Achieve HW #14

[Jayden Arevalo 2B]

For this problem, we are given the following, "A sample of an ideal gas in a cylinder of volume 3.81 L at 298 K and 2.22 atm expands to 7.68 L by two different pathways. Path A is an isothermal, reversible expansion. Path B has two steps. In the first step, the gas is cooled at constant volume to 1.25 atm. In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.25 atm until the final volume is 7.68 L."

For the first part, it requires us to find the work for path A. In doing so, I began with calculating the amount of moles in the process, since it is needed to calculate the work. I did this by using the ideal gas law (PV=nRT), thus I made my equation
(2.22 atm)(3.81L) = n(8.314)(298K) and solved for n which provided me with n = .0034139082 moles of the gas

Then, I plugged the information I had into the work equation for an isothermal/reversible expansion.
w = -(.0034139082)(8.314)(298)(ln(7.68/3.81)) = -5.929116575 J

However, this is incorrect, achieve tells me, "You have not correctly determined the work for path A. You may have used the wrong ideal gas constant value to calculate the work done. Use the value 8.314 J⋅mol−1⋅K−1 instead of 0.08206 L⋅atm⋅ mol−1⋅K−1 to calculate the work."

What am I doing wrong? :(

[Katie Shi 1F]

When using the ideal gas law, PV = nRT, you want to use R = .08206 L*atm/mol*K to be consistent with the units in the equation. For the work equation for an isothermal/reversible reaction, you will then use R = 8.314 J/mol*K.