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 find the value of \( x \) in the compound \( SO_x \), we can follow these steps:

### Step 1: Calculate the number of moles of the gas
We know that at standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Given that the volume of the gas is 5.6 L, we can calculate the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{Volume (L)}}{22.4 \, \text{L/mol}} \]

Substituting the given volume:

\[ \text{Number of moles} = \frac{5.6 \, \text{L}}{22.4 \, \text{L/mol}} = 0.25 \, \text{moles} \]

### Step 2: Relate the number of moles to the mass
We are given that the mass of the gas is 16 g. The relationship between mass, number of moles, and molar mass is given by:

\[ \text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} \]

Let the molar mass of \( SO_x \) be \( M \). We can set up the equation:

\[ 0.25 = \frac{16 \, \text{g}}{M} \]

### Step 3: Solve for the molar mass
Rearranging the equation to find \( M \):

\[ M = \frac{16 \, \text{g}}{0.25} = 64 \, \text{g/mol} \]

### Step 4: Determine the molar mass of \( SO_x \)
The molar mass of \( SO_x \) can be expressed as:

\[ M = \text{Molar mass of S} + x \times \text{Molar mass of O} \]

The molar mass of sulfur (S) is approximately 32 g/mol, and the molar mass of oxygen (O) is approximately 16 g/mol. Thus, we can write:

\[ 64 = 32 + x \times 16 \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):

\[ 64 - 32 = x \times 16 \]
\[ 32 = x \times 16 \]
\[ x = \frac{32}{16} = 2 \]

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

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