Textbook Problem 4.7

[Amy Shimizu 1J]

Problem 1.7 reads:
(a) Calculate the work that must be done against the atmosphere for the expansion of the gaseous products in the combustion of 1.00 mol C6H6 (l) at 25 degrees C and 1.00 bar.

For this first part of the problem, the equation that was used was
w = -P*deltaV = -delta(n)*R*T, where delta(n) was the net change in moles of gas. Why do we use delta(n) here instead of just the 1.00 mol given?

Overall, how do we know to use delta(n) instead of just n in the ideal gas law equation?

[Sophia Schiro]

I'm not 100% sure but maybe it uses delta n because it's in expansion?

[Rena Wu 3E]

Hi Amy,
Like what Sophia said, we have to use delta(n) to solve for the work done by the system because the volume is changing. Since the temperature and pressure of the system are constant, a change in volume would require a proportional change in moles, as seen in the ideal gas equation. So our equation is now P*delta(V) = delta(n)*R*T, where P, R, and T are all constant values. We also know that work for constant-pressure systems is written as w = -P*delta(V). We can put these two statements together to get w = -delta(n)*R*T, where you can then solve for the work done by the system (or the work done against the atmosphere/surroundings). A side note: I believe that Dr. Lavelle did a similar example in Friday's lecture—if you wanted further clarification about this kind of calculation. Hope this helps!