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On a summer day the temperature and (relative) humidity were $95^{\circ} \mathrm{F}$ and $65 $percent, respectively, in Florida. What would be the volume of water in a typical student dormitory room if all of the water vapor were condensed to liquid?

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Assuming a room with dimensions 5ft 6in x 6ft 7 in x 5ft 6in, $$146 \mathrm{mL}$$

Chemistry 102

Chapter 11

Intermolecular Forces and Liquids and Solids

Liquids

Solids

Carleton College

Drexel 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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the first thing I want to do here is ST Simple Assumption. And that is gonna be the room Dimensions went for the purposes of this problem we are going to define as five feet six inches by five feet, six inches by six feet, seven interests. And the reason we've chosen this will become clear after we calculate the volume of the room to make our lives a little bit easier. But this would be pretty typical for what you could possibly see in a dormitory room. So from here, we want to calculate what the volume of the room is gonna be. So that volume is gonna be 5.5 feet times 5.5 feet times 6.6 feet, which equals a total volume of 200 feet. Huge, pretty convenient round number to work with, isn't it? But we are gonna bend in that almost right away, and we're gonna move over to using a volume in meters cute, because that is going to be able to convert over to leaders, which is what we need to be working with. So from our volume here of 200 feet cube, if we convert that over two meters Cube. We're gonna find its five point 679 meters cubed, which is equal to 5679 leaders. Okay, so now that we've got our volume, let's figure out what our temperature is gonna be because they've given our temperature in Fahrenheit. But we're gonna need it in Calvin. So first off, we're going to start by converting that to 35 degrees Celsius, which we can then add 273.15 to to get a temperature of 308 0.15 Kelvin. Okay, so now that we have our temperature, there's just one last thing to figure out. And that is our pressure now, because we are working under relative humidity circumstances, we need to remember that relative humidity is the percentage humidity relative to the standard vapor pressure. So that means that our pressure is going to be 0.65 times the pressure of our vapor, which in this case we do know because it's given to us in table 5.3. So at 35 degrees Celsius, the vapour pressure is 42.18 millimeters Mercury, so we'll take 0.65 times 42 0.18 millimeters, not nanometers millimeters of mercury. And that is gonna give us a final relative humidity of 27 point for two millimeters of mercury. And if we convert that over, that's gonna be equal to 3.65 five k p a. Okay, now that we have that, let's go ahead and set up our ideal gas law, whereas always PV equals and our teeth. This time we are solving for and because we want to know how much water is going to be in this air before we can determine what volume that water would have if it were a liquid so and equals p V over R T, which equals 3.655 k. P a. Times our volume of 5679 leaders divided by 8.314 Jules per mole Calvin times are temperature of 308 0.15 Kelvin, calculate that all out and we see that n is equal to 8.102 animals. Okay, No, let's go ahead and calculate our mess. Remembering that are Mass is just equal to our molar mass. Times are amount. So that's gonna be 18.2 grams Permal times 8.102 Moles for an amount that equals 146 grams. If we go ahead and compute the volume that that is going to be equal to If it was a liquid, well, we just need to remember the density of water, which is one leader per one kilogram Times are mass, which is also equal to one millimeter per one gram times again our mass of 1 46 grams. So our volume is 146 milliliters of water. If you were to condense an average student room at 35 degrees Celsius with 200 cubic feet of air in that room at 65% humidity.

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