Which solution has the lower freezing point? 11.0 g of methanol in 100. g of water OR 22.0 g of ethanol in 200. g of water?
Use the same procedure as for Sean (by the way it is easier for us if you stick to the same screen name).
mols = grams/molar mass and
m = mols/kg solvent
Substitute and solve for delta T.
Remember new freezing point is 0-delta T.
To determine which solution has a lower freezing point, we need to calculate the freezing point depression for both solutions. The formula for calculating freezing point depression is:
ΔTf = Kf * m
Where:
ΔTf = freezing point depression
Kf = molal freezing point depression constant
m = molality of the solute
First, let's calculate the molality of each solute:
For 11.0 g of methanol in 100 g of water:
1. Calculate the moles of methanol:
moles of methanol = mass / molar mass = 11.0 g / 32.04 g/mol = 0.343 mol
2. Calculate the molality:
molality = moles of solute / mass of solvent (in kg) = 0.343 mol / 0.100 kg = 3.43 m
For 22.0 g of ethanol in 200 g of water:
1. Calculate the moles of ethanol:
moles of ethanol = mass / molar mass = 22.0 g / 46.07 g/mol = 0.477 mol
2. Calculate the molality:
molality = moles of solute / mass of solvent (in kg) = 0.477 mol / 0.200 kg = 2.385 m
Next, we need to determine the freezing point depression constant (Kf) for water. For water, Kf is approximately 1.86 °C/m.
Now, let's calculate the freezing point depression (ΔTf) for each solution:
For 11.0 g of methanol in 100 g of water:
ΔTf = Kf * m = 1.86 °C/m * 3.43 m = 6.38 °C
For 22.0 g of ethanol in 200 g of water:
ΔTf = Kf * m = 1.86 °C/m * 2.385 m = 4.43 °C
Comparing the two freezing point depressions, we can see that the solution with methanol has a higher freezing point depression (6.38 °C) compared to the solution with ethanol (4.43 °C). Therefore, the solution with methanol has the lower freezing point.
To determine which solution has the lower freezing point, we can compare the freezing point depressions caused by each solute.
Freezing point depression is a colligative property, which means it depends on the number of solute particles present rather than the nature of the solute itself. The more solute particles in a solution, the greater the freezing point depression.
To find the freezing point depression, we need to calculate the molality of the solute in each solution. Molality (m) is calculated by dividing the moles of solute by the mass of the solvent (in kilograms).
For the first solution, 11.0 g of methanol (CH3OH) in 100. g of water, we need to calculate the molality of methanol.
Step 1: Calculate the moles of methanol.
Molar mass of methanol (CH3OH) = 32.04 g/mol.
moles of methanol = mass / molar mass
moles of methanol = 11.0 g / 32.04 g/mol
Step 2: Calculate the molality.
molality (m) = moles of solute / mass of solvent (in kg)
mass of solvent (water) = 100. g / 1000 g/kg
molality (m) = moles of methanol / (mass of water in kg)
molality (m) = moles of methanol / 0.100 kg
Now, repeat the steps for the second solution, 22.0 g of ethanol (C2H5OH) in 200. g of water.
Step 1: Calculate the moles of ethanol.
Molar mass of ethanol (C2H5OH) = 46.07 g/mol.
moles of ethanol = mass / molar mass
moles of ethanol = 22.0 g / 46.07 g/mol
Step 2: Calculate the molality.
molality (m) = moles of solute / mass of solvent (in kg)
mass of solvent (water) = 200. g / 1000 g/kg
molality (m) = moles of ethanol / (mass of water in kg)
molality (m) = moles of ethanol / 0.200 kg
Now that we have the molality values for each solution, we can compare them. The solution with the higher molality will have the lower freezing point.
Compare the molality values for methanol (Solution 1) and ethanol (Solution 2). Whichever has the higher value will correspond to the solution with the lower freezing point.
If the molality of methanol (Solution 1) is higher than the molality of ethanol (Solution 2), then Solution 1 (methanol) will have the lower freezing point. However, if the molality of ethanol (Solution 2) is higher, then Solution 2 (ethanol) will have the lower freezing point.