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Problem 66

Consider the reaction:

$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$

Estimate $\Delta G^{\circ}$ for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change too much within the given temperature range.)

\begin{equation}\begin{array}{lllll}{\text { a. } 298 \mathrm{K}} & {\text { b. } 1055 \mathrm{K}} & {\text { c. } 1455 \mathrm{K}}\end{array}\end{equation}

Answer

PART $\mathrm{A} : \Delta G^{\circ}=131.5 \mathrm{kJ}$ and nonspontaneous

PART $\mathrm{B} : \Delta G^{\circ}=10.2 \mathrm{kJ}$ and nonspontaneous

PART $\mathrm{C} : \Delta G^{\circ}=-53.9 \mathrm{kJ}$ and spontaneous

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## Discussion

## Video Transcript

So for this problem, we're given the reaction. Uh, calcium carbonate. See a CIA three as a solid decomposing to calcium outside and carbon dioxide as a gas on. What they want us to do is calculate Delta G not cool is predicted at during temperatures. Hey, 2 98 Tim Pitt guy and 14 55 cover. And so do that. We first need to calculate. Well, think back to this former Delta G equals that a trustee does s so we need to go back and found out. What about that age? Don't that I saw her and so we could find those out. Are doing this or that Age equals aches. No products by this, the it'll be information of the reactors and when we have to account for the study geometry. But it's all went toe once that there's no Moeller co efficiency to consider. So you can find these numbers Same thing for Delta s. And so you can find these values and your textbook an appendix. And so I've already looked him up so that the h no equals negative. 6 34 Wait, not minus 3 93 Quite Bob cities your products ministry reacted, which is negative. Went to a 7.6. I said I get to 1 79 point to kill Jules. Delta s can be found similarly that that's not you're looking at the values in your textbook. So it a close to 13.8 plus 30 8.1 minus 91.7. Does it add equals was for Kevin. And so this isn't colored jewels. And Mrs Angel's a little convert this to killer jewels to have 1000. So you get 10000.160 killed Jules Coven, and I would have to plug in this into this equation at varying temperatures. Tito this no and so will do tonight. Calvin considered equals the Jeannot equals 1 79.2 minus 2 98 times 0.160 And that gives us 1 31 Kill Jules. And so then ask you determine where this reaction of spontaneous at these temperatures. And so to do that you look at the sign of Dr Gina and because, you know, it's positive it is non spontaneous, which I had to know an s for this purpose. So now it's thio 10 55 come in. So you plug in the values just as before you find out the G not equals 10.4 killed Jules and so still positive, even those very less positive than before. So it's still non spontaneous, Ennis and now at 10 45. So for that 14 50,000 coven don't g not equals negative 53.6 schedules. And so now the sun has changed too negative. Zoe's reaction is spontaneous, so as you increase in temperature, the reaction becomes more, more spontaneous.

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