A sample of an ideal gas at 15.0 atm and 10.0 L is allowed to expand against a constant externam pressure of 2.00 atm at a constant temperature. Calculate the work in KJ for the gas expansion (Boyle's law applies)

To calculate the work done during the gas expansion, we can use the formula:

work = -P_ext * ΔV

where:
- work is the work done by the gas,
- P_ext is the external pressure,
- ΔV is the change in volume.

In this case, the external pressure is given as 2.00 atm, and the initial volume is 10.0 L. To calculate the change in volume, we can use Boyle's law, which states that P * V = constant at constant temperature. We can rearrange the formula to solve for the final volume, V_f:

V_f = (P_i * V_i) / P_f

where:
- V_f is the final volume,
- P_i is the initial pressure,
- V_i is the initial volume,
- P_f is the final pressure.

Given that P_i = 15.0 atm and P_f = 2.00 atm, we can substitute these values into the equation:

V_f = (15.0 atm * 10.0 L) / 2.00 atm
V_f = 75.0 L

Now, we can calculate the change in volume, ΔV:

ΔV = V_f - V_i
ΔV = 75.0 L - 10.0 L
ΔV = 65.0 L

Substituting these values into the work formula, we can calculate the work done:

work = -P_ext * ΔV
work = -(2.00 atm) * (65.0 L)

Converting the units from atm * L to kJ, we can use the conversion factor:

1 atm * L = 101.325 J
1 J = 0.001 kJ

So, the conversion factor is 0.101325 kJ/atm * L. Multiplying the work by the conversion factor, we get:

work = - (2.00 atm) * (65.0 L) * (0.101325 kJ/atm * L)
work ≈ -131.63 kJ

Therefore, the work done by the gas expansion is approximately -131.63 kJ. The negative sign indicates that work is being done on the gas, rather than by the gas.