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A closed vessel of volume $9.6 \mathrm{L}$ contains $2.0 \mathrm{g}$ of water. Calculate the temperature (in $^{\circ} \mathrm{C}$ ) at which only half of the water remains in the liquid phase. (See Table 5.3 for vapor pressures of water at different temperatures.)

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$$328 \mathrm{K}=55^{\circ} \mathrm{C}$$

Chemistry 102

Chapter 11

Intermolecular Forces and Liquids and Solids

Liquids

Solids

Carleton College

Rice University

University of Kentucky

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 to solve this problem, we need to think about two different things. First of all, as the temperature changes, so will the vapor pressure of the water. But once the paper is a vapor, it's going to follow the ideal gas law, which means that we can put the pressure. We can relieve the pressure in the temperature. Using PV equals NRT to with the table they gave us. They give us the pressures and the temperatures that relate to each other, so let's find a ratio for those. So let's say, still has divide both sides by t be over tee times v equals and r. The divide by the and puberty equals and R divided by V, and I tell us that we start off with two grams of water and half of that is going to be in the vapor phase. So then our gas is going to be one gram of water, and so that's going to equal 1/18 molds. Water. That's the end. Now they give us are in millimeters of mercury, so we're going to use our millimeters mercury, which is going to be 62 point 363 leaders times millimeters of mercury divided by most times cabins and the volume that they give us is nine 0.6 leaders. Now this is going to give us a pressure to temperature ratio, which we can look for in our table for a match. So if we go ahead and solve this, it's going to give us 0.36 05 millimeters of mercury per Kellman, right? So now let's go over to the table. So these the different pressures and temperatures, their temperatures are in Celsius. So we need to make sure that we change those into Kelvin by adding 273 teach. And now we need to find the pressure to temperature ratio of each one because that's the thing that we solved for. And there's a few different ways to solve this problem. This is just the way that I'm doing it. For each side we divide the pressure, the temperature and Kelvin and we see right here at a temperature of 55 degrees Celsius. That gives us the ratio 0.359 which is the closest to ratio 0.36 So that means that at a temperature of 55 degrees Celsius, 1/2 of our water would have evaporated

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