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(a) Use the van't Hoff equation in Problem 14.118 to derive the following expression, which relates the equilibrium constants at two different temperatures$$\ln \frac{K_{1}}{K_{2}}=\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T_{2}}-\frac{1}{T_{1}}\right)$$How does this equation support the prediction based on Le Châtelier's principle about the shift in equilibrium with temperature? (b) The vapor pressures of water are $31.82 \mathrm{mmHg}$ at $30^{\circ} \mathrm{C}$ and $92.51 \mathrm{mmHg}$ at $50^{\circ} \mathrm{C} .$ Calculate the molar heat of vaporization of water.

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$(\mathrm{a})\left(\frac{K_{1}}{K_{2}}\right)=\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T_{2}}-\frac{1}{T_{1}}\right)$(b) $\Delta H^{\circ}=40,000 \mathrm{J} / \mathrm{mol}$

Chemistry 102

Chapter 14

Chemical Equilibrium

Carleton College

University of Central Florida

University of Maryland - University College

Lectures

10:03

In thermodynamics, a state of thermodynamic equilibrium is a state in which a system is in thermal equilibrium with its surroundings. A system in thermodynamic equilibrium is in thermal equilibrium, mechanical equilibrium, electrical equilibrium, and chemical equilibrium. A system is in equilibrium when it is in thermal equilibrium with its surroundings.

00:54

In chemistry, chemical equilibrium (also known as dynamic equilibrium) is a state of chemical stability in which the concentrations of the chemical substances do not change in the course of time due to their reaction with each other in a closed system. Chemical equilibrium is an example of dynamic equilibrium, a thermodynamic concept.

00:58

The van't Hoff equati…

04:08

10:55

The dependence of the equi…

04:37

okay. There are several ways in order to derive this equation using the equation and problem 14.1 18. The easiest way I think, is to set both of them equal to see. So we've got K one and t one, which can, which will equal C if we have. If we write it as natural log of K one minus the n tal p over R T that will equal C. Then we would have natural log of K two minus Delta age over our tea too. And that will also equal. See. So if they both equal, see then they both equal each other. Then we do a little bit of algebra. We'll subtract natural log of two from both sides and add on Delta H r t t one to both sides and we get this expression here. Then we remember our log rules. Natural log of K one minus natural. Log of K two is natural. Log of K one over K two and then we'll pull out dealt H standard over our and we'll be left with one over T one minus one over t two. And yes, if you look at this if we have an extra thermic reaction where this is negative. Then if we increase T one, we're going to end up with a smaller cave value and if dealt ages positive. If we increase the temperature, we're going to increase the K value for an Endo thermic reaction Then to solve for Delta H, we could rearrange the equation to get this right here. Now when solving for Delta H, these are equilibrium constants. They didn't give us equilibrium. Constants. They gave us vapor pressures for water in water, then is going to be age 20 liquid goes to H 20 gas. And because there's only pressure involved in this equilibrium expression because liquids are not part of an equilibrium expression, weaken, substitute the pressures for the equilibrium constants. So when solving for Delta H, we can plug in pressures here and corresponding temperatures here. When we do that, we need to remember because we're solving for a Delta H value, which is an energy value than our needs to have the value of 8.314 uh, jewels for lead her per Kelvin mole instead of the 0.8 to 1. So we'll plug in our pressures, we'll plug in our temperatures multiplied by the our value and we get around 40,000 jewels for the delta H of vaporization of pure water.

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