A solution is prepared by dissolving 56.5g of ethylene glycol in 874 g of water. Calculate the change in the boiling point and the freezing point.

mols ethylene glycol = grms/molar mass = ?. Solve for mols.

m ethylene glycol = mols/kg solvent
Solve for m and substitute into the two equations below.
dT = Kf*m and
dT = Kb*m

To calculate the change in boiling point and freezing point of a solution, we need to use the equations provided by the colligative properties. These properties depend on the number of solute particles, rather than their individual identity.

1. Change in Boiling Point (ΔTb):
The equation for the change in boiling point is given by:
ΔTb = Kb * m * i

Where:
- ΔTb is the change in boiling point
- Kb is the boiling point elevation constant for the solvent (water, in this case)
- m is the molality of the solution
- i is the van 't Hoff factor, which depends on the number of particles the solute dissociates into

For ethylene glycol (C2H6O2), the van 't Hoff factor (i) is 1 because it does not dissociate into ions in water.

To find the molality (m) of the solution:
molality = moles of solute / mass of the solvent (in kg)

First, we need to calculate the moles of ethylene glycol using its molar mass:
Molar mass of C2H6O2 = (2 * atomic mass of C) + (6 * atomic mass of H) + (2 * atomic mass of O)
= (2 * 12.01 g/mol) + (6 * 1.01 g/mol) + (2 * 16.00 g/mol)
= 62.08 g/mol

moles of ethylene glycol = mass of ethylene glycol / molar mass of ethylene glycol
= 56.5 g / 62.08 g/mol

Next, we need to calculate the molality:
molality = moles of solute / mass of solvent (in kg)
= moles of ethylene glycol / (mass of water / 1000)
= moles of ethylene glycol / (874 g / 1000)

Now, we have the molality (m) value, and we can calculate the change in boiling point (ΔTb) using the equation mentioned earlier.

2. Change in Freezing Point (ΔTf):
The equation for the change in freezing point is given by:
ΔTf = Kf * m * i

The variables in this equation have the same meaning as in the boiling point equation.

However, in this case, the van 't Hoff factor (i) depends on the solute's properties. For ethylene glycol (C2H6O2), it is also 1.

Using the molality (m) obtained earlier, we can calculate the change in freezing point (ΔTf) using the equation mentioned above.

Note: The boiling point elevation constant (Kb) and freezing point depression constant (Kf) for water is not mentioned in the question. These properties are specific to the solvent and can be found in tables or provided in the question itself.