Which of the following solutes dissolved in 1000 g of water would provide a solution with the LOWEST freezing point?
A. 0.030 mole urea, CO(NH2)2
B. 0.030 mole acetic acid, CH3COOH
C. 0.030 mole ammonium nitrate, NH4NO3
D. 0.030 mole calcium sulfate, CaSO4
E. 0.030 mole barium chloride, BaCl2
To determine which of the solutes would provide a solution with the lowest freezing point, we need to consider the concept of freezing point depression.
The freezing point depression is directly proportional to the concentration of solute particles in a solution. Therefore, the solute that will result in the lowest freezing point will have the highest number of solute particles.
To find the number of solute particles, we can use the equation:
Number of particles = moles of solute × number of particles per mole
1. For urea (CO(NH2)2):
Number of particles = 0.030 mol × 1 = 0.030 particles
2. For acetic acid (CH3COOH):
Number of particles = 0.030 mol × 1 = 0.030 particles
3. For ammonium nitrate (NH4NO3):
Number of particles = 0.030 mol × 2 = 0.060 particles (1 mole of NH4NO3 produces 2 moles of particles)
4. For calcium sulfate (CaSO4):
Number of particles = 0.030 mol × 3 = 0.090 particles (1 mole of CaSO4 produces 3 moles of particles)
5. For barium chloride (BaCl2):
Number of particles = 0.030 mol × 3 = 0.090 particles (1 mole of BaCl2 produces 3 moles of particles)
Comparing the number of particles, we find that ammonium nitrate (NH4NO3), calcium sulfate (CaSO4), and barium chloride (BaCl2) will provide solutions with the lowest freezing point.
Therefore, the correct answer is: C. 0.030 mole ammonium nitrate, NH4NO3, D. 0.030 mole calcium sulfate, CaSO4, and E. 0.030 mole barium chloride, BaCl2.
To determine which solute will provide a solution with the lowest freezing point, we need to understand the concept of freezing point depression.
Freezing point depression occurs when a solute is dissolved in a solvent, such as water. The presence of the solute lowers the freezing point of the solvent. The extent of the freezing point depression depends on the concentration of the solute. The greater the concentration of the solute, the greater the lowering of the freezing point.
To compare the freezing point depression caused by each solute, we can use the equation:
∆Tf = Kf * m
Where:
- ∆Tf is the change in freezing point
- Kf is the molal freezing point depression constant of the solvent
- m is the molality of the solute (moles of solute per kilogram of solvent)
In this case, we are given the same number of moles (0.030) for each solute dissolved in 1000 grams of water. However, to calculate molality, we need to convert grams to kilograms.
Step 1: Convert 1000 grams to kilograms:
1000 g = 1000 / 1000 = 1 kg
Step 2: Calculate the molality (m) for each solute:
For solute A:
m = (0.030 mol) / 1 kg = 0.030 mol/kg
For solute B:
m = (0.030 mol) / 1 kg = 0.030 mol/kg
For solute C:
m = (0.030 mol) / 1 kg = 0.030 mol/kg
For solute D:
m = (0.030 mol) / 1 kg = 0.030 mol/kg
For solute E:
m = (0.030 mol) / 1 kg = 0.030 mol/kg
Since the molality (m) is the same for all solutes, the freezing point depression will be directly proportional to the molal freezing point depression constant (Kf) of the solvent.
Different solvents have different Kf values. In this case, since we are dealing with water as the solvent, the Kf value is 1.86 °C/m. The solute that will provide the solution with the lowest freezing point is the one with the greatest molal freezing point depression constant.
Comparing the solutes given:
A. Urea (CO(NH2)2) does not have a known freezing point depression constant.
B. Acetic acid (CH3COOH) does not have a known freezing point depression constant.
C. Ammonium nitrate (NH4NO3) does not have a known freezing point depression constant.
D. Calcium sulfate (CaSO4) does not have a known freezing point depression constant.
E. Barium chloride (BaCl2) does not have a known freezing point depression constant.
Since we do not have the freezing point depression constants for each solute, we cannot determine which solute will provide the solution with the lowest freezing point.
In this case, none of the options provided can be determined to have the lowest freezing point based on the given information.
delta T = i*K*m
The largest i*m will give the largest delta T.