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 balance the equation by determining the values of \( x \), \( y \), and \( z \).

### Step 1: Identify the number of carbon atoms
In the reactant \( H_2C_2O_4 \) (oxalic acid), there are 2 carbon atoms. In the product \( yCO_2 \), each \( CO_2 \) contains 1 carbon atom. Therefore, to balance the carbon atoms, we set:
\[ y = 2 \]

### Step 2: Write down the equation with the known value of \( y \)
Now we can rewrite the equation with \( y = 2 \):
\[ H_2C_2O_4 + xH_2O_2 \rightarrow 2CO_2 + zH_2O \]

### Step 3: Count the oxygen atoms
Next, we need to balance the oxygen atoms. On the left side, \( H_2C_2O_4 \) has 4 oxygen atoms, and \( xH_2O_2 \) contributes \( 2x \) oxygen atoms. Therefore, the total number of oxygen atoms on the left side is:
\[ 4 + 2x \]
On the right side, \( 2CO_2 \) contributes \( 2 \times 2 = 4 \) oxygen atoms, and \( zH_2O \) contributes \( z \) oxygen atoms. Thus, the total number of oxygen atoms on the right side is:
\[ 4 + z \]

### Step 4: Set up the equation for oxygen balance
Now we can set up the equation for balancing oxygen:
\[ 4 + 2x = 4 + z \]
By simplifying, we find:
\[ 2x = z \]

### Step 5: Balance the hydrogen atoms
Next, we need to balance the hydrogen atoms. On the left side, \( H_2C_2O_4 \) has 2 hydrogen atoms, and \( xH_2O_2 \) contributes \( 2x \) hydrogen atoms. Therefore, the total number of hydrogen atoms on the left side is:
\[ 2 + 2x \]
On the right side, \( zH_2O \) contributes \( z \) hydrogen atoms. Thus, we have:
\[ 2 + 2x = z \]

### Step 6: Substitute \( z \) from the previous equation
From the previous step, we know \( z = 2x \). We can substitute this into the hydrogen balance equation:
\[ 2 + 2x = 2x \]
This simplifies to:
\[ 2 = 0 \]
This indicates that the equation is consistent for any value of \( x \) greater than or equal to 1.

### Step 7: Determine the minimum integer value for \( x \)
To find the minimum integer value for \( x \), we can set \( x = 1 \):
\[ z = 2x = 2(1) = 2 \]

### Final Values
Thus, we have:
\[ x = 1, \quad y = 2, \quad z = 2 \]

### Conclusion
The values of \( x \), \( y \), and \( z \) are:
\[ x = 1, \quad y = 2, \quad z = 2 \]