What will be the value of x, y and z in the following equation?
`H_(2)C_(2)O_(4)+xH_(2)O_(2)rarr yCO_(2)+zH_(2)O`

Options

A. 2, 1, 2
B. 1, 2, 2
C. 2, 2, 1
D. 1, 2, 1

Answer

To solve the equation \( H_2C_2O_4 + xH_2O_2 \rightarrow yCO_2 + zH_2O \), we need to find the values of \( x \), \( y \), and \( z \).

### Step 1: Identify the reactants and products
The reactants are oxalic acid (\( H_2C_2O_4 \)) and hydrogen peroxide (\( H_2O_2 \)). The products are carbon dioxide (\( CO_2 \)) and water (\( H_2O \)).

### Step 2: Write the unbalanced equation
The unbalanced equation is:
\[ H_2C_2O_4 + xH_2O_2 \rightarrow yCO_2 + zH_2O \]

### Step 3: Balance the carbon atoms
In \( H_2C_2O_4 \), there are 2 carbon atoms. Therefore, to balance the carbon atoms, we need 2 \( CO_2 \) on the product side:
\[ H_2C_2O_4 + xH_2O_2 \rightarrow 2CO_2 + zH_2O \]

### Step 4: Balance the hydrogen atoms
Now, let's count the hydrogen atoms. On the reactant side, there are 2 hydrogen atoms from \( H_2C_2O_4 \) and \( x \) from \( H_2O_2 \). On the product side, there are \( 2z \) hydrogen atoms from \( zH_2O \). Therefore, we have:
\[ 2 + 2x = 2z \]

### Step 5: Balance the oxygen atoms
Now, let's balance the oxygen atoms. In \( H_2C_2O_4 \), there are 4 oxygen atoms. In \( H_2O_2 \), there are \( 2x \) oxygen atoms. On the product side, there are \( 2 \times 2 = 4 \) oxygen atoms from \( 2CO_2 \) and \( z \) from \( zH_2O \). Therefore, we have:
\[ 4 + 2x = 4 + z \]

### Step 6: Solve the equations
From the hydrogen balance equation:
\[ 2 + 2x = 2z \]
We can rearrange it to:
\[ z = 1 + x \] (Equation 1)

From the oxygen balance equation:
\[ 4 + 2x = 4 + z \]
We can rearrange it to:
\[ z = 2x \] (Equation 2)

### Step 7: Substitute Equation 1 into Equation 2
Now, substitute \( z \) from Equation 1 into Equation 2:
\[ 1 + x = 2x \]
Solving for \( x \):
\[ 1 = 2x - x \]
\[ 1 = x \]
Thus, \( x = 1 \).

### Step 8: Find \( z \) using \( x \)
Using \( x = 1 \) in Equation 1:
\[ z = 1 + 1 = 2 \]

### Step 9: Find \( y \)
Now, we have \( y \) from the balanced equation. Since we have 2 \( CO_2 \):
\[ y = 2 \]

### Final Values
Thus, the values are:
- \( x = 1 \)
- \( y = 2 \)
- \( z = 2 \)

### Summary
The final balanced equation is:
\[ H_2C_2O_4 + H_2O_2 \rightarrow 2CO_2 + 2H_2O \]