Consider the following reaction
`x MnO_(4)^(-) + C_(2)O_(4)^(2-) + zH^(+) rarr x Mn^(2+) + 2y CO_(2) + (z)/(2)H_(2)O`
The value of x, y and z in the reaction are respectively

Options

A. 2, 5 and 8
B. 2, 5 and 16
C. 5, 2 and 8
D. 5, 2 and 16

Answer

To solve the given reaction and find the values of \( x \), \( y \), and \( z \), we will follow these steps:

### Step 1: Write the unbalanced reaction
The unbalanced reaction is given as:
\[ x \text{MnO}_4^{-} + \text{C}_2\text{O}_4^{2-} + z \text{H}^{+} \rightarrow x \text{Mn}^{2+} + 2y \text{CO}_2 + \frac{z}{2} \text{H}_2\text{O} \]

### Step 2: Identify oxidation states
- For \( \text{MnO}_4^{-} \):
- Oxidation state of Mn = +7
- For \( \text{C}_2\text{O}_4^{2-} \):
- Oxidation state of C = +3
- For \( \text{CO}_2 \):
- Oxidation state of C = +4
- For \( \text{Mn}^{2+} \):
- Oxidation state of Mn = +2

### Step 3: Determine changes in oxidation states
- Mn changes from +7 to +2 (reduction, gaining 5 electrons).
- C changes from +3 to +4 (oxidation, losing 1 electron).

### Step 4: Balance the half-reactions
- For the reduction half-reaction (Mn):
\[ 2 \text{MnO}_4^{-} + 10 \text{e}^{-} \rightarrow 2 \text{Mn}^{2+} \]
- For the oxidation half-reaction (C):
\[ 5 \text{C}_2\text{O}_4^{2-} \rightarrow 10 \text{CO}_2 + 10 \text{e}^{-} \]

### Step 5: Combine the half-reactions
Adding both half-reactions gives:
\[ 2 \text{MnO}_4^{-} + 5 \text{C}_2\text{O}_4^{2-} \rightarrow 2 \text{Mn}^{2+} + 10 \text{CO}_2 \]

### Step 6: Balance oxygen and hydrogen
- Count the oxygen atoms:
- Left side: \( 2 \times 4 + 5 \times 4 = 28 \) O
- Right side: \( 10 \times 2 = 20 \) O + \( z/2 \) H2O
- To balance, add \( 7 \text{H}_2\text{O} \) on the right side:
\[ 2 \text{MnO}_4^{-} + 5 \text{C}_2\text{O}_4^{2-} + 15 \text{H}^{+} \rightarrow 2 \text{Mn}^{2+} + 10 \text{CO}_2 + 7 \text{H}_2\text{O} \]

### Step 7: Finalize the balanced equation
Now the balanced equation is:
\[ 2 \text{MnO}_4^{-} + 5 \text{C}_2\text{O}_4^{2-} + 16 \text{H}^{+} \rightarrow 2 \text{Mn}^{2+} + 10 \text{CO}_2 + 8 \text{H}_2\text{O} \]

### Step 8: Identify the values of \( x \), \( y \), and \( z \)
From the balanced equation:
- \( x = 2 \) (from \( 2 \text{MnO}_4^{-} \))
- \( 2y = 10 \) → \( y = 5 \) (from \( 10 \text{CO}_2 \))
- \( z = 16 \) (from \( 16 \text{H}^{+} \))

### Final Answer
The values of \( x \), \( y \), and \( z \) are:
\[ x = 2, \quad y = 5, \quad z = 16 \]