Question

1.95 mol of an ideal gas at 300 K and 3.00

atm expands from 16 L to 28 L and a final
pressure of 1.20 atm in two steps:
(1) the gas is cooled at constant volume
until its pressure has fallen to 1.20 atm, and
(2) it is heated and allowed to expand
against a constant pressure of 1.20 atm un-
til its volume reaches 28 L.
Which of the following is CORRECT?
1. w = 0 for (1) and w = −1.46 kJ for (2)
2. w = −4.57 kJ for (1) and w = −1.46 kJ
for (2)
3. w = 0 for the overall process
4. w = −4.57 kJ for the overall process
5. w = −6.03 kJ for the overall process

Answer 1

[AI-generated answer — Explain Bot]

To determine the correct option, we need to calculate the work done in each step and then determine the total work done for the overall process.

Step 1: Cooling at constant volume until the pressure falls to 1.20 atm.
Since the volume remains constant, the work done in this step is given by the equation:
w = -P * ΔV
where P is the pressure and ΔV is the change in volume.
In this case, P = 3.00 atm (initial pressure) and ΔV = 0 L (no change in volume).
Therefore, the work done in step 1 is w = -3.00 atm * 0 L = 0.

Step 2: Heating and allowing expansion against a constant pressure of 1.20 atm until the volume reaches 28 L.
The work done in this step can be calculated using the equation:
w = -P * ΔV
where P is the constant pressure and ΔV is the change in volume.
In this case, P = 1.20 atm (constant pressure) and ΔV = 28 L - 16 L = 12 L.
Therefore, the work done in step 2 is w = -1.20 atm * 12 L = -14.4 L.atm.

Now, let's calculate the total work done for the overall process by adding the work done in each step:
Total work done = work done in step 1 + work done in step 2
= 0 + (-14.4 L.atm)
= -14.4 L.atm

The correct option is 4. w = -4.57 kJ for the overall process.

Note:
To convert the units from L.atm to kJ, we use the conversion factor: 1 L.atm = 101.325 J = 0.101325 kJ.
Therefore, -14.4 L.atm = -14.4 * 0.101325 kJ = -1.45956 kJ, which is approximately -1.46 kJ.