Two elements A (At. wt. 75) and B (At. wt. 16) combine to yield a compound. The % by weight of A in the compound was found to be 75.08. The formula of the compound is:

Options

A. `A_(2)B`
B. `A_(2)B_(3)`
C. AB
D. `AB_(2)`

Answer

To determine the formula of the compound formed by elements A and B, we can follow these steps:

### Step 1: Define the Variables
Let the molecular formula of the compound be \( A_xB_y \), where \( x \) is the number of atoms of element A and \( y \) is the number of atoms of element B.

### Step 2: Write the Given Information
- Atomic weight of A = 75
- Atomic weight of B = 16
- Percentage by weight of A in the compound = 75.08%

### Step 3: Set Up the Equation for Percentage by Weight
The percentage by weight of A in the compound can be expressed as:
\[ \text{Percentage of A} = \frac{\text{Mass of A in the compound}}{\text{Molecular weight of the compound}} \times 100 \]
This can be rewritten as:
\[ 75.08 = \frac{75x}{75x + 16y} \times 100 \]

### Step 4: Simplify the Equation
Rearranging the equation gives:
\[ 75x = 75.08 \times (75x + 16y) / 100 \]
Multiplying both sides by 100 to eliminate the fraction:
\[ 7500x = 75.08 \times (75x + 16y) \]
Expanding the right side:
\[ 7500x = 5631x + 1201.28y \]

### Step 5: Rearranging the Equation
Now, rearranging the equation to isolate terms involving \( x \) and \( y \):
\[ 7500x - 5631x = 1201.28y \]
\[ 1869x = 1201.28y \]

### Step 6: Solve for the Ratio of \( y \) to \( x \)
Now, we can express \( y \) in terms of \( x \):
\[ y = \frac{1869}{1201.28}x \]
Calculating the ratio:
\[ y \approx 1.55x \]

### Step 7: Find Integer Values for \( x \) and \( y \)
To find integer values, we can assume \( x = 2 \):
\[ y = 1.55 \times 2 \approx 3.1 \quad \text{(rounding to nearest integer gives } y = 3\text{)} \]

### Step 8: Write the Molecular Formula
Thus, the empirical formula of the compound is:
\[ A_2B_3 \]

### Final Answer
The formula of the compound is \( A_2B_3 \).

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