Given information:
- Mass of O2 in the cylinder = 16 g
- Volume of the cylinder is reduced to 75% of its original volume
- Temperature of the gas is constant at 27°C
- Universal gas constant (R) = 8.31 J/(mole K)

Calculating the number of moles of O2:
To calculate the number of moles of O2, we need to use the ideal gas 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 universal gas constant
- T is the temperature of the gas

Since the volume and temperature are constant, we can rewrite the equation as:

n = P * V / (R * T)

Calculating the initial number of moles:
Since the initial volume is not given, we cannot directly calculate the initial number of moles. However, we can use the given information to calculate the initial pressure.

Calculating the initial pressure:
We can use the ideal gas equation to calculate the initial pressure:

PV = nRT

Since we know the mass of O2, we can calculate the number of moles using the molar mass of O2 (32 g/mol):

n = mass / molar mass = 16 g / 32 g/mol = 0.5 mol

Substituting the values into the ideal gas equation:

P * V = n * R * T

P = (n * R * T) / V

P = (0.5 mol * 8.31 J/(mol K) * (27 + 273) K) / V

Calculating the final number of moles:
The final volume is given as 75% of the original volume. Therefore, the final volume is:

Final volume = 0.75 * Initial volume

Since the temperature is constant, the final number of moles can be calculated using the ideal gas equation:

n = (P * V) / (R * T)

n = (P * 0.75 * Initial volume) / (R * T)

Calculating the work done:
The work done during the compression of a gas at constant temperature can be calculated using the formula:

Work done (W) = -P * ΔV

Where:
- P is the pressure of the gas
- ΔV is the change in volume

Since the temperature is constant, the change in volume can be calculated as:

ΔV = Initial volume - Final volume

Substituting the values, the work done is:

W = -P * ΔV

W = -(P * (Initial volume - Final volume))

Substituting the values:
Substituting the calculated values into the equation:

W = -((0.5 mol * 8.31 J/(mol K) * (27 + 273) K) / V) * (Initial volume - 0.75 * Initial volume)

Simplifying the equation:

W = -((0.5 * 8.31 * 300) / V) * (1 - 0.75)

W = -((0.5 * 8.31 * 300) / V)