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A very long pipe is capped at one end with a semipermeable membrane. How deep (in meters) must the pipe be immersed into the sea for freshwater to begin to pass through the membrane? Assume the water to be at $20^{\circ} \mathrm{C}$ and treat it as a $0.70 \mathrm{M} \mathrm{NaCl}$ solution. The density of seawater is $1.03 \mathrm{g} / \mathrm{cm}^{3}$ and the acceleration due to gravity is $9.81 \mathrm{m} / \mathrm{s}^{2}$.

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$34.5 \mathrm{m}$

Chemistry 102

Chapter 12

Physical Properties of Solutions

Solutions

University of Central Florida

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03:58

In chemistry, a solution is a homogeneous mixture composed of two or more substances. The term "solution" is also used to refer to the resultant mixture. The solution is usually a fluid. The particles of a solute are dispersed or dissolved in the solvent. The resulting solution is also called the solvent. The solvent is the continuous phase.

05:06

In physics and thermodynamics, the natural tendency of a system to change its state is its tendency to increase the entropy of the system. It is a measure of the disorder in a system.

03:01

A very long pipe is capped…

02:40

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02:02

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01:14

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01:45

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01:04

A waterproof rubber ball i…

02:58

Water flows through a Vent…

okay, in this question, we have a very, very, very long tube, Okay? And at the end of this tube, who have a membrane, let me draw here little main brain right here. So only water can get through this membrane, and we're going to submerge this tube this pipe into seawater. Okay, so what's gonna happen is the, um ah. First you might think what water will get into the tube. Right. But there is a pressure that it's keeping in their water outside. And that's the osmotic pressure, right? Because if any water gets through the membrane, it will be pure water in here. So the pure water won't be happy here. It will one to go back to the more council treated environment, which is the seawater. Okay, so in order to overcome this, the pressure off the water column. So here we have a pressure due to the column of water, this pressure has to be greater than the osmotic pressure. Okay, so I wonder task in this problem this first to find the osmotic pressure off the seawater and then compute how deep this pipe has to go in order to, um, the two pressures to be equal, and then the pure water be allowed to enter the pipe. Okay, so first of all, let's compute the osmotic pressure. We know that the formula C r t I Okay, um, let's plug in the numbers. So C is the concentration most per leader we have that the problem told us that 0.7 moles per leader. Okay, Our I'm gonna use zero a two a t m. Later. Kelvin Mo. And then the temperature is 20 Celsius. That will be 293 Calvin and I remember for a see how you should have memorized by now that this is a close to Okay, so if you compute the osmotic pressure, you should get something around 33.7 80 m. So it's a very It's a huge pressure. Okay, So you would think to overcome this huge pressure, you would need to go really, really being deep. Okay, The next step. Now, what's the formula for the pressure of the water column? The density times the height off that column of water, which in our case, it means the depth. Okay. In the gravity, we have the G and we have the pressure We're just computed so we can find age by taking P and dividing by D N g. So let's try to do this so age will be equal 33.7 a. T. M. Okay. And then you divide this by 1.3 grams person centimeters to the mind. Three. And then you put the gravity meters per second and manages to and then you you should see a problem here. The units are all awkward. Okay, So when you have a situation like this, the most, um, safe thing to do is to fall back to S I units. So this is a sigh Units. The gravity's in S I units, the density and the pressure is not so Let's convert them 1st 33.78 p. M. Let's convert that to Moscow. So we have one A. This value here. Big number 1013 to 5. Pascal poorer 1 80 m. That would be a the converting factor here. Okay. And if you do this computation, you will find something. The big number two, 3.41 to the times 10 to the sixth. All right. What's the units here? does Haskell, which is equivalent, Remember, pass cow is Newton per meter square. Okay, we can further we can further decomposed that by remembering that Newton is mass times acceleration. So mass is kilograms. Acceleration is meters per second square. So minus During this case, all the I'm saying minus two because instead of putting down here, I'm putting up here. That's why I hope that's clear in, um and we have them meter to the minus two that we had already. Okay, so the final units decomposed to basic s I units is kilograms second, minus two meter minus one. Okay, great. Now let's do the same for density. So the density is 1.3 grams per centimeter. A cube came. So to do this, converting the way I like to do. I don't know What's the conversion to centimeter cubic two meters meter or cubic. But I do know that 100 centimeters it's equivalent to one meter. So you take this conversion factor here and raised to the third. Okay? Because then you have centimeters to the third meters to the third. Okay. We also won the grams to being kilograms. So one kilogram is equivalent to 100 grips who, if you do this conversion, you see the, um, things will work out for you. Great. We'll have kilograms, Prue meter to the third. And that is 1030 kilograms. Neither to the third. Cool. All this labor. Now we can go back and plugging the plug. Everything into the in the former for the height. Okay, so that would be the pressure. So our pressures right here we converted. So three point for 1 10 to the sixth. And the units are kilograms permit er per centimeter of minus two. Okay, um, then we have the density killer grounds meter to the minus three. And then we have the gravity, which is, uh, meters second minus two. Okay, second minds to goes away. Kilograms use way, and then the meters. What's gonna happen that you have this meter minus three here? Uh, so, since it has this minus three, you can actually throw with upwards and flip the sign. So let's just work out the units here. This meter goes down meter to one. This meter goes up meeting to the third. This meter just stays there. Meter. So three now we have three minus two. Okay, so the final unit will be just meter. So everything that we did were 1000 yen. Okay, Uh, usually, if you really use everything s I units, you don't have to worry, because you're gonna get a SA unit radiant. But it's always due to do the senator check if you want to make sure that your answer is consistent. All right, so just compute this. And I got a very big number 337 meters, so that's how deep that pipe would have to be.

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