### Consider the reaction: \begin{array}{c}{\mathr…

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Problem 74

Use data from Appendix IIB to calculate the equilibrium constants at $25^{\circ} \mathrm{C}$ for each reaction. $\Delta G_{\mathrm{f}}^{\circ}$ for BrCl $(g)$ is $-1.0 \mathrm{kJ} / \mathrm{mol}$ .
$$\begin{array}{l}{\text { a. } 2 \mathrm\ {NO}_{2}(g) \Longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)} \\ {\text { b. } \mathrm{Br}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm\ {BrCl}(g)}\end{array}$$

Answer

PART $\mathrm{A} : K=3.1$
PART B: $K=7.8$

## Discussion

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## Video Transcript

So this problem wants us to find out what the equilibrium, constant K is for the reactions given. So, first off, we need to figure out how we confound K based off a delta G. It so don't g is equal to negative. Artie. Ellen. Okay, As announced apparel, adult G is for these reactions. So the 1st 1 we have two and no to the gas going to into four. It's a gas. And so we can solve this by taking the Delta Gee information of your product into a four minus two times the delta G information of you know, to your reacted Dr G is equal to Can you combine these values in your textbook? Find us to account for the two here times 51.3 and that gets us negative. 0.1 killed Jules. And so then you just plug into this equation, you need to keep it a reminder that our, which is a constant, is 8.314 jewels for Calvin Mole. And so we need to convert this to killer Jules. So the about 5000 approximately and so we split into this equation. Don't the G, Is it the minus 5.1, which is equal to negative zero point. Uh uh, eight times room temperature tweet about the greasy. But Kelvin, So to nearly eight times natural log, okay? And so if you divide both sides and then raise each sad to the power e, you get that Kay is equal to 7.8. So same thing with reaction be, Yeah, rooming gas go with chlorine gas going t o two be our CEO. And so you could find this that give you deputy information of to be our CEO. So that's minus one to do two times minus one minus. Your reactant CE, which is 3.1 plus zero for chlorine, is that I also gets you minus 5.1 killer, Jules. And so you don't even you can just look to our previous problem, which was minus 5.1. You see that cable also equal 7.8 since that room temperature as well