How to calculate the freezing point of a solution?

Understand the Problem

The question is asking how to determine the freezing point of a solution, which typically involves understanding colligative properties and the appropriate formulas to use for calculating the depression of freezing point.

Answer

Subtract the freezing point depression from the solvent's normal freezing point.
Answer for screen readers

The freezing point of the solution is obtained by calculating the depression in the freezing point and subtracting it from the normal freezing point of the pure solvent.

Steps to Solve

  1. Determine the freezing point depression constant ($K_f$) for the solvent

The freezing point depression constant is a property of the solvent. This value is known and can be found in reference tables. For example, the $K_f$ for water is $1.86^ ext{°C kg/mol}$.

  1. Identify the molality ($m$) of the solution

Molality ($m$) is the number of moles of solute per kilogram of solvent. It can be calculated using the formula:

$$ m = \frac{ ext{moles of solute}}{ ext{kg of solvent}} $$

  1. Calculate the freezing point depression ($ riangle T_f$)

Using the formula:

$$ riangle T_f = K_f imes m $$

Substitute the values for $K_f$ and $m$ into the formula to find $ riangle T_f$.

  1. Determine the new freezing point of the solution

Subtract the freezing point depression ($ riangle T_f$) from the normal freezing point of the solvent. For example, the normal freezing point of water is $0^ ext{°C}$. The formula is:

$$ ext{Freezing point of solution} = ext{freezing point of solvent} - riangle T_f $$

The freezing point of the solution is obtained by calculating the depression in the freezing point and subtracting it from the normal freezing point of the pure solvent.

More Information

Freezing point depression is one of the colligative properties, which are properties that depend on the number of solute particles but not on their identity.

Tips

A common mistake is to mix up molality (moles of solute per kg of solvent) with molarity (moles of solute per liter of solution). Ensure you're using the correct concentration unit.

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