A compound contains atoms X, Y and Z. The oxidation number of X is `+3`, Y is `+5` and Z is `-2`. The possible formula of the compound is

Options

A. XYZ
B. `Y_(2)(XY_(3))_(2)`
C. `X_(3)(XY_(4))_(3)`
D. `X_(3)(Z_(4)Y)_(3)`

Answer

To determine the possible formula of the compound containing atoms X, Y, and Z with given oxidation states, we need to ensure that the total oxidation state of the compound sums to zero. Let's break down the steps:

### Step 1: Identify the oxidation states
- The oxidation state of X = +3
- The oxidation state of Y = +5
- The oxidation state of Z = -2

### Step 2: Set up the equation
Let the number of atoms of X, Y, and Z in the compound be represented as \( a \), \( b \), and \( c \) respectively. The total charge contributed by each atom can be expressed as:
- Contribution from X = \( a \times (+3) \)
- Contribution from Y = \( b \times (+5) \)
- Contribution from Z = \( c \times (-2) \)

The equation for the net charge being zero can be set up as:
\[ 3a + 5b - 2c = 0 \]

### Step 3: Find integer values for a, b, and c
We need to find integer values for \( a \), \( b \), and \( c \) that satisfy this equation.

1. **Assume values for \( a \) and \( b \)**:
- Let's start with \( a = 1 \) and \( b = 1 \):
\[ 3(1) + 5(1) - 2c = 0 \implies 3 + 5 - 2c = 0 \implies 8 - 2c = 0 \implies 2c = 8 \implies c = 4 \]
- This gives us \( a = 1 \), \( b = 1 \), and \( c = 4 \).

### Step 4: Write the formula
Using the values found:
- \( a = 1 \) (for X)
- \( b = 1 \) (for Y)
- \( c = 4 \) (for Z)

The formula for the compound can be written as:
\[ X^1 Y^1 Z^4 \quad \text{or simply} \quad XY Z_4 \]

### Step 5: Verify the formula
Now, let's verify that the total oxidation states sum to zero:
- Contribution from X = \( 1 \times (+3) = +3 \)
- Contribution from Y = \( 1 \times (+5) = +5 \)
- Contribution from Z = \( 4 \times (-2) = -8 \)

Total charge:
\[ +3 + 5 - 8 = 0 \]
This confirms that the formula \( XY Z_4 \) is correct.

### Final Answer
The possible formula of the compound is \( XY Z_4 \).

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