16 g of `SO_(x)` gas occupies 5.6 L at 1 atm and 273 K.What will be the value of x ?

Answer

To determine the value of \( x \) in the compound \( SO_x \), we will follow these steps:

### Step 1: Identify the given data
- Mass of \( SO_x \) gas = 16 g
- Volume = 5.6 L
- Pressure = 1 atm
- Temperature = 273 K

### Step 2: Use the ideal gas law to find the number of moles
At normal temperature and pressure (NTP), 1 mole of gas occupies 22.4 L. To find the number of moles of \( SO_x \):
\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar volume at NTP}} = \frac{5.6 \, \text{L}}{22.4 \, \text{L/mol}} = 0.25 \, \text{moles} \]

### Step 3: Relate mass and moles to find the molar mass
The relationship between mass, moles, and molar mass is given by:
\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar mass}} \]
Rearranging this gives:
\[ \text{Molar mass} = \frac{\text{Mass}}{\text{Moles}} = \frac{16 \, \text{g}}{0.25 \, \text{moles}} = 64 \, \text{g/mol} \]

### Step 4: Set up the equation for the molar mass of \( SO_x \)
The molar mass of \( SO_x \) can be expressed as:
\[ \text{Molar mass} = \text{Atomic mass of S} + x \times \text{Atomic mass of O} \]
Substituting the known values:
\[ 64 \, \text{g/mol} = 32 \, \text{g/mol} + x \times 16 \, \text{g/mol} \]

### Step 5: Solve for \( x \)
Rearranging the equation:
\[ 64 = 32 + 16x \]
Subtract 32 from both sides:
\[ 32 = 16x \]
Now, divide both sides by 16:
\[ x = \frac{32}{16} = 2 \]

### Conclusion
The value of \( x \) is 2, which means the gas is \( SO_2 \).

---