Assuming 100% dissociation, calculate the freezing point and boiling point of 2.44 m Na2SO4(aq)
delta T = i*Kf*m for freezing point, subtract 0 C - delta T.
i for Na2SO4 = 3
delta T = i*Kb*m for boiling point add delta T + 100 = ?
To calculate the freezing point and boiling point of a solution, we need to use the concept of colligative properties. Colligative properties depend on the number of solute particles, but not their identity.
First, we need to determine the van't Hoff factor (i) for Na2SO4(aq). The van't Hoff factor can be defined as the number of particles into which one formula unit of the solute dissociates in the solution.
For Na2SO4, it dissociates into 3 ions when it is 100% dissociated in water: 2 Na+ ions and 1 SO4- ion. Therefore, the van't Hoff factor (i) for Na2SO4 is 3.
Now, we can use the following formulas to calculate the freezing point depression and boiling point elevation:
1. Freezing point depression (∆Tf): ∆Tf = Kf * molality * i
2. Boiling point elevation (∆Tb): ∆Tb = Kb * molality * i
Where:
- Kf is the cryoscopic constant (freezing point depression constant) for the solvent.
- Kb is the ebullioscopic constant (boiling point elevation constant) for the solvent.
- molality is the concentration of the solute in moles per kilogram (mol/kg).
- i is the van't Hoff factor.
For water, the cryoscopic constant (Kf) is 1.86 °C/m, and the ebullioscopic constant (Kb) is 0.512 °C/m.
Given that the molality (m) of the Na2SO4(aq) solution is 2.44 m and the van't Hoff factor (i) is 3, we can now calculate the freezing and boiling point changes.
1. Freezing point depression (∆Tf): ∆Tf = 1.86 °C/m * 2.44 m * 3
2. Boiling point elevation (∆Tb): ∆Tb = 0.512 °C/m * 2.44 m * 3
Calculating these values will give us the freezing point depression and boiling point elevation of the solution. However, to determine the actual freezing point and boiling point, we need to apply these values to the known values of the pure solvent.
For example, the freezing point of pure water is 0 °C. So, we would subtract the calculated freezing point depression (∆Tf) from 0 °C to find the freezing point of the Na2SO4(aq) solution.
Similarly, the boiling point of pure water is 100 °C. So, we would add the calculated boiling point elevation (∆Tb) to 100 °C to find the boiling point of the Na2SO4(aq) solution.
It's important to note that these calculations assume ideal behavior and complete dissociation of the solute, which may not always be the case in reality.