What will be the empirical formula of a compound if the percentage of elements present is A= 39.56 %, B = 7.74%, C = 52.70% ? (Atomic mass of A= 12, B= 1, C= 16)

Options

A. ABC
B. `A_3B_7C_3`
C. `A_6 B_7 C_3`
D. `A_3 B_3 C_6`

Explanation

To find the empirical formula of a compound based on the given percentages of elements A, B, and C, we follow these steps:

### Step 1: Write down the percentages and atomic masses
- Element A: 39.56%, Atomic mass = 12
- Element B: 7.74%, Atomic mass = 1
- Element C: 52.70%, Atomic mass = 16

### Step 2: Convert percentages to grams
Assuming we have 100 grams of the compound, the mass of each element will be equal to its percentage:
- Mass of A = 39.56 g
- Mass of B = 7.74 g
- Mass of C = 52.70 g

### Step 3: Calculate the number of moles of each element
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{atomic mass (g/mol)}} \]

- Moles of A = \(\frac{39.56 \, \text{g}}{12 \, \text{g/mol}} = 3.2967 \, \text{mol}\)
- Moles of B = \(\frac{7.74 \, \text{g}}{1 \, \text{g/mol}} = 7.74 \, \text{mol}\)
- Moles of C = \(\frac{52.70 \, \text{g}}{16 \, \text{g/mol}} = 3.29375 \, \text{mol}\)

### Step 4: Find the simplest mole ratio
To find the simplest ratio, we divide the number of moles of each element by the smallest number of moles calculated.

The smallest number of moles is approximately 3.29375 (for A and C).

- Ratio of A = \(\frac{3.2967}{3.29375} \approx 1\)
- Ratio of B = \(\frac{7.74}{3.29375} \approx 2.35\)
- Ratio of C = \(\frac{3.29375}{3.29375} = 1\)

### Step 5: Convert to whole numbers
Since we cannot have fractional subscripts in a formula, we multiply all ratios by a common factor to convert them to whole numbers. The closest whole number can be found by multiplying by 3 (to eliminate the decimal in B):

- A: \(1 \times 3 = 3\)
- B: \(2.35 \times 3 \approx 7\)
- C: \(1 \times 3 = 3\)

### Step 6: Write the empirical formula
The empirical formula is represented by the whole number ratios of the elements:
\[ \text{Empirical formula} = A_3B_7C_3 \]

Thus, the empirical formula of the compound is **A3B7C3**.

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