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.
Use the same system used for the KBr, Al2(SO4)3. Mg(NO3)2 problem EXCEPT use Kb for the boiling point constant instead of Kf (the freezing point constant).
i = 4 for AlCl3
i = 2 for NaCl
i = 1 for ethanol
i = 3 for MgCl2
To determine the amount of solute needed for each solution, we need to use the formula for calculating the change in freezing point or boiling point, known as colligative properties.
1. NaCl and MgCl2 solution:
The change in freezing point (\Delta Tf) is given by the equation:
\Delta Tf = Kf * m
where:
- \Delta Tf is the change in freezing point,
- Kf is the cryoscopic constant specific to the solvent (water in this case),
- m is the molality of the solute, which is the number of moles of solute per kilogram of solvent.
In this case, we want a change of 10 degrees in the freezing point, so:
\Delta Tf = 10 °C
The cryoscopic constant for water (Kf) is approximately 1.86 °C/m.
To calculate the molality (m), we first need to determine the number of moles of NaCl (sodium chloride) and MgCl2 (magnesium chloride) required.
The molecular weight of NaCl is approximately 58.44 g/mol.
The molecular weight of MgCl2 is approximately 95.21 g/mol.
Let's assume we need x grams of NaCl and y grams of MgCl2.
The moles of NaCl can be calculated as:
moles of NaCl = (mass of NaCl / molecular weight of NaCl)
The moles of MgCl2 can be calculated as:
moles of MgCl2 = (mass of MgCl2 / molecular weight of MgCl2)
Since we want a 100mL aqueous solution, the total mass of the solution is 100 grams (since the density of water is close to 1 g/mL).
Therefore, we have the equation:
x + y + 100 = 100 (since the mass of the solution is x + y + 100 grams)
Substituting these values into the equation for \Delta Tf, we have:
10 °C = 1.86 °C/m * (moles of NaCl + moles of MgCl2)
or
10 = 1.86 * (x / (58.44 g/mol) + y / (95.21 g/mol))
Now we have two variables (x and y) and two equations. Solving this system of equations will give us the values of x and y.
2. AlCl3 and ethanol solution:
The change in boiling point (\Delta Tb) is calculated using a similar formula:
\Delta Tb = Kb * m
where:
- \Delta Tb is the change in boiling point,
- Kb is the ebullioscopic constant specific to the solvent (ethanol in this case),
- m is the molality of the solute, again in moles of solute per kilogram of solvent.
The ebullioscopic constant for ethanol (Kb) is approximately 1.2 °C/m.
Again, we want a change of 10 degrees in the boiling point, so:
\Delta Tb = 10 °C
To calculate the amount of solute needed for AlCl3 and ethanol solution, the same approach as described for NaCl and MgCl2 solution can be followed. Substitute the appropriate molecular weights and constants, and solve for the unknown variables.
Remember, always double-check your calculations, and consult reference resources for accurate values of molecular weights and constants.