The volume occupied by 4.75g of acetylene gas at ` 50^(@)C and 740` mmHg pressure is _________L. (Rounded off to the nearest integer )
[Given R= 0.0826 L atm `K^(-1)` `"mol"^(-1)`]

Answer

To find the volume occupied by 4.75 g of acetylene gas at 50°C and 740 mmHg pressure, we can use the Ideal Gas Law equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant (0.0826 L atm K\(^{-1}\) mol\(^{-1}\))
- \( T \) = temperature (in Kelvin)

### Step 1: Convert the pressure from mmHg to atm
Given:
- Pressure \( P = 740 \) mmHg

To convert mmHg to atm, we use the conversion factor \( 1 \) atm = \( 760 \) mmHg:

\[ P = \frac{740 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 0.974 \, \text{atm} \]

### Step 2: Convert the temperature from Celsius to Kelvin
Given:
- Temperature \( T = 50^\circ C \)

To convert Celsius to Kelvin, we add 273.15:

\[ T = 50 + 273.15 = 323.15 \, K \]

### Step 3: Calculate the number of moles of acetylene
The molar mass of acetylene (C\(_2\)H\(_2\)) can be calculated as follows:
- Carbon (C) = 12 g/mol × 2 = 24 g/mol
- Hydrogen (H) = 1 g/mol × 2 = 2 g/mol

Thus, the molar mass of acetylene is:

\[ \text{Molar mass} = 24 + 2 = 26 \, \text{g/mol} \]

Now, we can calculate the number of moles \( n \):

\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{4.75 \, \text{g}}{26 \, \text{g/mol}} \approx 0.1827 \, \text{mol} \]

### Step 4: Substitute values into the Ideal Gas Law equation
Now we can substitute \( P \), \( V \), \( n \), \( R \), and \( T \) into the Ideal Gas Law equation to find \( V \):

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

Substituting the known values:

\[ V = \frac{(0.1827 \, \text{mol}) \times (0.0826 \, \text{L atm K}^{-1} \text{mol}^{-1}) \times (323.15 \, K)}{0.974 \, \text{atm}} \]

Calculating the numerator:

\[ = 0.1827 \times 0.0826 \times 323.15 \approx 4.675 \, \text{L} \]

Now, divide by the pressure:

\[ V \approx \frac{4.675}{0.974} \approx 4.8 \, \text{L} \]

### Step 5: Round off to the nearest integer
Rounding off \( 4.8 \) to the nearest integer gives us:

\[ V \approx 5 \, \text{L} \]

### Final Answer
The volume occupied by 4.75 g of acetylene gas at 50°C and 740 mmHg pressure is approximately **5 L**.

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