How to calculate the freezing point of an aqueous solution

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Key Concepts
Some Boiling-Point Elevation and Freezing-Point Depression Constants
Example: Calculating Boiling and Freezing Point of a Nonelectrolyte Solution
Example: Calculating Boiling and Freezing Point of an Electrolyte Solution
Example: Calculating Molar Mass of Solute
How do you find the freezing point of aqueous solution?
How do you determine freezing point?
What is the freezing point of 1% na2so4 solution?
What is the freezing point of an aqueous 1 m?

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Key Concepts

Boiling Point Elevation:

A liquid boils at the temperature at which its vapor pressure equals atmospheric pressure.

The presence of a solute lowers the vapor pressure of the solution at each temperature, making it necessary to heat the solution to a higher temperature to boil the solution.

In dilute solutions with a nonvolatile solute, the boiling point elevation is proportional to the molality of the solute particles:
ΔTb = Kbm
ΔTb = the amount by which the boiling point is raised
m = molality (moles solute particles per kg of solution)
Kb = molal boiling-point elevation constant (solvent dependent)

Boiling Point of solution = normal boiling point of solvent + ΔTb

Freezing Point Depression:

A solute lowers the freezing point of a solvent.

In dilute solutions, the freezing point depression is proportional to the molality of the solute particles:
ΔTf = -Kfm
ΔTf = the amount by which the freezing point is lowered
m = molality (moles solute particles per kg of solution)
Kf = molal freezing-point depression constant (solvent dependent)

Freezing Point of solution = normal freezing point of solvent + ΔTf

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Some Boiling-Point Elevation and Freezing-Point Depression Constants

solvent	normal boiling point (oC)	Kb (oCm-1)	normal freezing point (oC)	Kf (oCm-1)
benzene	80.2	2.53	5.5	5.12

water	100.0	0.512	0.000	1.855

acetic acid (ethanoic acid)	118.5	3.07	16.6	3.90

camphor	208.3	5.95	178.4	40.0

naphthalene	218.0	5.65	80.2	6.9

Example: Calculating Boiling and Freezing Point of a Nonelectrolyte Solution

For a 0.262 m solution of sucrose in water, calculate the freezing point and the boiling point of the solution.

Freezing Point Calculation	Boiling Point Calculation
Calculate the freezing point depression: ΔTf = -Kfm Kf = 1.855 (from table above) m = 0.262 m ΔTf = -1.855 × 0.262 = -0.486oC Calculate the freezing point of the solution: Tf (solution) = normal freezing point + ΔTf Tf (solution) = 0.000 - 0.486 = -0.486oC	Calculate the boiling point elevation: ΔTb = Kbm Kb = 0.512 (from table above) m = 0.262 m ΔTb = 0.512 × 0.262 = 0.134oC Calculate the boiling point of the solution: Tb (solution) = normal boiling point + ΔTb Tb (solution) = 100.00 + 0.134 = 100.134oC

Example: Calculating Boiling and Freezing Point of an Electrolyte Solution

Calculate the freezing point and boiling point for a 0.15 m aqueous solution of sodium chloride.

Freezing Point Calculation	Boiling Point Calculation
Calculate the freezing point depression: ΔTf = -Kfm Kf = 1.855 (from table above) Since: NaCl → Na+(aq) + Cl-(aq): m(Na+) = 0.15 m m(Cl-) = 0.15 m m(NaCl(aq)) = 0.15 + 0.15 = 0.30 m ΔTf = -1.855 × 0.30 = -0.557oC Calculate the freezing point of the solution: Tf (solution) = normal freezing point + ΔTf Tf (solution) = 0.000 - 0.557 = -0.557oC	Calculate the boiling point elevation: ΔTb = Kbm Kb = 0.512 (from table above) Since: NaCl → Na+(aq) + Cl-(aq): m(Na+) = 0.15 m m(Cl-) = 0.15 m m(NaCl(aq)) = 0.15 + 0.15 = 0.30 m ΔTb = 0.512 × 0.30 = 0.154oC Calculate the boiling point of the solution: Tb (solution) = normal boiling point + ΔTb Tb (solution) = 100.00 + 0.154 = 100.154oC

Example: Calculating Molar Mass of Solute

Boiling Point Elevation Problem:

1.15 g of an unknown, nonvolatile compound raises the boiling point of 75.0 g benzene (C6H6) by 0.275oC.
Calculate the molar mass of the unknown compound.

Boiling Point Elevation Problem Solution:

Calculate the molality of solute particles:
m = ΔTb ÷ Kb
ΔTb = 0.275oC
Kb = 2.53oCm-1 (from table above)
m = 0.275 ÷ 2.53 = 0.109 m

Calculate the moles of solute present:
molality = moles solute ÷ kg solvent
moles(solute) = m × kg solvent = 0.109 × 75.0 × 10-3 = 8.175 × 10-3 mol

Calculate the molar mass of the solute:
moles(solute) = mass(solute) ÷ molar mass(solute)
molar mass(solute) = mass(solute) ÷ moles(solute) = 1.15 ÷ 8.175 × 10-3 = 141 g mol-1

How do you find the freezing point of aqueous solution?

Example: Calculating Boiling and Freezing Point of a Nonelectrolyte Solution.

Calculate the freezing point depression: ΔTf = -Kfm. Kf = 1.855 (from table above) m = 0.262 m. ... .

Calculate the freezing point of the solution: Tf (solution) = normal freezing point + ΔTf Tf (solution) = 0.000 - 0.486 = -0.486oC..

How do you determine freezing point?

To calculate the freezing point of an electrolytic solution, we can use the same formula ∆T_f = K_f m that is used to calculate the freezing point using molality. But before using the formula, we have to analyze the number of ions and calculate its molality.