a student determines the molar mass of methanol by the method used in this experiment. she found that the equilibrium temperature of a mixture of ice and pure water was .4 degrees Celsius on her thermometer. when she added 10g of her sample to the mixture, the temperature, after thorough stirring, fell to -5.4 degrees Celsius. she poured off the solution through a screen into a beaker. the mass of the solution was 101.8 g.
what was the freezing point depression?
what was the molality of the methanol?
how much methanol was in the decanted solution?
how much water was in the decanted solution?
how much methanol would there be in the solution with 1 kg of water, with methanol at the same concentration as she had in her experiment?
what did she find to be molar mass of methanol, assuming she made the calculation properly?
To determine the answers to these questions, we need to understand the concept of freezing point depression and the equation that relates it to molality. Let's break it down step by step:
1. What is freezing point depression?
Freezing point depression is the phenomenon where the freezing point of a solvent is lowered when a non-volatile solute is added to it. The amount by which the freezing point is lowered depends on the molality of the solute in the solution.
2. How to calculate freezing point depression?
The equation to calculate freezing point depression is ∆T = K_f x m, where ∆T is the freezing point depression, K_f is the cryoscopic constant (a property of the solvent), and m is the molality of the solute.
3. What is the molality of the methanol in the solution?
The molality (m) is calculated by dividing the moles of the solute by the mass of the solvent (in kg). In this case, the solvent is water, and the solute is the methanol. To calculate the molality, we first need the moles of methanol.
The moles of methanol can be calculated using the molar mass of methanol and the mass of methanol used in the experiment. The molar mass of methanol (CH3OH) is 32.04 g/mol.
To calculate the moles, we divide the mass of methanol (10 g) by the molar mass of methanol (32.04 g/mol):
moles of methanol = 10 g / 32.04 g/mol
4. What is the freezing point depression (∆T)?
To calculate the freezing point depression, we need the change in temperature (∆T) by subtracting the equilibrium temperature of the mixture (0.4 °C) from the final temperature of the solution (-5.4 °C):
∆T = -5.4 °C - 0.4 °C
5. What is the molality of the methanol in the solution?
Using the molality equation, ∆T = K_f x m, we can rearrange it to solve for molality (m):
m = ∆T / K_f
You will need to find the cryoscopic constant (K_f) for water, which is 1.86 °C/m.
6. How much methanol was in the decanted solution?
To find the amount of methanol in the decanted solution, we need to convert the mass of the solution (101.8 g) to moles using the molar mass of the methanol (32.04 g/mol).
7. How much water was in the decanted solution?
To find the amount of water in the decanted solution, we subtract the mass of methanol from the mass of the solution.
8. How much methanol would there be in a solution with 1 kg of water?
To determine the amount of methanol in a solution with 1 kg of water, we need to use the same molality as in the experiment. First, convert 1 kg of water to grams. Then, use the molality equation to find the mass of methanol needed.
9. What is the molar mass of methanol?
The molar mass of methanol is found by dividing the mass of methanol used (10 g) by the moles of methanol obtained earlier (step 3).
By following these steps and performing the necessary calculations, you should be able to find the answers to the questions.
To find the answers to the questions, we need to use the formula for freezing point depression:
ΔTf = Kf * m * n
Where:
ΔTf = freezing point depression
Kf = cryoscopic constant (constant for the solvent)
m = molality (moles of solute per kilograms of solvent)
n = number of particles into which the solute dissociates
Since methanol does not dissociate, n = 1. Also, Kf and ΔTf are specific to water.
1. Calculating the freezing point depression (ΔTf):
ΔTf = 0.4°C - (-5.4°C)
ΔTf = 5.8°C
2. Calculating the molality of the methanol (m):
m = ΔTf / Kf
To find the value of Kf for water, we need to look it up (approximately 1.86°C/m for water).
m = 5.8°C / 1.86°C/m
m ≈ 3.12 mol/kg
3. Calculating the amount of methanol in the decanted solution:
First, we need to find the mass of methanol in the solution.
Mass of methanol = initial mass of solution - final mass of solution
Mass of methanol = 101.8g - 10g
Mass of methanol = 91.8g
4. Calculating the amount of water in the decanted solution:
Mass of water = final mass of solution - mass of methanol
Mass of water = 101.8g - 91.8g
Mass of water = 10g
5. Calculating the amount of methanol in a solution with 1 kg of water:
First, we need to convert the mass of water from grams to kilograms:
Mass of water = 10g = 0.01kg
Now we can calculate the amount of methanol:
Amount of methanol = m * mass of water
Amount of methanol = 3.12mol/kg * 0.01kg
Amount of methanol = 0.0312 mol
6. Assuming she made the calculation properly, the molar mass of methanol is found by dividing the mass of methanol by the amount of substance (moles):
Molar mass of methanol = mass of methanol / amount of methanol
Molar mass of methanol = 91.8g / 0.0312 mol
Molar mass of methanol ≈ 2939.7 g/mol
Therefore, the freezing point depression is 5.8°C, the molality of methanol is approximately 3.12 mol/kg, the amount of methanol in the decanted solution is 91.8 grams, the amount of water in the decanted solution is 10 grams, and the calculated molar mass of methanol is approximately 2939.7 g/mol.
I don't want to do all of this but I can get you started. You can post back here if there is something you don't understand.
what was the freezing point depression?
Wouldn't that be the difference between -5.4 and 0.4 or 5.8 degrees C?
what was the molality of the methanol?
delta T = Kf*m
You know delta T and Kf, solve for m
how much methanol was in the decanted solution?
Doesn't the problem tell you that she added 10g to the ice bath?
how much water was in the decanted solution?
Hmm...The mass of the decanted material was 101.8g and the methanol was 10 g so.....
how much methanol would there be in the solution with 1 kg of water, with methanol at the same concentration as she had in her experiment?
what did she find to be molar mass of methanol, assuming she made the calculation properly?