The empirical formula of a substance whose composition includes H, C, O and N in the mass ratio 1 : 3 : 4 : 7 is

Options

A. `HC_(3)O_(4)N_(7)`
B. `H_(4)CON_(2)`
C. `HC_(4)O_(4)N_(2)`
D. none of these

Answer

To determine the empirical formula of a substance based on the given mass ratios of its constituent elements (H, C, O, and N), we will follow these steps:

### Step 1: Identify the mass ratios
The mass ratios given for the elements are:
- Hydrogen (H): 1
- Carbon (C): 3
- Oxygen (O): 4
- Nitrogen (N): 7

### Step 2: Convert mass ratios to moles
To find the empirical formula, we need to convert these mass ratios into moles by dividing each ratio by the molar mass of the respective element.

- Molar mass of H = 1 g/mol
- Molar mass of C = 12 g/mol
- Molar mass of O = 16 g/mol
- Molar mass of N = 14 g/mol

Now, we calculate the moles for each element:

- Moles of H = 1 g / 1 g/mol = 1 mol
- Moles of C = 3 g / 12 g/mol = 0.25 mol
- Moles of O = 4 g / 16 g/mol = 0.25 mol
- Moles of N = 7 g / 14 g/mol = 0.5 mol

### Step 3: Find the simplest whole number ratio
Next, we need to find the simplest whole number ratio of the moles calculated above. We do this by dividing each mole value by the smallest number of moles calculated.

The smallest number of moles is 0.25 (from C and O).

- Ratio of H = 1 mol / 0.25 mol = 4
- Ratio of C = 0.25 mol / 0.25 mol = 1
- Ratio of O = 0.25 mol / 0.25 mol = 1
- Ratio of N = 0.5 mol / 0.25 mol = 2

### Step 4: Write the empirical formula
Now that we have the simplest whole number ratios, we can write the empirical formula. The ratios we found are:

- H: 4
- C: 1
- O: 1
- N: 2

Thus, the empirical formula is:

**C1H4O1N2 or simply C H4 O N2**

### Final Answer:
The empirical formula of the substance is **C H4 O N2**.

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