240 mL of a dry gas measured at 27°C and 750 mm pressure weighed 0.64 g. What is the molecular mass of the gas ?

Answer

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

\[ PV = nRT \]

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 of the gas (in Kelvin)

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

1. **Volume**: Convert 240 mL to liters:
\[ V = 240 \, \text{mL} = 0.240 \, \text{L} \]

2. **Temperature**: Convert 27°C to Kelvin:
\[ T = 27 + 273 = 300 \, \text{K} \]

3. **Pressure**: Convert 750 mmHg to atm:
\[ P = \frac{750 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 0.9868 \, \text{atm} \]

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

Using the Ideal Gas Law, rearranging for \( n \):
\[ n = \frac{PV}{RT} \]

Substituting the values:
\[ n = \frac{(0.9868 \, \text{atm}) \times (0.240 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (300 \, \text{K})} \]

Calculating:
\[ n = \frac{0.236832}{24.63} \approx 0.0096 \, \text{mol} \]

### Step 3: Relate moles to mass and molecular mass

We know that:
\[ n = \frac{m}{M} \]
Where:
- \( m \) = mass of the gas (0.64 g)
- \( M \) = molecular mass of the gas

Rearranging gives:
\[ M = \frac{m}{n} \]

Substituting the values:
\[ M = \frac{0.64 \, \text{g}}{0.0096 \, \text{mol}} \approx 66.67 \, \text{g/mol} \]

### Final Answer

The molecular mass of the gas is approximately **66.67 g/mol**.

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