In a balanced equation
`H_(2)SO_(4)toxHItoH_(2)S+yI_(2)+zH_(2)O`
The values of x,y,z are

Options

A. x=3,y=5,z=2
B. x=4,y=8,z=5
C. x=8,y=4,z=4
D. x=5,y=3,z=4

Explanation

To solve the problem of balancing the equation \( H_2SO_4 + xHI \rightarrow H_2S + yI_2 + zH_2O \), we will follow a systematic approach to balance the equation step by step.

### Step 1: Write the Unbalanced Equation
We start with the unbalanced equation:
\[ H_2SO_4 + xHI \rightarrow H_2S + yI_2 + zH_2O \]

### Step 2: Balance Atoms Other than Hydrogen and Oxygen
The atoms we need to focus on are sulfur (S) and iodine (I).

- Sulfur: There is 1 sulfur atom on both sides (1 in \( H_2SO_4 \) and 1 in \( H_2S \)), so sulfur is balanced.
- Iodine: There is 1 iodine atom in \( HI \) and \( y \) iodine atoms in \( I_2 \). To balance iodine, we need to ensure that the number of iodine atoms on both sides is equal.

Since \( I_2 \) contains 2 iodine atoms, we can set \( y = 4 \) (to balance with 8 iodine atoms from \( HI \)). Therefore, we multiply \( HI \) by 8:
\[ H_2SO_4 + 8HI \rightarrow H_2S + 4I_2 + zH_2O \]

### Step 3: Balance the Oxygen Atoms
Next, we balance the oxygen atoms.

- On the left side, \( H_2SO_4 \) has 4 oxygen atoms.
- On the right side, each \( H_2O \) has 1 oxygen atom.

To balance the oxygen atoms, we set \( z = 4 \) (since \( 4H_2O \) will give us 4 oxygen atoms):
\[ H_2SO_4 + 8HI \rightarrow H_2S + 4I_2 + 4H_2O \]

### Step 4: Balance the Hydrogen Atoms
Now, we balance the hydrogen atoms.

- On the left side, \( H_2SO_4 \) has 2 hydrogen atoms and \( 8HI \) has \( 8 \times 1 = 8 \) hydrogen atoms, giving a total of \( 2 + 8 = 10 \) hydrogen atoms.
- On the right side, \( H_2S \) has 2 hydrogen atoms and \( 4H_2O \) has \( 4 \times 2 = 8 \) hydrogen atoms, giving a total of \( 2 + 8 = 10 \) hydrogen atoms.

Since both sides have 10 hydrogen atoms, the equation is now balanced.

### Final Balanced Equation
The complete balanced equation is:
\[ H_2SO_4 + 8HI \rightarrow H_2S + 4I_2 + 4H_2O \]

### Values of x, y, z
From the balanced equation, we can now identify the values of \( x, y, z \):
- \( x = 8 \)
- \( y = 4 \)
- \( z = 4 \)

### Final Answer
Thus, the values of \( x, y, z \) are:
- \( x = 8 \)
- \( y = 4 \)
- \( z = 4 \)

---