An ionic compound when dissolved in water has produced m `A^(n-), n B^(m-)` ions. What is the formula of the compound ?

Options

A. `A_(m)B_(n)`
B. `A_(n)B_(m)`
C. `A_(m)B_(m)`
D. `A_(n)B_(n)`

Explanation

To determine the formula of the ionic compound that produces \( A^{n-} \) and \( B^{m-} \) ions when dissolved in water, we can follow these steps:

### Step 1: Identify the ions produced
When the ionic compound dissolves in water, it produces two types of ions:
- An anion \( A^{n-} \)
- A cation \( B^{m+} \)

### Step 2: Understand the charges
The charges of the ions indicate how they will combine to form a neutral compound. The anion \( A^{n-} \) has a charge of \( n- \), and the cation \( B^{m+} \) has a charge of \( m+ \).

### Step 3: Balance the charges
To form a neutral compound, the total positive charge must equal the total negative charge. Therefore, we can set up the following relationship based on the number of ions:
- The total negative charge from \( A^{n-} \) ions is \( n \times \text{number of } A^{n-} \)
- The total positive charge from \( B^{m+} \) ions is \( m \times \text{number of } B^{m+} \)

### Step 4: Determine the ratio of ions
To achieve charge neutrality, we can express the ratio of the number of \( A^{n-} \) ions to \( B^{m+} \) ions. This can be represented as:
\[ \text{Number of } A^{n-} = m \quad \text{and} \quad \text{Number of } B^{m+} = n \]
This means that for every \( m \) anions \( A^{n-} \), there are \( n \) cations \( B^{m+} \).

### Step 5: Write the formula
The formula of the ionic compound can be written by combining the cations and anions in the ratio determined above:
\[ \text{Formula} = A_m B_n \]
This implies that the formula of the compound is \( A^m B^n \).

### Final Answer
Thus, the formula of the ionic compound is \( A^m B^n \).

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