HW Week 3 & 4 Achieve #14

[Alyssa Ly 2G]

Hi!
"A sample of an ideal gas in a cylinder of volume 3.55 L at 298 K and 2.46 atm expands to 8.95 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 1.15 atm. In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.15 atm until the final volume is 8.95 L. Calculate the work for path A. Calculate the work for path B."

How do we know which equation to use for calculating work when it states that it is an isothermal, reversible expansion?

Thank you!

[Katie Shi 1F]

For an isothermal, reversible reaction we will use the formula w = -nRT*ln(v_f/v_i). First, for path A, we have to find the number of moles of gas using the ideal gas law, PV = nRT, where R = .08206 L*atm/mol*K. Next, we will use that n in that first formula, where R = 8.314 J/mol*K. This will give us the work for path A. Next, for path B as the first step has constant volume we know work = 0. For the second step, we will use the formula w = -pdeltaV. Our answer will be in L*atm so we will have to convert that to joules by multiplying it by 101.325.