Osmotic Pressure Problems - Chemistry - Colligative Properties, Osmosis
INSTRUCTOR: In this video, we're going to go over osmotic pressure. So here we have a glass U tube. And on the left, we have water on the left side. This is pure H2O. And on the right side, we still have water, but we have a solution, let's say sodium chloride. So basically, this is a saltwater solution. Now, this red line represents the semi-permeable membrane. A semi-permeable membrane allows some things to pass through but not everything. So this particular membrane is going to allow water to pass through but not the solute ions, such as sodium and chloride.
Now, water is going to flow from a region of high osmotic potential to a region of low osmotic potential, the same way as a ball travels from a high position to a low position. Water is going to flow from a region of high concentration to a region of low concentration. On the left side, we have a high concentration of solvent. On the right side, we have a low concentration of solvent. Now, keep in mind, on the right side, the concentration of solute is high because it's very salty on the right side. There's a lot of solute ions, which means that the concentration of the solvent is low.
So water is going to flow from a region of high solvent concentration or high H2O concentration to a region of low solvent concentration. So it's going to flow from left to right, from the pure solvent towards the solution. So as a result, the mass on the right side will increase. So the height of this column will increase as well. And you can see that on the right side. So osmosis is the driving force that causes the water molecules to travel from left to right.
Now, eventually, the weight of this fluid is going to cause the solution to reach a state of equilibrium. Gravity is going to apply a downward force, which is going to oppose the direction of the driving force provided by osmosis. So once these two forces are equal and opposite in direction, once they cancel out, then this side will no longer increase in height. The solution or the system will reach a state of equilibrium.
Now, the pressure that's required to basically push back the solvent molecules to the left such that we can have the same height as we did before, if you apply a force, you can force the water molecules back towards the left. And the pressure required to cause the situation or to cause the U tube to look like this, that pressure is the osmotic pressure. Pressure is defined by force over area, defined by this equation. So as you apply a force over this area, you are exerting the pressure. And the pressure required to make the height of the two liquid levels equal is the osmotic pressure.
Now, you can come up with the osmotic pressure equation from the ideal gas law equation, PV=nRT. If you divide both sides by the volume, you'll see that pressure is mols divided by volume times RT. And we know that the solution concentration molarity is equal to mols of solute divided by the liters of solution. So therefore, the osmotic pressure, which has the symbol pi, is equal to the molarity concentration times RT. And of course, if you have, let's say, an ionic solute, you need to multiply this by the van't Hoff factor. So for sodium chloride, which has two ions, the van't Hoff factor is 2. For magnesium chloride, which contains three ions, the van't Hoff factor is 3.
Let's try this problem. Calculate the osmotic pressure of a 300 milliliter solution made by dissolving 80 grams of sodium hydroxide at 27 degrees Celsius. So let's use the equation pi is equal to MRTi. So we need to find the molarity of the solution. So let's convert grams into mols. And let's divide mols by liters. Keep in mind, molarity is the mols of solute divided by the liters of solution.
So we have 80 grams of sodium hydroxide. And we need to find the molar mass. So using the periodic table, the molar mass of sodium hydroxide is going to be 23 for Na plus 16 for O and 1 for hydrogen, which is 40 grams per mol. So 1 mol of sodium hydroxide has a mass of 40 grams. Therefore, 80 grams of NaOH equates to 2 mols. So we have two mols of sodium hydroxide.
Next, let's divide it by the liters of solution. So how can we convert 300 milliliters into liters? To convert milliliters into liters, divide by 1,000. And 1 liter is equal to 1,000 milliliters. To divide 300 by 1,000, simply move the decimal point three units to the left. So this is 0.3 liters. So 2 mols divided by 0.3 liters. 2 divided by 0.3 is about 6.67. So that's the molarity of the solution.
Now that we have the molarity of the solution, let's calculate the osmotic pressure. So it's going to be the molarity, which is 6.67, times R, which is the gas constant 0.08206. The temperature has to be in Kelvin. Right now, it's in Celsius. So let's add 273 to 27 degrees Celsius. This is going to be 300 Kelvin. And sodium hydroxide contains two ions, the sodium plus cation and the hydroxide anion. So therefore, the van't Hoff factor is equal to 2.
6.67 times 0.08206 times 300 times 2 is equal to 328.4. Now, what is the unit of osmotic pressure? Is it torr, atm, millimeters of mercury, which one is it? It turns out that our answer is units of atm. So we have a pretty large number. Now let's understand the units behind the equation. Molarity has the units mols per liter. And the gas constant R is 0.08206. And the units is liters times atm divided by mols times Kelvin. And a temperature has the unit Kelvin. So as you can see, the Kelvin unit will cancel, the mols will cancel, and liters will cancel, which means that pi has the unit atm. So if you use the gas constant 0.08206, the osmotic pressure will be in atm.
It turns out that if you dissolve a solute in a solution, and if you measure the osmotic pressure at a certain temperature or at any temperature, you can use that information to determine the molar mass of the sun. So consider the problem that we have. 9 grams of nonelectrolyte solute was dissolved in enough water to produce a 500 milliliter solution. The osmotic pressure is 1871.1 torr measured at 300 Kelvin. What is the molar mass of the solute?
So the equation is pi is equal to MRTi. Now, what is the van't Hoff factor of the solute? Is it 1, 2, 3, or 4? How do we know since we don't know the formula of the solute? Now, the problem stated that it was a nonelectrolyte solute. So it's not ionic. Ionic compounds, when dissolved in water, conduct electricity. So therefore, they're electrolytes. When you dissolve a nonelectrolyte in water, let's say like sugar, it does not conduct electricity. That's why it's called a nonelectrolyte.
Nonelectrolytes have a van't Hoff factor of 1, since they don't ionize in water. They don't split off into two or three ions. So now that we know the van't Hoff factor, we can solve for what we're looking for. Now, in order to find the molar mass of the solute, we need to know how many moles of solute is in the solution. The molar mass, or molecular weight, is the number of grams divided by the number of moles. It's the ratio between mass and mols.
We already know the mass of the solute. It's 9 grams. All we need to do is find the mols. And this is what we're missing. If we can calculate the mols of the solute, then we could find the molar mass. Now, how can we calculate the mols of the solute? The only thing that's in this equation that can help us is the molarity, because molarity is defined as mols over liters. So let's calculate the molarity of the solution.
Now, what is the osmotic pressure in this problem? Notice that the units is measured in torr. If we're going to use the gas constant 0.08206 for R, the unit has to be an atm. So let's begin by converting torr into atm. It turns out that 1 atm is equal to 760 units of torr. So if we divide these two numbers, this will give us a pressure of 2.462 atm. So this is the number that we need to plug into the equation, unless you replace that with pi.
Now let's solve for the molarity. Let's replace R with 0.08206. And the Kelvin temperature is 300. The van't Hoff factor is 1. So let's solve for M. 2.462 divided by 0.08206, that's 30. And then divide it by 300. You get 0.1. So the molarity of the solution is 0.1, which is really 0.1 mols per liter. And we have the volume of the solution. So using the volume and the molarity, we can calculate the mols. So we have 500 milliliters of solution. Let's convert that to liters.
And 1 liter is equal to 1,000 milliliters. And using the molarity, we can convert from liters to mols. So there's 0.1 mols of solute for every one liter of solution. So therefore, 500 milliliters of solution, which is 0.5 liters, should have half of 0.1, which is 0.05. 500 divided by 1,000 times 0.1 is equal to 0.5 mols of solute. Now that we have the mols of solute, we can calculate the molar mass. So the molar mass, or the molecular weight, is going to be 9 grams divided by 0.05 mols. So the molar mass is 180 grams per mol. This is the answer.