two solutions are prepared using the same solute
solution a: 0.27g of the solute disolves in 27.4g of t-butanol
solution b: 0.23g of the solute disolves in 24.8g of cyclohexane
which solution has the greatest freesing point change? show calculations and explain.
To determine which solution has the greatest freezing point change, we can use the equation for freezing point depression:
ΔT = Kf * m * i
where ΔT is the freezing point change, Kf is the cryoscopic constant, m is the molality of the solute (mol solute/kg solvent), and i is the van't Hoff factor.
In this case, since we are given the mass of the solute and the mass of the solvent, we need to calculate the molality of the solute in each solution.
Molality (m) is calculated using the formula:
m = moles of solute / mass of solvent (in kg)
First, we need to convert the mass of the solute and solvent from grams (g) to kilograms (kg).
For Solution a:
Mass of solute = 0.27g
Mass of solvent = 27.4g
Mass of solute (kg) = 0.27g / 1000 = 0.00027kg
Mass of solvent (kg) = 27.4g / 1000 = 0.0274kg
For Solution b:
Mass of solute = 0.23g
Mass of solvent = 24.8g
Mass of solute (kg) = 0.23g / 1000 = 0.00023kg
Mass of solvent (kg) = 24.8g / 1000 = 0.0248kg
Next, we need to calculate the moles of solute using the molar mass of the solute.
Let's assume the molar mass of the solute is M.
For Solution a:
moles of solute = mass of solute / molar mass
moles of solute = 0.00027kg / M
For Solution b:
moles of solute = mass of solute / molar mass
moles of solute = 0.00023kg / M
Since we are comparing the solutions, it is not necessary to calculate the value of M.
Now, we can calculate the molality (m) for each solution using the moles of solute and the mass of solvent.
For Solution a:
m = moles of solute / mass of solvent (in kg)
m = (0.00027kg / M) / 0.0274kg
For Solution b:
m = moles of solute / mass of solvent (in kg)
m = (0.00023kg / M) / 0.0248kg
Finally, let's compare the freezing point changes (ΔT) for each solution.
The ΔT is proportional to the molality (m) and the van't Hoff factor (i), but since the solute is the same in both solutions, the van't Hoff factor remains constant.
Therefore, the solution with the greatest molality (m) will have the greatest freezing point change (ΔT).
By comparing the molality (m) values calculated for each solution, we can determine which one has the greater freezing point change.
To determine which solution has the greatest freezing point change, we can use the formula for calculating the freezing point depression:
∆Tf = Kf * m
Where:
∆Tf is the freezing point change
Kf is the cryoscopic constant, which is a property of the solvent
m is the molality of the solute in the solution
First, let's calculate the molality of the solute in each solution.
Molality (m) is defined as the number of moles of solute per kilogram of solvent. We can calculate it using the following formula:
m = n / m (kg)
Where:
n is the number of moles of solute
m (kg) is the mass of the solvent in kilograms
Now, let's calculate the number of moles of solute in each case:
For Solution A:
Mass of solute (0.27g) ÷ molar mass of solute = number of moles
(Make sure you know the molar mass of the solute to perform this calculation)
For Solution B:
Mass of solute (0.23g) ÷ molar mass of solute = number of moles
Next, let's calculate the molality for each solution:
For Solution A:
m = number of moles ÷ mass of solvent (27.4g of t-butanol)
For Solution B:
m = number of moles ÷ mass of solvent (24.8g of cyclohexane)
Now that we have the molality (m) for both solutions, we need the cryoscopic constant (Kf) for each solvent. The cryoscopic constant is specific to each solvent and can be obtained from reference tables or textbooks.
Finally, we can calculate the freezing point change (∆Tf) using the formula:
∆Tf = Kf * m
For Solution A:
∆Tf (A) = Kf (t-butanol) * m (A)
For Solution B:
∆Tf (B) = Kf (cyclohexane) * m (B)
By comparing the ∆Tf values for both solutions, we can determine which one has the greatest freezing point change. The solution with the higher ∆Tf value will have the greater magnitude of the freezing point depression.
delta T = Kf*m
molality = mols/kg solvent.
I think the easy way to do this is to make up a number for the molar mass of the solute. It doesn't matter what number is used since it is the same in both solvents. I think 10 is a good number.
m for t-butanol is (0.27/10)/0.027 = 0.98 or so but you can do it more accurately.
Then m for cyclohexane is
(0.23/10)/0.0248 = 0.93 or so.
Which of those times Kf will produce the larger delta T value.If your prof is picky about significant figures you want to be careful with the explanation part and not use too many s.f.