What volume of ethylene glycol (HOCH2 CH2 OH,. density =1.12...

What volume of ethylene glycol $\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH},\right.$ density $=1.12 \mathrm{g} \mathrm{mL}^{-1}$ ) must be added to $20.0 \mathrm{L}$ of water $\left(K_{\mathrm{f}}=1.86^{\circ} \mathrm{C} \mathrm{kg} \mathrm{mol}^{-1}\right)$ to produce a solution that freezes at $-10^{\circ} \mathrm{C} ?$

Key Concepts

Freezing Point Depression

This concept refers to the lowering of the freezing point of a solvent when a solute is added. It is quantitatively described by the equation ?Tf = Kf * m, where ?Tf is the change in freezing point, Kf is the cryoscopic constant (a property of the solvent), and m is the molality of the solution. It is a colligative property meaning that it depends on the number of solute particles rather than their identity.

Molality

Molality is a concentration unit that measures the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it does not change with temperature, unlike volume-based measures. In the context of freezing point depression, knowing the molality allows for the direct computation of the temperature change related to the addition of solute.

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of solute particles present, regardless of their specific type. These include boiling point elevation, vapor pressure lowering, osmotic pressure, and freezing point depression. They are important for understanding how solutes affect solvent properties, especially in applications such as antifreeze formulations.

Density

Density is the mass per unit volume of a substance. In solution preparation problems, density is used to convert between the mass of a solute and its volume. This conversion is essential when the amount of a substance is given in mass but needs to be measured in volume, or vice versa, as it ensures accurate determination of the quantities involved.

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