4) An aqueous solution is 1.65 m glucose. What are the boiling point and freezing point of this solution?
delta T = Kf*m
Substitute and subtract delta T from 0C to find f.p.
delta T = Kb*m
Substitute and add delta T to 100 C find b.p.
To determine the boiling point and freezing point of a solution, we can use the concept of colligative properties. Colligative properties depend on the number of solute particles in a solution, rather than the type of particles.
The two colligative properties we will focus on are boiling point elevation and freezing point depression. These properties state that the boiling point of a solution will be higher and the freezing point will be lower compared to the pure solvent.
To find the boiling point elevation, we use the equation:
ΔTb = Kb * m
where ΔTb is the boiling point elevation, Kb is the molal boiling point elevation constant, and m is the molality of the solution.
Similarly, to find the freezing point depression:
ΔTf = Kf * m
where ΔTf is the freezing point depression, Kf is the molal freezing point depression constant, and m is the molality of the solution.
First, we need to calculate the molality (m) of the solution.
Molality (m) is defined as the moles of solute divided by the mass of the solvent (in kg). In this case, the solute is glucose, and the solvent is water.
Given that the aqueous solution is 1.65 m glucose, it means that there are 1.65 moles of glucose per kilogram of water.
To calculate the mass of water, we need to know the density of the solution or the volume of the solution, as the density of water is 1 kg/L.
Once we have the mass of water, we can calculate the boiling point elevation and freezing point depression using the respective constant values.
The boiling point elevation constant (Kb) for water is approximately 0.52 °C/m.
The freezing point depression constant (Kf) for water is approximately 1.86 °C/m.
Let's assume the total mass of the solution is 1 kg for simplicity. After determining the mass of water, we can proceed with the calculations.
Now, we have all the necessary information to calculate the boiling and freezing points of the solution:
1. Calculate the molality:
molality (m) = moles of solute / mass of solvent (in kg)
2. Determine the boiling point elevation:
ΔTb = Kb * m
3. Determine the freezing point depression:
ΔTf = Kf * m
4. Calculate the boiling point:
boiling point = boiling point of the solvent (water) + ΔTb
5. Calculate the freezing point:
freezing point = freezing point of the solvent (water) - ΔTf
Please note that the values obtained will be approximate, as we made assumptions about the mass of the solution. Additionally, if you have the actual density or volume of the solution, you can use them to calculate the mass of water more accurately.