**Given Information:**
- Number of moles of gas (n) = 3
- Final volume of gas (Vf) = 2 L
- Work done (W) = 2.983 kJ
- Temperature (T) = 22°C

**Calculating Initial Volume:**
To calculate the initial volume of the gas, we need to use the ideal gas law equation:

PV = nRT

Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature in Kelvin

Since the compression is isothermal (constant temperature), the temperature remains constant throughout the process. Therefore, we can use the ideal gas law to calculate the initial volume.

**Converting Temperature to Kelvin:**
The given temperature is 22°C. To convert it to Kelvin, we need to add 273.15 to the Celsius temperature.

T = 22°C + 273.15 = 295.15 K

**Rearranging the Ideal Gas Law Equation:**
Rearranging the ideal gas law equation, we can solve for the initial volume (Vi):

Vi = (nRT) / P

**Finding the Pressure (P):**
To find the pressure, we can use the formula for work done during an isothermal process:

W = -PΔV

Where:
- W is the work done
- P is the pressure
- ΔV is the change in volume

Since the work done is positive (2.983 kJ), we can substitute the values into the formula:

2.983 kJ = -P(2 L - Vi)

Simplifying the equation:

2.983 kJ = -P(2 L) + PVi

**Solving for P:**
Since the work done is done during an isothermal and reversible process, we can assume the gas follows the ideal gas law. Therefore, the pressure remains constant throughout the process.

2.983 kJ = PVi - 2P L

PVi = 2.983 kJ + 2P L

**Substituting Values into the Ideal Gas Law Equation:**
Now, we can substitute the known values into the ideal gas law equation to calculate the initial volume (Vi).

Vi = (nRT) / P

Vi = (3 moles * 0.0821 L·atm/(mol·K) * 295.15 K) / P

**Solving for Vi:**
We can substitute the expression for P from the previous step into the equation for Vi.

Vi = (3 moles * 0.0821 L·atm/(mol·K) * 295.15 K) / (2.983 kJ + 2P L)

Calculating the value:

Vi = (72.578 L·atm) / (2.983 kJ + 2P L)

**Simplifying the Equation:**
Since the initial volume (Vi) is given in liters and the work done (W) is given in kilojoules, we need to convert the units for consistency.

1 L·atm = 101.325 J
1 kJ = 1000 J

Converting the values:

Vi = (72.578 L·atm) / (