The Colligative Properties - Online Tutor, Practice Problems & Exam Prep

Colligative properties describe how a pure solvent changes when a solute is added. Boiling point and osmotic pressure increase, while freezing point and vapor pressure decrease with more solute. The van't Hoff factor (I) indicates the number of ions produced from a solute: ionic compounds dissociate into multiple ions, while covalent compounds remain intact, giving I a value of 1. Osmolarity and osmolality, calculated as $\mathrm{Osmolarity}=IM$ and $\mathrm{Osmolality}=Im$, help determine solute effects on boiling and freezing points.

The Colligative Properties Concept 1

Now, the 4 colligative properties discuss what happens to a pure solvent as a solute is added to it. So they're discussing what happens as our pure solvent transitions into a solution because remember when we add solute to a solvent, it becomes a solution. We're going to say as solute is added to a solvent, some colligative properties will increase while others will decrease. Now, here when we take a look at boiling point and osmotic pressure, we're going to say that these two colligative properties will increase the more solute we add to our solvent. Conversely, we're going to say that our freezing point and vapor pressure, the more solute I add to my solvent the lower they go. Okay. So just remember these are the effects of adding solute to a pure solvent. Now, let's discuss these four colligative properties a little bit more closely.

So, boiling point, remember, boiling point is just the temperature where we're going to have an equilibrium between our liquid and gas phases. Alright. So remember, we have our liquid becoming a gas, so vaporization, then we have our gas condensing back into our liquid. Boiling point is when there's an equilibrium between these two changes. Freezing point, well, freezing point is where there's an equilibrium between our solid phase and our liquid phase. So going from solid to liquid, we have melting or fusion occurring, and then going from liquid to solid we have freezing occurring. Freezing point is when both of these phase change properties or processes are happening at the same time, so they are at equilibrium with one another.

Now, vapor pressure, we're going to say here that vapor pressure is basically the pressure exerted by a gas at the surface of a liquid. And we're going to say this is measurable also again the whole idea of being at equilibrium. Finally, we have osmotic pressure. Osmotic pressure is just the force that drives osmosis, remember the movement of water, from an area of low concentration to an area of high concentration. So here, we have an illustration where this side is more concentrated and so water would rush towards this side here. What does this effect have? Well, the right side, the water level will be lower and the left side, the water has increased because again water moved from an area of low concentration to an area of high concentration.

Alright, so we'll go a little bit more in detail in terms of the mathematical applications of each of these colligative properties, but for now realize that they have to do with our transition from a pure solvent to a solution through the addition of some type of solute.

The Colligative Properties Concept 2

Now the van't Hoff factor, which uses the variable I, equals the number of ions produced from dissolving a soluble solute. When we talk about solutes, we group them as being either ionic or covalent in nature. Remember, ionic compounds are composed of a positive ion connected to a negative ion. The positive ion can be in the form of the ammonium ion or a metal, and the negative ion will be in the form of a nonmetal. Let's take a look at three ionic compounds: sodium hydroxide, ammonium carbonate, and aluminum sulfate. Each one, because they're ionic, can break up into ions. Sodium hydroxide breaks up into Na+OH-, which breaks up into 2 ions. The van't Hoff factor in this case is the number of ions produced when a soluble solute dissolves, so here, I equals 2. Ammonium carbonate breaks up into 2 ammonium ions plus 1 carbonate ion, for a total of 3 ions. Hence, I equals 3. Aluminum sulfate breaks up into 2 aluminum ions and 3 sulfate ions, for a total of 5 ions. Therefore, I equals 5.

On the other hand, covalent compounds are just compounds composed only of nonmetals. Because of this, they are nonvolatile and nonionizable, or non-electrolytes. For example, glucose, chlorine, methanol, and urea are all covalent in nature, and therefore they are nonvolatile, which means they don't break up into ions, and they're non-electrolytes, which also means they don't break up into ions. Consequently, I equals 1. Technically, zero ions are formed, so they just stay in the form they're in, which still counts. I for them would equal 1. It's important to correctly identify ionic and covalent compounds, as ionic compounds break up into ions, and it's crucial to get the number correct for I, while for covalent solutes, they don't break up into ions, so their I will always just be 1 in its value.

The Colligative Properties Example 2

Which of the following compounds will have the largest value for the Van't Hoff factor? Alright. So for the first one, we have aluminum chloride, which is an ionic compound, so it breaks up into ions. It's composed of 1 aluminum ion and 3 chloride ions. So in total that's 4 ions, so I equals 4. For the next one, it's covalent because it's only nonmetals together, so I equals 1. For the next one, it's ionic again because zinc is a metal, oxygen is a nonmetal. So it breaks up into zinc ion and oxide ion. That's 2 ions total, so I equals 2. Next we have ammonium, which is NH3. It's covalent because it's only nonmetals, so I equals 1. And then we have P2S5, which is also covalent. It's only nonmetals together, so I equals 1. We can see the one with the greatest Van't Hoff factor value is a, I equals 4 for aluminum chloride. So here the answer would be option a.

The Colligative Properties Concept 3

So remember, for the colligative properties, the more solute you add, the more they can be affected. Boiling point and osmotic pressure will keep going up, freezing point and vapor pressure will go down. Now the solute amount added equals the number of ions of that solute, well, remember that the van't Hoff factor, so that's I, times the concentration of that compound or solute. Now this concentration could represent either molarity or molality, and if we're incorporating ions with molarity or molality, then they become osmolarity and osmolality. So remember, osmolarity is ionic molarity, osmolality is ionic molality. Alright.

So for osmolarity, solute formula, we're going to say osmolarity, which is the amount of solute, equals I, the number of ions for the solute, times the molarity of the compound as a whole. Osmolality is the same kind of idea. It equals I, the number of solute ions that we have, times the molality of the compound. These two formulas will help us determine the amount of solute that a solute given to us represents. And that'll help us determine which one will have the highest boiling point or which one will have the lowest freezing point, etcetera. So keep this in mind. We use osmolarity and osmolality to determine the amount of solute that is.

The Colligative Properties Example 3

What is the ionic molality of potassium ions in a 1.18 molal solution of potassium phosphate? Alright. So we want the ionic molality of potassium ions. Alright. So we're going to say ionic molality is just osmolality. Here it will equal the ions of potassium ions times the molality of the compound. If we break this up, it breaks up into 3 potassium ions plus 1 phosphate ion. So how many potassium ions do we have? We have 3. That would be 3 times the molality of the entire compound, which is 1.18 mol/kg. So, 3×1.18 molal gives us the ionic molality of potassium ions. That would give us 3.54 moles of potassium ions.

Which of the following compounds will have the highest boiling point?

• A. 0.10 M sucrose
• B. 0.10 M AgCl
• C. 0.25 M NH₄NO₃
• D. 0.45 M pure water

Which of the following compound will have the highest vapor pressure?

• A. 0.45 m dinitrogen pentoxide
• B. 0.10 m aluminum chloride
• C. 0.50 m iron (III) perchlorate
• D. 0.15 m calcium phosphate
• E. 0.30 m Potassium sulfide

Here’s what students ask on this topic:

What are the four colligative properties and how do they change with the addition of a solute?

The four colligative properties are boiling point, freezing point, vapor pressure, and osmotic pressure. When a solute is added to a pure solvent, the boiling point and osmotic pressure increase, while the freezing point and vapor pressure decrease. Boiling point elevation occurs because the solute disrupts the liquid phase, requiring more energy (higher temperature) to reach equilibrium between liquid and gas phases. Freezing point depression happens because the solute interferes with the formation of a solid phase, lowering the temperature needed for equilibrium between solid and liquid phases. Vapor pressure lowering occurs as the solute reduces the number of solvent molecules at the surface, decreasing the pressure exerted by the vapor. Osmotic pressure increases as the solute creates a concentration gradient, driving water movement through a semipermeable membrane.

What is the van't Hoff factor and how is it determined for ionic and covalent compounds?

The van't Hoff factor (i) represents the number of ions produced when a solute dissolves in a solvent. For ionic compounds, it is determined by the total number of ions formed upon dissociation. For example, NaOH dissociates into Na⁺ and OH^-, giving i = 2. Ammonium carbonate (NH₄)₂CO₃ dissociates into 2 NH₄⁺ and 1 CO₃^2-, giving i = 3. For covalent compounds, which do not dissociate into ions, the van't Hoff factor is always 1. Examples include glucose and urea, which remain intact in solution, thus i = 1.

How do osmolarity and osmolality differ and how are they calculated?

Osmolarity and osmolality both measure the concentration of solute particles in a solution, but they differ in their basis of measurement. Osmolarity is the number of solute particles per liter of solution, while osmolality is the number of solute particles per kilogram of solvent. They are calculated using the van't Hoff factor (i) and the concentration of the solute. The formulas are:

$\mathrm{Osmolarity}=iM$

$\mathrm{Osmolality}=im$

where M is molarity and m is molality. These values help determine the effect of solutes on colligative properties like boiling and freezing points.

Why do boiling point and osmotic pressure increase with the addition of a solute?

Boiling point increases with the addition of a solute because the solute particles disrupt the solvent's liquid phase, requiring more energy (higher temperature) to reach the equilibrium between the liquid and gas phases. This phenomenon is known as boiling point elevation. Osmotic pressure increases because the solute creates a concentration gradient across a semipermeable membrane, driving the movement of water from an area of low solute concentration to an area of high solute concentration. This pressure, known as osmotic pressure, is the force needed to stop this water movement, and it increases as more solute is added.

How does the addition of a solute affect the freezing point and vapor pressure of a solvent?

The addition of a solute lowers the freezing point of a solvent, a phenomenon known as freezing point depression. This occurs because the solute particles interfere with the formation of the solid phase, requiring a lower temperature to achieve equilibrium between the solid and liquid phases. Vapor pressure is also lowered when a solute is added. This is because the solute particles reduce the number of solvent molecules at the surface, decreasing the rate at which solvent molecules escape into the vapor phase, thus lowering the vapor pressure.