3.2g of a gas occupies 550 cc of volume at `22^@C` and 770 mm of Hg pressure. Find the molecular mass of the gas.

Answer

To find the molecular mass of the gas, we can use the Ideal Gas Law, which is expressed as:

\[ PV = nRT \]

Where:
- \( P \) = pressure in atm
- \( V \) = volume in liters
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin

### Step 1: Convert the given values to appropriate units

1. **Convert volume from cc to liters**:
\[ V = 550 \, \text{cc} = 550 \times 10^{-3} \, \text{L} = 0.55 \, \text{L} \]

2. **Convert temperature from Celsius to Kelvin**:
\[ T = 22^\circ C + 273 = 295 \, \text{K} \]

3. **Convert pressure from mmHg to atm**:
\[ P = \frac{770 \, \text{mmHg}}{760 \, \text{mmHg/atm}} \approx 1.014 \, \text{atm} \]

### Step 2: Calculate the number of moles (n)

Using the formula for number of moles:
\[ n = \frac{mass}{molecular \, weight} \]
We can rearrange the Ideal Gas Law to express \( n \):
\[ n = \frac{PV}{RT} \]

Substituting the values:
\[ n = \frac{(1.014 \, \text{atm}) \times (0.55 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (295 \, \text{K})} \]

Calculating the right-hand side:
\[ n = \frac{0.5567}{24.30795} \approx 0.0229 \, \text{moles} \]

### Step 3: Calculate the molecular weight (M)

Now we can find the molecular weight using the mass of the gas and the number of moles:
\[ M = \frac{mass}{n} \]

Substituting the values:
\[ M = \frac{3.2 \, \text{g}}{0.0229 \, \text{moles}} \approx 139.25 \, \text{g/mol} \]

### Final Answer
The molecular mass of the gas is approximately **139 g/mol**.

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