2.5gms. of a gas is present in 750ml. flask at `32^@C` and 770mm, of Hg pressure. Calculate the molecular mass of the gas.  

Answer

To calculate the molecular mass of the gas, we will use the Ideal Gas Law equation, which is given by:

\[ PV = nRT \]

Where:
- \( P \) = pressure of the gas (in atm)
- \( V \) = volume of the gas (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 the appropriate units

1. **Mass of the gas**: Given as 2.5 g (no conversion needed).
2. **Volume of the gas**: Given as 750 mL. Convert to liters:
\[ V = 750 \, \text{mL} = \frac{750}{1000} = 0.750 \, \text{L} \]
3. **Temperature**: Given as 32°C. Convert to Kelvin:
\[ T = 32 + 273 = 305 \, \text{K} \]
4. **Pressure**: Given as 770 mmHg. Convert to atm:
\[ P = \frac{770 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 1.013 \, \text{atm} \]

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

From the Ideal Gas Law, we can express the number of moles \( n \) as:
\[ n = \frac{PV}{RT} \]

Substituting the values we have:
\[ n = \frac{(1.013 \, \text{atm}) \times (0.750 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (305 \, \text{K})} \]

Calculating the denominator:
\[ 0.0821 \times 305 = 25.1065 \]

Now substituting back:
\[ n = \frac{(1.013) \times (0.750)}{25.1065} = \frac{0.75975}{25.1065} \approx 0.0302 \, \text{mol} \]

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

Molecular mass \( M \) can be calculated using the formula:
\[ M = \frac{\text{mass}}{n} \]

Substituting the values:
\[ M = \frac{2.5 \, \text{g}}{0.0302 \, \text{mol}} \approx 82.78 \, \text{g/mol} \]

### Final Answer

The molecular mass of the gas is approximately **82.78 g/mol**.

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