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JF

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Problem 41

(a) Find $\Delta S_{\mathrm{rxn}}^{\circ}$ for the formation of $\mathrm{CH}_{3} \mathrm{OH}(l)$ from its elements.

(b) Calculate $\Delta S_{\text { univ }},$ and state whether the reaction is spontaneous at 298 $\mathrm{K}$ .

Answer

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## Discussion

## Video Transcript

okay. To start this problem, we need to first find are balanced reaction. So on the right side here we have ch 30 h. So this is made of carbon, hydrogen and oxygen. So that means we're going to start with Carbon, which in its standard state, it's just a solid sorry. It's a little messy and then we're going to have hydrogen, which in its standard state is I didn't gas plus O two, which in its oxygen plus offset in, Which is it Standard state is oxygen gas. Now let's balance his equation. So we already have one carbon. So that's OK. We have four h is So we'll add it to in front of this and then we have one oxygen so we'll add a one half in front of this. From there, we're going to use our equation products minus reactant. It's so let's fill in our template here. So we have our products. So we're gonna use thes standard entropy of ch 30 h minus, um, one times thes standard entropy of carbon. And it's solid form plus who times thes standard entropy of H two gas plus one half the standard entropy of 02 bass saving a little time. I'm not writing in the states. Um, so again, you can find the standard Entropy is online if you Google standard entropy use, and they should all be in a table, but just for ease thes air, the standard entropy is we're working with. So if we, um, insert these into all the places we need them in this equation, so that would go There are h two would go here, and then our 02 would go here and then plug and chug through that. The delta s of the action comes out to be negative. 240 to 0.4 Jules per Kelvin. Okay, so that's part one of the question to do part Two of the question. We want to know the delta s of the universe, so we know the delta s of the universe right here. Left side is the belt s of the reaction which we have already found its are 242.4, plus the delta s of the surroundings. So we just need to find the delta s of the surroundings. So the delta s of the surroundings are equal to the delta. H the change in in Philippi of the reaction. So again, our reaction up here divided by the temperature, which we know is 298. Um, because they say that in the problem 298 coming so again we're going to use our products minus reactant to find the Delta h of reaction. So it's just like the Delta. Um Ah, Delta s the change in entropy, but we're using three Delta H information. So again, you can Google search these online and you can find a Delta H information for each of these molecules. Just for time's sake. I'm going, Teoh, jump ahead. But again, you would just plug and chug threw that in for the Delta h of the reaction. You should get negative 238 0.6 killer jewels. All right, so then we're gonna plug that back into our equation for the Delta s the delta. Um, the change in entropy of the surroundings which will be you know what? I forgot a negative. There's a negative sign here. So is negative. Um, the negative dealt h the negative change in entropy of the reaction, which we already found is 238.6, divided by the temperature, which was 2 98. And so we are going to get, um and make sure this, uh OK, so we're going to well, jumping back here, since this is killing jewels and we're gonna add this number are Delta s of surrounding to our delta s of reaction, which is in jewels were gonna multiply this by 1000. So instead of killer jewels, we get Jules. So the delta s of surroundings is going to be 800. Sorry for my messy handwriting. Here, 0.7 Jules, her Calvin. And then what we're gonna do is add our delta s of surrounding which again is the 800 0.7 plus our delta s of reaction, which we found up here is our negative to 42.4 waas Negative. 2. 40 2.4. And together we are going to get an answer of 558 0.3. She waas her Calvin