Two elemets `X(` atomic weight `=75)` and `Y(` atomic weight `=16)` combine to give a compound having `75.8%` X.` The formula of the compound is

Options

A. XY
B. `X_(2)Y`
C. `X_(2)Y_(2)`
D. `X_(2)Y_(3)`

Answer

To find the formula of the compound formed by elements X and Y, we can follow these steps:

### Step 1: Identify the given data
- Atomic weight of element X = 75
- Atomic weight of element Y = 16
- Percentage of element X in the compound = 75.8%

### Step 2: Calculate the percentage of element Y
To find the percentage of element Y, we subtract the percentage of element X from 100%:
\[ \text{Percentage of Y} = 100\% - 75.8\% = 24.2\% \]

### Step 3: Set up the ratio of the elements
We will now find the ratio of the number of moles of each element in the compound using their percentages and atomic weights.

\[ \text{Moles of X} = \frac{\text{Percentage of X}}{\text{Atomic weight of X}} = \frac{75.8}{75} \]
\[ \text{Moles of Y} = \frac{\text{Percentage of Y}}{\text{Atomic weight of Y}} = \frac{24.2}{16} \]

### Step 4: Calculate the moles
Calculating the moles for each element:
\[ \text{Moles of X} = \frac{75.8}{75} \approx 1.01 \]
\[ \text{Moles of Y} = \frac{24.2}{16} \approx 1.51 \]

### Step 5: Find the simplest whole number ratio
To find the simplest whole number ratio, we divide both values by the smallest value obtained:
\[ \text{Ratio of X} = \frac{1.01}{1.01} \approx 1 \]
\[ \text{Ratio of Y} = \frac{1.51}{1.01} \approx 1.49 \approx 1.5 \]

### Step 6: Convert to whole numbers
To convert the ratio into whole numbers, we can multiply both values by 2 to eliminate the fraction:
\[ \text{X} = 1 \times 2 = 2 \]
\[ \text{Y} = 1.5 \times 2 = 3 \]

### Step 7: Write the empirical formula
From the whole number ratio, we can write the empirical formula of the compound as:
\[ \text{Formula} = X_2Y_3 \]

### Final Answer
The formula of the compound is \( X_2Y_3 \).

---