## Practice Midterm #3A

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

Jessica Lutz 2E
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### Practice Midterm #3A

Lex Luthor is trying to design a gaseous mixture of Krypton gas and Helium gas to make Superman weak and have a high voice at the same time! But first, he wants to quickly review entropy. He finds a sealed box that has two compartments. He puts 9.00 g of Helium gas in the first compartment, and 125g of Krypton gas in the second compartment. The compartment with Krypton is 3 times the size of the compartment with Helium (triple the volume). He then removes the separating divider, allowing the gases to mix, and sees that temperature then increases from 50.0 to 75.0 oC.
A) Assuming the gases are ideal monatomic gases throughout the process, what is the total change in entropy of the system?

I cannot figure out which equations for entropy to use for this problem. Any help would be great.

Chem_Mod
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### Re: Practice Midterm #3A

As discussed in the review session, there is an entropy change associated with three things. First, the Helium undergoes a volume change. Second, the Krypton gas undergoes a volume change. Third, the entire system undergoes a temperature change. See the formula sheet for entropy equations involving a volume change and then find another for the temperature change. For further clarification, feel free to drop into Hedrick room 125 tomorrow, 2/12, where I will be covering for Michael's UA session.

Aijun Zhang 1D
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Joined: Tue Oct 10, 2017 7:13 am

### Re: Practice Midterm #3A

So you can first write down all the equations related to entropy.
Since entropy is a state function, it can be added and substracted.
$\Delta S = nRln\frac{V2}{V1}$
$\Delta S = nCln\frac{T2}{T1}$
$\Delta S =\frac{q_{w}}{T}$
$\Delta S = k_{b}\ln W$

Helium gas and Krypton are in a sealed apparatus, so the volume ratio of He to Kr is 1:3.
There are 3 changes needed to be calculated.

1. He volume change
In this case, n = 9.00(mass of helium)/4.00 = 2.2483mol
R = 8.314 J/K$\cdot$mol
$\frac{V_{2}}{V_{1}}$=(3+1)/1=4
$\Delta S1 = nRln\frac{V2}{V1}$ = 25.913J/K

2. Kr volume change
In this case, n = 125(mass of helium)/83.79 = 1.49168mol
R = 8.314 J/K$\cdot$mol
$\frac{V_{2}}{V_{1}}$=(3+1)/3=4/3
$\Delta S2 = nRln\frac{V2}{V1}$ = 3.56779J/K

3. entropy change caused by temperature change in the final process.
n=n(Kr) + n(He) = 3.48mol
Since the total volume in the system does not change, so we use $C_{v}=\frac{3}{2}R$
T2 = 75 degrees celcius
T1 = 50.0 degrees celcius
Turn them into Kelvin and calculate the ratio.
$\Delta S = nCln\frac{T2}{T1}$ = 3.48 J/K

Then you add all the three entropies together to get the total entropy change.
Total $\Delta S$ = 33.0 J/K