16 g of an ideal gas `SO_(x)` occupies 5.6 L at STP. What is its molecular mass ? What is the value of `X` ?

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the conditions at STP
At Standard Temperature and Pressure (STP), 1 mole of an ideal gas occupies 22.7 liters.

### Step 2: Calculate the number of moles of the gas
Given that the gas occupies 5.6 liters, we can calculate the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{Given volume}}{\text{Volume of 1 mole at STP}} = \frac{5.6 \, \text{L}}{22.7 \, \text{L/mol}} \]

Calculating this gives:

\[ \text{Number of moles} = \frac{5.6}{22.7} \approx 0.246 \, \text{moles} \]

### Step 3: Relate moles to mass and molecular mass
The number of moles can also be expressed in terms of mass and molecular mass:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molecular mass}} = \frac{16 \, \text{g}}{M} \]

Where \( M \) is the molecular mass we need to find. Setting the two expressions for the number of moles equal gives:

\[ \frac{5.6}{22.7} = \frac{16}{M} \]

### Step 4: Solve for the molecular mass
Cross-multiplying to solve for \( M \):

\[ 5.6 \cdot M = 16 \cdot 22.7 \]

Calculating the right side:

\[ 5.6M = 363.2 \]

Now, divide both sides by 5.6:

\[ M = \frac{363.2}{5.6} \approx 64.86 \, \text{g/mol} \]

For practical purposes, we can round this to:

\[ M \approx 64 \, \text{g/mol} \]

### Step 5: Determine the value of \( X \)
The molecular mass of the gas \( SO_x \) can be expressed as:

\[ \text{Molecular mass of } SO_x = \text{Atomic mass of S} + x \cdot \text{Atomic mass of O} \]

Using the known atomic masses:

- Atomic mass of sulfur (S) = 32 g/mol
- Atomic mass of oxygen (O) = 16 g/mol

Thus, we have:

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

### Step 6: Solve for \( x \)
Rearranging the equation:

\[ 64 - 32 = x \cdot 16 \]

\[ 32 = x \cdot 16 \]

Now, divide both sides by 16:

\[ x = \frac{32}{16} = 2 \]

### Conclusion
The molecular mass of the gas \( SO_x \) is approximately 64 g/mol, and the value of \( x \) is 2. Therefore, the gas is \( SO_2 \) (sulfur dioxide).

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