A binary compound contains 50% A (at. mass `= 16`) and 50% B (at. mass 32). The empirical formula of the compound is _____________.

Answer

To find the empirical formula of the binary compound containing 50% A (atomic mass = 16) and 50% B (atomic mass = 32), we can follow these steps:

### Step 1: Determine the mass of each element
Since the compound is 50% A and 50% B, we can assume we have 100 grams of the compound for simplicity. Therefore:
- Mass of A = 50 grams
- Mass of B = 50 grams

### Step 2: Calculate the number of moles of each element
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

For element A:
\[ \text{Moles of A} = \frac{50 \text{ g}}{16 \text{ g/mol}} = 3.125 \text{ moles} \]

For element B:
\[ \text{Moles of B} = \frac{50 \text{ g}}{32 \text{ g/mol}} = 1.5625 \text{ moles} \]

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

Smallest number of moles is 1.5625 (for B).

For A:
\[ \text{Ratio of A} = \frac{3.125}{1.5625} \approx 2 \]

For B:
\[ \text{Ratio of B} = \frac{1.5625}{1.5625} = 1 \]

### Step 4: Write the empirical formula
The ratio of A to B is approximately 2:1. Therefore, the empirical formula of the compound can be written as:
\[ \text{Empirical formula} = A_2B_1 \text{ or simply } A_2B \]

### Final Answer:
The empirical formula of the compound is **A₂B**.

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