Two crystalline forms of white phosphorus are known. Both forms contain $\mathrm{P}_{4}$ molecules, but the molecules are packed together in different ways. The $\alpha$ form is always obtained when the liquid freezes. However, below $-76.9^{\circ} \mathrm{C},$ the $\alpha$ form spontaneously converts to the $\beta$ form:

$$\mathrm{P}_{4}(s, \alpha) \longrightarrow \mathrm{P}_{4}(s, \beta)$$

a. Predict the signs of $\Delta H$ and $\Delta S$ for this process.

b. Predict which form of phosphorus has the more ordered crystalline structure (has the smaller positional probability).

## Discussion

## Video Transcript

Hi guys. So in problem 50 we are acts to predict the sign on calculate. Be stunned, that intro piece for the following reactions. So let's start with the 1st 1 Just say to predict the entropy for the 1st 1 we look at be reactant ce on the products. So moving from the accent to the product, I'm running from gushes face to liquid face. I want that doors is to decrease. Did this orderliness of this system on By so doing, we're decreasing the entropy so they can trapeze. Negative. So let's calculate that to calculate that we know that entropy is a state function, which means it depends only on the initial on final states of this system. So we have the sum of the entropy is off the product. My nose this summer, Offifty trapeze off the reactant ce so can look up cool. The entropy is off each off d involved in species from this ton Dad tables pretty much any at the back off. Any physical chemistry textbook this ah standards. I'm here tabulated. I bet you can find them on appendix. So for the product in this case, we have just one so which is 70. Um, forgive me. So we need to include the most. So, how many Morse off the product we have this one, right? So we have one more off that which is off water. All right, I'm a toss. 17 Joe Kelvin. Mole minus one more off hydrogen. Right. Got this is the liquid. We should indicate the state's a swell. This is gas, which has to go file you carving mall. So this is plus how more off oxygen on oxygen House one for everyone. Ju Park children more. So in each case, the more I can slot. In each case, the more counts watch, right? And then when you do this, you we'll get negative 1 64 ju park calving doesn't wall is gone, so you can see that we predict it. Delta asked to be negative, and it was a sneaky too. So let's look at this second, uh, problem. The second problem has gases in both reactant on park site. So everything and this system is gashes. Both reactions on part. In that case, you someone the the most of it rattles and then some more off the product and compare So here we have two plus three, just five miles. Oh, gashes molecules on here. We have to pose for six months of guy his molecules. So because we have more Moors Oh guy, shal smaller, close in product side. It means that it's an increase. And this older Dennis off the system on his doctors, it's positive. Yes, this increased. So that is the prediction. It's Louis. Say, Mom, See? We'll get Remember we said Delta S is We're going by the summation off the entropy is off to product minus summation of the entropy of the reacted. So the entropy of the product starting with Come on, fog side now. True moles. Oh, see. Or two Ben. So to house to one full. When my dean it is Jew children more. We're all of them. So I mean, not show them all. What do you know? It is the same, sir. Plus what this is for, um, for malls off water. What gas? What? Bye bye. One. It's nine. Jew by Kelvin Moore. All right, My house. No, not off reactant. We have two moles. Oh, me, fennel, Cass. And that will be so fine. Right? Your fork over. No, Oh, oh, Class through Moore's excision, guys. Um, so I think the but off eternal ISS 2 40 In this case, Yeah, it's to 40. I'm not of oxygen is too awful to a fire. So 2 14 and then the oxygen is two Fire Joe Pa Kelvin Moore. So again, the more councils are no, councils are no. Councils are most council. So when you compute four, the daughter s here. You have 89 Jule Barcoding. We just positive as predicted here. Right. So finally here We're moving from Gashes State two I, as a solution clearly were decreasing. Did this orderliness off this system? And since we're decreasing the this orderliness off the system Dota is well Okay, negative again. Delta is Is the submission off the It's off. T minus a mission of this off our right. We're pee on our product and reactant respectively. And we have in this case, one more off. It was accused, and it has entropy off zero. All right, Plus, we have, well, more off. Cool, right? I am a curious which has entropy off 57 Jew of in more minus. We have the entropy off. How's you chloride gas, which is one more I've dredging. Cool, right Gas hiss 1 87 Jew. Wow, Kelvin, No. Right. So more goes with more No counselors out. The more I hear clearly, this is zero. So you don't even need to come up with anything, then the small councils of this. So you be left with this. So when you compute for this, you have this number. Community 1 30 Jewels are killing. Well predicted, designed to be negative. And it's negative. So this is how you predict the sign? I'm the calculate the entropy off any given system provided, you know, the equation of the reaction. I'm the state's off the species involved in the reaction.

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