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Problem 20

Predict the sign of $\Delta S$ for each process

$$\begin{array}{l}{\text { (a) } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)(350 \mathrm{K} \text { and } 500 \text { torr) } \longrightarrow} \\ {\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)(350 \mathrm{K} \text { and } 250 \text { torr) }}\end{array}$$

$$\begin{array}{l}{\text { (b) } \mathrm{N}_{2}(g)(298 \mathrm{K} \text { and } 1 \mathrm{atm}) \longrightarrow \mathrm{N}_{2}(a q)(298 \mathrm{K} \text { and } 1 \mathrm{atm})} \\ {\text { (c) } \mathrm{O}_{2}(a q)(303 \mathrm{K} \text { and } 1 \mathrm{atm}) \longrightarrow \mathrm{O}_{2}(g)(303 \mathrm{K} \text { and } 1 \mathrm{atm})}\end{array}$$

Answer

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## Discussion

## Video Transcript

Chuck the 20 Problem 20th asking us to predict the entropy of a change. Entropy for a process and so first thing to remember is that contributes to freedom of particle motion, of the dispersion of energy, the greater the entropy, their greater freedom of that of those particles and the greater the NGO is dispersed in that system. This can happen when you're going from a solid phase. Two. The liquid phase to a gas phase right? A gas has for particles that have a larger freedom of motion. They have more energy to spread out the systems that's larger, contributing something that's a look, whether something that's a gas, you can also have a greater entropy by increasing your temperature, I should put. That's a greater change of entropy as you go from one face to another as you increase the temperature. You, the product, was have more kinetic energy, and that is dispersed throughout the system, allowing them to have a greater Freeman particle motion. You could also have a greater inter Pete when you decrease pressure. So let's think about that if you have a container on it with the lead and you pushed the lead down to here and let's say you have a gas in this container and there's three gas particles and molecules in this container moving around when you remove the pressure on the system, going to bring the lead up to the top. Now those particles have a greater freedom of motion. They're able to disperse MAWR throughout the system, and so therefore, there's a greater entropy when you go from a low pressure to a high pressure when you I'm sorry from a high pressure to low pressure when you remove the pressure on the system. So let's look at three examples. Let's say we're starting off with something in his gas phase. A compound that's a gas will call that compound A, and this has a hi tip. Well, let's do it this way. The temperature of it is 350 Calvin, and the pressure is 500 tour. I'm gonna put T for tour at the end. We still have that same substance. A. It's still in its gas phase. However, at the end the pressure has decreased, so we still have 3 50 k is our pressure, but our tour is now 250 k what we had here. We're particles a in this in the, um, container at a high pressure. Well, this should actually be It should be tour here t. And then we were moved. Pressure from the system allowing the particles to move around more and ended up here with a low pressure in this area should also be here ended up here with a lower pressure. So we went from a high pressure to low pressure. We decreased the change in pressure and therefore we increase that entropy. So in this case, there is greater entropy, your freedom of particle motion at the end, At dinner at the end, there is a larger freedom of particle motion. Then at the beginning, I had a smaller freedom of product emotion because there was a greater pressure. So in this case, we're gonna consider the entropy of the systems. This is a state function. It is a final entropy minus your initial interpreting. If you have a large final entropy l a for large and your initial entropy a small s m. For small. You'll end up with a positive sign because you're doing this large value minus is smaller. value if you start out with the small initial entropy. I'm sorry if you start if you finish with the small initial interview a small entropy and you began with a large entropy. The change entropy of this system is more likely to be negative. So if your final entropy is larger than your initial, you have a positive value. If you're found, entropy is smaller than your initial in tribute and you have a negative value. In this case, our final entropy is larger than our initial entropy. So we're going to have a positive Delta s sorry sign here would be positive. Let's do another example where we have a system where we have a That's also a guess and in this case, the pressure of a and the temperature of a They say the same, but we end up with a that is now a qui ists and angriest is slightly different from a liquid. A liquid is pure. Acquis is ah solution of whatever that a Maybe so we have a liquid of a or a solution of a. So we moved from the gas phase two, the liquid phase and we know that gas has a larger entropy than a liquid. So in this case, we're starting off with the large entropy, and we finish with the smaller in its entropy. So we do our small minus our initial large entropy in this case are sign for adults s is going to be negative. Lastly, let's do an example where the pressure temperature still stay the same but are a goes from a quiz to something that is gas again with the same pressure and temperatures. We don't take those two into account, but we do know that a gas phase has a larger entropy than a liquid or a quickest phase, which is smaller. So we're gonna do our final large value minus our initial smaller value, and we will end up with a positive Don't s so again. When you think about tells s you want to think about the faces change where the greater than particle motion of that phase, the more entropy it has, you will think about the change in temperature as you increase the temperature of the system. Their product was able to move further farther around, have a large degree of freedom and therefore larger entropy, and as you decrease the pressure. You also allow the particles to move further around, giving a large entropy at the end than there was at the beginning.

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