Calculate the volume occupied by `5.0 g` of acetylene gas at `50^(@)C` and `740 mm` pressure.

Explanation

To calculate the volume occupied by 5.0 g of acetylene gas (C2H2) at 50°C and 740 mmHg, we will use the Ideal Gas Law, which is given by the equation:

\[ PV = nRT \]

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

### Step-by-Step Solution:

**Step 1: Calculate the number of moles of acetylene gas.**

To find the number of moles, we use the formula:

\[ n = \frac{\text{mass}}{\text{molar mass}} \]

The molar mass of acetylene (C2H2) can be calculated as follows:
- Carbon (C) has a molar mass of approximately 12 g/mol, and there are 2 carbon atoms.
- Hydrogen (H) has a molar mass of approximately 1 g/mol, and there are 2 hydrogen atoms.

Calculating the molar mass:

\[ \text{Molar mass of C2H2} = (2 \times 12) + (2 \times 1) = 24 + 2 = 26 \text{ g/mol} \]

Now, substituting the values into the moles formula:

\[ n = \frac{5.0 \text{ g}}{26 \text{ g/mol}} = 0.1923 \text{ mol} \]

**Step 2: Convert the pressure from mmHg to atm.**

To convert mmHg to atm, we use the conversion factor:

\[ 1 \text{ atm} = 760 \text{ mmHg} \]

Thus, the pressure in atm is:

\[ P = \frac{740 \text{ mmHg}}{760 \text{ mmHg/atm}} = 0.9737 \text{ atm} \]

**Step 3: Convert the temperature from Celsius to Kelvin.**

To convert Celsius to Kelvin, we use the formula:

\[ T(K) = T(°C) + 273.15 \]

So, for 50°C:

\[ T = 50 + 273.15 = 323.15 \text{ K} \]

**Step 4: Substitute the values into the Ideal Gas Law equation.**

Now we have:
- \( n = 0.1923 \text{ mol} \)
- \( R = 0.0821 \text{ L·atm/(K·mol)} \)
- \( T = 323.15 \text{ K} \)
- \( P = 0.9737 \text{ atm} \)

Substituting these values into the Ideal Gas Law:

\[ V = \frac{nRT}{P} \]

Calculating the volume:

\[ V = \frac{(0.1923 \text{ mol}) \times (0.0821 \text{ L·atm/(K·mol)}) \times (323.15 \text{ K})}{0.9737 \text{ atm}} \]

Calculating the numerator:

\[ = 0.1923 \times 0.0821 \times 323.15 \approx 4.878 \text{ L·atm} \]

Now, dividing by the pressure:

\[ V \approx \frac{4.878}{0.9737} \approx 5.007 \text{ L} \]

### Final Answer:

The volume occupied by 5.0 g of acetylene gas at 50°C and 740 mmHg is approximately **5.007 liters**.