For statements (I) and (II), state for each if they are true or false. (I) A one-molar glucose solution and a one-molar K2SO4 solution boil at the same temperature. (II) A one-molar glucose solution and a one-molar K2SO4 solution contain the same number of dissolved particles per liter of solution. If both are true, state if (II) is a correct explanation for (I).
When a solute is added to a liquid, such as water, to make an aqueous solution, it changes the boiling point and melting point of that liquid. This is because when a liquid boils, it’s because particles in the liquid have enough energy to escape the surface of the liquid. When one of the particles has enough energy to escape the liquid, it becomes vapor. The boiling point is reached when enough of these particles escape the liquid phase and enter the gas phase so that the liquid phase and the gas phase are in equilibrium with each other.
But when we have an aqueous solution with solute particles in liquid water, it’s going to be more difficult for the liquid water to reach the boiling point because the solute particles are in the way of the particles escaping from the liquid phase. Because it’s going to be harder for the particles of the liquid to escape the liquid phase and turn into the gaseous phase in order to reach the boiling point. It’s going to take more energy in order for the solution to boil, which results in the boiling point being higher.
We can calculate the increase in the boiling point due to the addition of a solute using this formula. This formula tells us that the change in boiling point temperature is going to be equal to a van’t Hoff factor times the boiling point constant that’s unique to the solvent times the concentration in molality. Which is moles of the solute divided by kilograms of the solvent. The van’t Hoff factor tells us the number of particles the solute dissociates into. For example, sodium chloride or table salt will disassociate to form sodium ions and chlorine ions when introduced to a liquid. Because sodium chloride will dissociate to form sodium ions and chlorine ions, the van’t Hoff factor for it will be two.
So from what we’ve learned so far, we can see that this boiling point elevation or the increase in the boiling point due to the presence of a solute is related to a couple of different things. This boiling point elevation is related to the concentration of the solute. Which we can not only see from the formula, but we can also recognize. Because if we have more particles of the solute in the solution, it’s going to be harder for the solution to boil. Because those particles are going to get in the way of the liquid particles escaping the liquid phase. And it will also be related to the number of particles the solute creates when it dissociates in the solution. Since, again, the more particles there are, the harder it’s going to be for the particles of the liquid to escape the liquid phase to reach the boiling point.
So we can also see that this change in boiling point due to the presence of the solute is not related to the identity of the solute. It’s only related to the amount of particles that will be in the solution. Statement (I) is asking us to compare the boiling points of two solutions that have the same concentration, one-molar glucose solution and a one-molar K2SO4 solution. So from what we’ve learned about boiling point elevation, since these two solutions have the same concentration, they will have the same boiling point if they can create the same amount of particles when they dissolve in the solution.
Glucose is an organic compound with the formula C6H12O6. When it’s dissolved in a liquid to create an aqueous solution of glucose, it does not dissociate into more particles. This means that 𝑖, the van’t Hoff factor, is going to be equal to one for glucose. Our other solute is K2SO4 or potassium sulfate. When K2SO4 dissolves in a liquid, it will disassociate into two potassium ions and a sulfate ion. That means that for potassium sulfate, the van’t Hoff factor or 𝑖 is equal to three.
So even though our one-molar glucose solution and our one-molar potassium sulfate solution have the same concentration, we wouldn’t expect them to have the same boiling point. Because the potassium sulfate solution creates more particles when it dissociates. So that means it will have a higher boiling point because there are more particles interfering with the liquid’s ability to enter the gas phase. So statement (I) is false. We would expect the one-molar potassium sulfate solution to have a higher boiling point than the one-molar glucose solution.
Our next statement says that our two solutions will contain the same number of dissolved particles per liter of solution. We’ve already seen that this statement is false. Since potassium sulfate dissociates to form three particles and glucose does not disassociate, the potassium sulfate will have more particles per liter of solution. Since statement (I) and statement (II) were both false, we don’t have to answer the last part of the question.