Can someone please help me ?
What mass of glycerol must be dissolved in 200.0 g of water to give a solution with a freezing point of -1.50?
im not sure how to even start this problem. I think i would find the moles in water first, then the grams in glycerol after?
Pleaseee help!
You want delta T = Kf*molality.
You know delta T and Kf, calculate molality.
Then molality = mols/kg solvent.
You know molality and kg solvent, calculate mols.
Then mols = g/molar mass.
You know mols and molar mass, calculate grams.
To solve this problem, you need to use the concept of freezing point depression and calculate the molality of the solution.
The freezing point depression is given by the equation:
ΔTf = Kf * molality
where ΔTf is the change in freezing point, Kf is the freezing point depression constant (for water, it is 1.86 °C·kg/mol), and molality is the number of moles of solute (glycerol) per kilogram of solvent (water).
First, determine the change in freezing point:
ΔTf = -1.50 °C (given)
Next, convert the mass of water to kilograms:
mass of water = 200.0 g = 0.200 kg
Now, substitute the values into the formula and rearrange to solve for molality:
ΔTf = Kf * molality
-1.50 °C = (1.86 °C·kg/mol) * molality
Solving for molality:
molality = (-1.50 °C) / (1.86 °C·kg/mol)
molality ≈ -0.806 mol/kg
Since molality is defined as moles of solute per kilogram of solvent, you need to multiply the molality by the mass of the solvent (water) to find the moles of glycerol required:
moles of glycerol = molality * mass of water
moles of glycerol = -0.806 mol/kg * 0.200 kg
moles of glycerol ≈ -0.161 mol
The negative sign indicates that you need to dissolve 0.161 moles of glycerol. However, moles cannot be negative in this context, so we take the absolute value:
moles of glycerol ≈ 0.161 mol
Finally, convert moles of glycerol to grams:
grams of glycerol = moles of glycerol * molar mass
The molar mass of glycerol is approximately 92.09 g/mol:
grams of glycerol = 0.161 mol * 92.09 g/mol
grams of glycerol ≈ 14.8 g
Therefore, approximately 14.8 grams of glycerol must be dissolved in 200.0 grams of water to obtain a solution with a freezing point of -1.50 °C.
Of course, I can help you with this problem!
To start solving this problem, you need to understand the concept of freezing point depression and how it relates to the concentration of solute in a solution. Freezing point depression occurs when a solute is added to a solvent, causing the freezing point of the solution to be lower than that of the pure solvent. The freezing point depression is directly proportional to the molal concentration of the solute in the solution.
To solve this problem, you can use the formula for freezing point depression:
ΔT = (K_f)(m)
Where:
ΔT is the change in freezing point
K_f is the molal freezing point depression constant (which is specific to the solvent)
m is the molal concentration of the solute
First, you need to find the molal freezing point depression constant (Kf) for water. For water, the value of Kf is 1.86 °C/kg.
Next, you need to calculate the molal concentration of the solute (glycerol) in the solution. The molal concentration (m) is defined as the moles of solute divided by the mass of the solvent (in kg).
To find the moles of solute, you can use the molar mass of glycerol, which is 92.09 g/mol.
Here's how you can calculate the moles and mass of glycerol:
1. Convert the mass of water from grams to kilograms:
Mass of water = 200.0 g = 0.2 kg
2. Calculate the molal concentration (m) of glycerol:
moles of glycerol = (mass of glycerol) / (molar mass of glycerol)
m = moles of glycerol / mass of water
3. Solve for the moles of glycerol:
moles of glycerol = m * mass of water
4. Finally, calculate the mass of glycerol:
mass of glycerol = moles of glycerol * molar mass of glycerol
By following these steps, you can determine the mass of glycerol that must be dissolved in 200.0 g of water to give a solution with a freezing point of -1.50 °C.