To determine the possible formula of the compound containing atoms X, Y, and Z with oxidation states of +2, +2, and -2 respectively, we can follow these steps:
### Step 1: Understand the oxidation states
The oxidation states of the atoms are given as follows:
- X: +2
- Y: +2
- Z: -2
### Step 2: Write the general formula
Let’s denote the number of atoms of X, Y, and Z in the compound as \(a\), \(b\), and \(c\) respectively. The general formula for the compound can be represented as \(X_a Y_b Z_c\).
### Step 3: Set up the equation for the sum of oxidation states
According to the rules of oxidation states, the sum of the oxidation states in a neutral compound must equal zero. Therefore, we can write the equation:
\[
a(+2) + b(+2) + c(-2) = 0
\]
This simplifies to:
\[
2a + 2b - 2c = 0
\]
or
\[
a + b = c
\]
### Step 4: Analyze the possible formulas
Now we will analyze the possible formulas based on the relationship \(a + b = c\).
1. **Option 1: \(XYZ_2\)**
- Here, \(a = 1\), \(b = 1\), \(c = 2\).
- Check: \(1 + 1 = 2\) (satisfies the equation).
- This formula is possible.
2. **Option 2: \(Y_2X_3Z\)**
- Here, \(a = 3\), \(b = 2\), \(c = 1\).
- Check: \(3 + 2 = 1\) (does not satisfy the equation).
- This formula is not possible.
3. **Option 3: \(X_3Y_4Z_2\)**
- Here, \(a = 3\), \(b = 4\), \(c = 2\).
- Check: \(3 + 4 = 2\) (does not satisfy the equation).
- This formula is not possible.
4. **Option 4: \(X_2Y_4Z_3\)**
- Here, \(a = 2\), \(b = 4\), \(c = 3\).
- Check: \(2 + 4 = 3\) (does not satisfy the equation).
- This formula is not possible.
### Conclusion
The only formula that satisfies the condition \(a + b = c\) is **Option 1: \(XYZ_2\)**.
### Final Answer
The possible formula of the compound is \(XYZ_2\).
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