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Problem 89

Is each statement true or false? If false, correct it.

(a) All spontaneous reactions occur quickly.

(b) The reverse of a spontaneous reaction is nonspontaneous.

(c) All spontaneous processes release heat.

(d) The boiling of water at $100^{\circ} \mathrm{C}$ and 1 atm is spontaneous.

(e) If a process increases the freedom of motion of the particles of a system, the entropy of the system decreases.

(f) The energy of the universe is constant; the entropy of the universe decreases toward a minimum.

(g) All systems disperse their energy spontaneously.

(h) Both $\Delta S_{\mathrm{sys}}$ and $\Delta S_{\mathrm{surr}}$ equal zero at equilibrium.

Answer

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## Discussion

## Video Transcript

So the first question is saying, if what's the relationship between spontaneity and speed of reaction and this really important thing to know is that a spontaneous reaction is governed by values like Delta G, not of a reaction or K equilibrium constant. But the speed is governed by lower case K. You can really tell, but lower case Cape, the kinetics, um, the kinetic rate constant. And so these two things are completely unrelated on an example, so that just because something is response, a distraction doesn't mean that it's fast. You know, a firework exploded that spontaneous once, you know, once he gets over the activation energy, but it's really fast, but iron rusting is also spontaneous. But it's nowhere is fast. And so there's really there's no relationship to, um, second question is about whether something going if something going from reactions, it's a products is spontaneous. What about the reverse reaction? So, um, the simple answer is that yes, the reverse it actually non spontaneous. Did you think about it? Let's just sort of obviously where Okay, if going this way is natural, the other way is gonna be unnatural. But the mathematical 15 minutes so if this is spontaneous, the K value if this is greater than one And when you reverse, um, reaction, you take the K of the reverse is one over the k of it forward. And so if this was greater than one the reverse the action to be less than one, which means non spontaneous. Um, now, this is this one that you have to be carefully, so Delta G equals Delta H minus T del test. This is our definition of, um, gives free energy that relates a temple p an injury. And so it says, What do all of these rations where they're spontaneous? In other words, Delta G is negative. Is Delta h negative? And often it is because that helps me Fine. We could have dealt h be positive. And if t. Delta Ass is enough positive selfies against Attracted and others that the entropy is positive, this will be a negative value of role, including the minus sign. And then we could have Delta's use Silver united. And so, in other words, even if Delta H is positive, which to say it absorbs heat, if the entropy is positive, there's more disorder in the system That means you can still have Delta G B negative at high enough temperatures. Example of this is dissolving sodium chloride on they see out in water is actually has a Delta H. That's positive, but the reason is spontaneous, and you would know that puts on your water is that, um, the entropy increases. And so there. Examples. Where Delta H is positive. Hey isn't released, but it's still a spontaneous process. What about taking water from a liquid to being a gas at 100 degrees Celsius and one atmosphere? Well, this is exactly the boiling point of water. And so this is one where there's a little bit of a catch here. There's sort of three different situations can happen. Um, you know, if Delta G is rare than zero, it's not spontaneous. If it's dull, Tages less than zero, it's spontaneous. If Delta G is equal to zero, it is at equilibrium, and this is the one that we often forget because less common. But in this case, where exactly at the boiling point, we're at a perfect equilibrium between liquid and gas. And so Ah, the answer is that it's not spontaneous right now at that temperature and pressure. It's at equilibrium. And that's why if you manage to actually get the temperature of your bar to be exactly how did degrees Celsius, you wouldn't see a boil. You have to get above at least slightly above to get it to boil. Um, the next one is just roughing. No, understand that entropy? Delta asked, increases as disorder motion. He etcetera increase. And so they, instead of the entropy of the system, decreasing, it's that it increases as the freedom emotion increases. And so, um, the next one, I just make a point here because it's related. This next question. When I was saying, Don't that's here, I'll start for the system. Um, but the delta s of the universe can never be negative. And this is a really important fact. If a process is at equilibrium, adults asked of the universe. Um, is I zero? But all other processes that was spontaneous. The don't ask the universe is greater than zero. And so the entropy of the universe always increases no matter what's happening. And that's why some people, and it's definitely true that at some point it will hit a maximum of but and you know we won't have any more heat, and no more reaction will happen. Everything will be an equilibrium. But this is not something to worry about. It will happen far, far, far later than humanity will survive. Um, and finally, uh, G relates to, uh, this question. So I'm gonna stay right here. Delta s of the universe increasing what this really means. That energy is being more equipped. Distribute seat with The main way that entropy increases is that he goes from hot places. So H two c, that's how he travels. And then these both sort of come to an equilibrium. And so he doesn't actually dispersing energies, natural dispersing in a spontaneous processes. So she is true. And our last one, um so not just keep it here because it relates it. I said it. That dealt, That's the universe at equilibrium is equal to zero. And so we have were discussing you deliver a process here, tell us of the universe is equal to Delta after the system. Plus, don't ask him the surroundings and yeah, they can both be zero intel task. The universal equals zero. It should, but they don't have to be We could have, you know, positive three and negative three. And in the doll test, the universal still equals zero. And so the question is that in this name is kind of true, Uh, some of these two equals zero, but they themselves have t equals zero, and that's yes.

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