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Find the temperatures at which reactions with the following $\Delta H$ and $\Delta S$ values would become spontaneous: (a) $\Delta H=-126 \mathrm{kJ} / \mathrm{mol}, \Delta S=84$ $\mathrm{J} / \mathrm{K} \cdot \mathrm{mol} ;$ (b) $\Delta H=-11.7 \mathrm{kJ} / \mathrm{mol}, \Delta S=-105$ $\mathrm{J} / \mathrm{K} \cdot \mathrm{mol}$.

K=111K

Chemistry 102

Chapter 17

Entropy, Free Energy, and Equilibrium

Thermodynamics

Carleton College

University of Central Florida

University of Maryland - University College

Brown University

Lectures

00:42

In thermodynamics, the zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

01:47

A spontaneous process is one in which the total entropy of the universe increases. In a spontaneous process, the system will move from an ordered state to a disordered state, such as from ice to water, or from a solid to a gas. The concept of spontaneity was introduced by Rudolf Clausius in 1850.

03:10

From the values of $\Delta…

04:04

so the temperatures at which the given reactions or the reactions with given properties of entropy and entropy change will be spontaneous. So what you want to do is so this is based on Delta G equals till the h minus t delta s and you want to know what values of temperature will make Delta G negative, and that will make that will be spontaneous conditions. Eso What you want to do is find out the temperature at which Delta G will be zero, and then you can reason what temperatures will make Delta gene negative. So setting Delta G equals zero eso first, subtract out age from each side and then divide both sides by the negative of Delta s on that will tell you the temperature at which Delta G zero and in the first instance that would be minus 126 1000 jewels Promote over 84 Jules per mole. Uh, negative 1000 500 tools promote Calvin. That's Kelvin's. So here we have a negative Delta H and a positive Delta s now in dealt H is negative. That makes a negative contribution to Delta G. And when Delta S is positive than multiplying it by the negative. T T has to be positive because that's Kelvin's. Uh and so, uh, the answer here is all temperatures, because as temperature increases, then we get a bigger and bigger negative for this product, since Delta asses positive and so it's all temperatures above negative 1500 Calvin. But there are no actual it's ah, physical in reality or unreality for the kelvin temperature to be negative. So that means all temperatures, which is always true when Delta H is negative and Delta s is positive. In the case of ah, a negative 11th seven. Notice that these Aaron killer jewels And if you don't take account of that, then you'll be off by a factor of 1000 on your temperature and you don't want to be there. That is 111 0.4 Kelvin's. Okay, so now do we want temperatures greater than this or temperatures less than this. We've got a negative value for Delta H and so that favors and negative value. Four Delta G. Uh, but still, toe s is negative, and the higher the temperature. We got a negative here in a negative on Delta s the more of a positive contribution that makes. And so, um, we want temperature to be less than 11.4 K because again, greater temperatures make Delta G more positive. We want the temperatures at which dealt it. He is going to be negative. So we went low temperatures because we've got a negative here and a negative here. And so that makes a positive contribution when temperatures below 111th.

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