Question 17, Achieve

[Harun Momin 1L]

Hello,

I was having a bit of trouble trying to solve #17 on the achieve assignment.

A 0.201 mol sample of SO2(g), initially at 298 K and 1.00 atm, is held at constant pressure while enough heat is applied to raise the temperature of the gas by 19.9 K. Calculate the amount of heat q required to bring about this temperature change, and find the corresponding total change in the internal energy ΔU of the gas.

Assume that the constant‑pressure molar specific heat for SO2(g), which consists of nonlinear molecules, is equal to 4R, where R=8.3145 J/(mol·K) is the ideal gas constant.

So I got the amount of heat, q, but I was having trouble solving for ΔU. I was using the ΔU = q+w equation but didn't know how to solve for work. If we know w=-PΔV, and PΔV= ΔnRT, how can we calculate work from our givens? Or is this even the method to take?

Thanks.

[ella3]

^^I was also having trouble with this one.

[Vivek Punn 1E]

For this question the first equation you want to use is q=nC(sp)delta T. Essentially you want to use the value of 4*R (or 4 times the ideal gas constant) as the specific heat. Using that, we can figure out a value for q. The next step is to solve for delta U. Since we know this is a CONSTANT-VOLUME, we can use the following equation to solve for the change in internal energy: delta U = n * C(v) delta T. Since we are at constant volume C(v) is the constant volume molar specific heat which can be calculated by C(p)-R = 3R. So our equation for this specific problem becomes delta U = number of moles * 3R * delta T. Hope that helps! The achieve question also has a good explanation of this question once you get it correct.