Answer:
approximately -7.6 kJ
Step-by-step explanation:
To solve this problem, we can use the ideal gas law: PV = nRT, where P is the pressure of the gas, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Since the expansion is isothermal, the temperature does not change, so we can assume T is constant.
We can rearrange the ideal gas law to solve for the pressure at the initial volume:
P = nRT / V
And then use this pressure to calculate the work done by the gas during the expansion using the formula:
W = -Pext * ΔV
Where Pext is the external pressure and ΔV is the change in volume (final volume - initial volume).
Substituting the known values:
n = 1450.0 mol T = 11.0 + 273.15 = 284.15 K V1 = 20.0 L V2 = 95.0 L R = 8.314 J/(mol*K)
We can calculate the initial pressure:
P1 = nRT/V1 = (1450.0 mol)(8.314 J/(mol*K))(284.15 K)/(20.0 L) = 27047.6 Pa
(Note that we converted the temperature to Kelvin.)
During the expansion, the external pressure is assumed to be constant, and equal to the pressure outside the system, so we can just use atmospheric pressure. Let's assume that the atmospheric pressure is 101325 Pa.
The change in volume is ΔV = V2 - V1 = 75.0 L
Then we can calculate the work done by the gas:
W = -Pext * ΔV = -(101325 Pa) * (75.0 L) = -7.6 kJ
(Note that we converted units from joules to kilojoules.
Therefore, the work done by the gas during the expansion is approximately -7.6 kJ. Note that the negative sign indicates that work is done on the gas by the surroundings.