determine the amount of solute needed to make 100ml aqueous solution of NaCl and MgCl2 that will cause a 10 degree change in freezing point. Determine the amounts of solute needed to make 100ml aqueous of AlCl3 and ethanol that will cause a 10 degree change in boiling point.
To determine the amount of solute needed to make a solution that will cause a specific change in freezing or boiling point, we need to use the concept of molality.
Molality (m) is defined as the number of moles of solute per kilogram of solvent. It is calculated using the formula:
m = moles of solute / mass of solvent in kg
First, let's calculate the amount of solute (NaCl and MgCl2) needed to make a 100 ml aqueous solution that will cause a 10-degree change in freezing point.
1. Determine the molality of the solution using the formula:
ΔT = Kf * m
In this case, the change in freezing point (ΔT) is 10 degrees. The freezing point depression constant (Kf) depends on the solvent. For water, the value is approximately 1.86 °C/m.
So, rearranging the formula:
m = ΔT / Kf
m = 10 / 1.86
2. Calculate the mass of solvent in kg. Since we have a 100 ml solution, the mass of the solvent (water) can be calculated using the density of water, which is 1 g/ml.
mass of solvent = volume of solvent * density
mass of solvent = 100 ml * 1 g/ml
mass of solvent = 100 g
Converting the mass of solvent to kg:
mass of solvent = 100 g / 1000
mass of solvent = 0.1 kg
3. Convert molality to moles of solute using the formula:
moles of solute = m * mass of solvent in kg
For NaCl and MgCl2, we'll assume they dissociate completely in water.
Now, you need to provide the concentration (molarity) or weight percentage of the NaCl and MgCl2 solutions, so that we can calculate their respective moles of solute.
Please provide the information for the NaCl and MgCl2 solutions.
To determine the amount of solute needed to cause a 10 degree change in freezing point for a 100ml aqueous solution of NaCl and MgCl2, you will need to consider the molal freezing point constant (Kf) for each compound. The formula you can use is:
ΔT = Kf * m
Where:
ΔT = change in freezing point (10 degrees for this question)
Kf = molal freezing point constant
m = molality of the solution
For NaCl:
The molal freezing point constant (Kf) for NaCl is 1.86 °C/molal.
To find the molality (m), you need to know the moles of solute and the mass of the solvent. Since we are dealing with a 100ml solution, we'll assume the mass of the solvent (water) is 100g (since 1 ml of water is approximately 1g).
Let's call the amount of NaCl needed X moles.
The molecular weight (molar mass) of NaCl is 58.44 g/mol.
Using the formula: moles = mass / molar mass, we can calculate the moles of NaCl.
X moles = mass NaCl / molar mass NaCl
X moles = X grams / 58.44 g/mol
Now, we need to find the mass of the solute NaCl that will yield X moles. We can use the formula: mass NaCl = X moles * molar mass NaCl.
Next, we need to calculate the molality (m) using the formula: molality = moles solute / kg solvent.
Since we are dealing with 100g of water as the solvent, the mass of water in kg is 0.1 kg.
Now, we can rearrange the original formula to solve for X (moles of NaCl):
ΔT = Kf * (moles / kg)
Substituting the known values, we have:
10 = 1.86 * (X / 0.1)
Solving for X, we get:
X = (10 * 0.1) / 1.86
The same steps can be applied to find the amount of MgCl2 needed, but first, let's solve for X:
X = (10 * 0.1) / 1.86
X ≈ 0.5376 moles
For MgCl2:
The molal freezing point constant (Kf) for MgCl2 is 3.61 °C/molal.
The molar mass of MgCl2 is 95.21 g/mol.
Following the same process as above, calculate the amount of MgCl2 needed to cause the desired freezing point change.
For AlCl3 and ethanol, the concept is similar, but this time we are dealing with boiling point elevation. The equation is:
ΔT = Kb * m
Where:
ΔT = change in boiling point (10 degrees for this question)
Kb = molal boiling point constant
m = molality of the solution
For AlCl3, the molal boiling point constant (Kb) is 0.51 °C/molal.
The molar mass of AlCl3 is 133.34 g/mol.
Using the same steps, calculate the amount of AlCl3 needed.
For ethanol, the molal boiling point constant (Kb) is 1.99 °C/molal.
The molar mass of ethanol is 46.07 g/mol.
Again, following the same process, calculate the amount of ethanol needed.
Note: When calculating the amounts of solute needed, it is important to consider the ideal behavior of the solutes in the solution. The calculations assume ideal behavior, so the results might differ slightly in reality due to factors like non-ideal behavior and other interactions.