`w SnO_(2) + x H_(2) to y Sn + z H_(2) O`
For which of the following values of w, x, y and z will the equation above be balanced?

Options

A. w=1, x=1, y=1, z=1
B. w=1, x=2, y=2, z=1
C. w=1, x=2, y=1, z=2
D. w=1, x=1, y=1, z=2

Answer

To balance the chemical equation \( w \text{SnO}_2 + x \text{H}_2 \rightarrow y \text{Sn} + z \text{H}_2\text{O} \), we need to ensure that the number of atoms of each element is equal on both sides of the equation. Let's go through the steps to find the correct values of \( w, x, y, \) and \( z \).

### Step 1: Identify the elements and their counts
- **Reactants**:
- \( w \) SnO\(_2\) contributes:
- Sn: \( w \)
- O: \( 2w \)
- \( x \) H\(_2\) contributes:
- H: \( 2x \)

- **Products**:
- \( y \) Sn contributes:
- Sn: \( y \)
- \( z \) H\(_2\)O contributes:
- H: \( z \)
- O: \( z \)

### Step 2: Set up equations based on the number of atoms
From the above counts, we can set up the following equations:

1. For Sn:
\[ w = y \]

2. For O:
\[ 2w = z \]

3. For H:
\[ 2x = 2z \quad \text{(which simplifies to)} \quad x = z \]

### Step 3: Solve the equations
From the equations:
- From \( w = y \), we can say \( y = w \).
- From \( 2w = z \), we can express \( z \) in terms of \( w \):
\[ z = 2w \]
- From \( x = z \), we can substitute \( z \):
\[ x = 2w \]

### Step 4: Assign values
Now we can assign values to \( w, x, y, \) and \( z \):
- Let’s assume \( w = 1 \) (the smallest integer value).
- Then:
- \( y = w = 1 \)
- \( z = 2w = 2 \)
- \( x = 2w = 2 \)

Thus, we have:
- \( w = 1 \)
- \( x = 2 \)
- \( y = 1 \)
- \( z = 2 \)

### Final Balanced Equation
The balanced equation is:
\[ 1 \text{SnO}_2 + 2 \text{H}_2 \rightarrow 1 \text{Sn} + 2 \text{H}_2\text{O} \]

### Conclusion
The values of \( w, x, y, \) and \( z \) that balance the equation are:
- \( w = 1 \)
- \( x = 2 \)
- \( y = 1 \)
- \( z = 2 \)