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Estimate the molar heat of vaporization of a liquid whose vapor pressure doubles when the temperature is raised from $85^{\circ} \mathrm{C}$ to $95^{\circ} \mathrm{C}$.

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$$\frac{7.59 \times 10^{4} \mathrm{J}}{\mathrm{mol}}$$

Chemistry 102

Chapter 11

Intermolecular Forces and Liquids and Solids

Liquids

Solids

Drexel University

University of Maryland - University College

University of Toronto

Lectures

04:08

In physics, a solid is a state of matter characterized by rigidity and resistance to changes of shape or volume. Solid objects have a definite volume, they resist forces (such as pressure, tension and shear) in all directions, and they have a shape that does not change smoothly with time. The branch of physics that studies solids is called solid-state physics. The physical properties of solids are highly related to their chemical composition and structure. For example, the melting point of ice is significantly lowered if its crystal structure is disrupted.

03:07

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, a liquid is one of the four fundamental states of matter (the others being solid, gas and plasma). A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena.

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Okay, So for this problem, we're going to need the classiest clapper on equation, which is that the natural log of Ah, the vapour. Pressure is equal to the negative heat. The vaporization divided by the constant are over tea, plus some constant C. They give us two different points, which means that we can get rid of C. We just need to figure out how to set it up. So first. So we know that the pressure at her first point is going to be 1/2 of the pressure on our second point because the pressure doubles from 0.12 point two. So the natural log of her first pressure is equal to the heat of vaporization. There are times t one do you want, by the way, is 85 degrees Celsius. You will probably need to turn into Calvin's in a minute and then the natural log our second pressure, which weaken put in terms of p one going to be the heat of vaporization authority to now in India or the constant. So one way to do that is we subtract the sign and we subtract this side from each other. So when we do that. We get the natural log, P one minus the natural log of PT equals negative vapor pressure over rt one plus the heat of vaporization of rt too, plus C minus e those cancel each other out. So now we need to put uh, So now we need to put the second pressure in terms. The first pressure to cancel those out the natural log of ah p one is equal to the natural log P one divided by two now, because of the properties of logs, weaken Separate this out even further. We can have the natural log p one minus the natural log, the one plus the natural log of to if you don't remember why we could do this. You have. I want to get a brush up on your country breath. So these are going to cancel out. And a right side is going to be cool to our ah, heat of vaporization. Just pulling this out of the equation of one over rt to minus one over are t one Now. We're really close. We just need to divide both sides. By this, we'll have the heat of vaporization equals the natural log of to divided by one over r t two minus one over r t one t to you, by the way, is 95 degrees Celsius. So we plug in all of the numbers that seem S O. R is going to be 0.314 Jules per mole times. Kelvin, go ahead and put our temperatures and Calvin. So that's going to be 368 Kelvin for the second temperature and one over 8.314 deals. Prum Old times, Calvin and 3 58 Good. This one. So we go through, plug in off the numbers and this should give us an answer in jewels Pro Bowl. Because that's what the rest of our units, Aaron, because we have one one side in Kelvin and the other side. And Calvin, it's important that we remember to convert these into Celsius air these from Celsius into Calvin so that it'll cancel out with our constant right here. Okay, so that gives us final answer. Um, 7.59 times 10 to the fourth Jules per mole or 75.9 killer jewels promote

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