divide each mole value by the smallest number (1.63):
- C: 1.67 / 1.63 ≈ 1.02 ≈ 1
- H: 6.66 / 1.63 ≈ 4.08 ≈ 4
- N: 3.38 / 1.63 ≈ 2.07 ≈ 2
- O: 1.63 / 1.63 = 1

### Step 5: Write the Empirical Formula
From the ratios, we can write the empirical formula:
- Empirical formula = C₁H₄N₂O₁ or simply CH₄N₂O

### Step 6: Calculate the Empirical Formula Mass
Now, we calculate the molar mass of the empirical formula:
- C: 12 g/mol
- H: 4 g/mol (4 × 1)
- N: 28 g/mol (2 × 14)
- O: 16 g/mol

Total empirical formula mass = 12 + 4 + 28 + 16 = 60 g/mol

### Step 7: Determine the Molecular Formula
Since the molar mass of the compound is given as 60 g/mol, which is equal to the empirical formula mass, we find:
- n = Molecular formula mass / Empirical formula mass = 60 g/mol / 60 g/mol = 1

Thus, the molecular formula is:
- Molecular formula = n × empirical formula = 1 × CH₄N₂O = CH₄N₂O

### Final Answer
The molecular formula of the compound is **CH₄N₂O**.

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