Ch.13 - Properties of Solutions

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.13 - Properties of Solutions

Problema 76

Capitolo 13, Problema 76

Using data from Table 13.3, calculate the freezing and boiling points of each of the following solutions: (a) 0.25 m glucose in ethanol; (b) 20.0 g of decane, C₁₀H₂₂, in 50.0 g CHCl₃; (c) 3.50 g NaOH in 175 g of water, (d) 0.45 mol ethylene glycol and 0.15 mol KBr in 150 g H₂O.

Guida verificata passo dopo passo

Identify the solute and solvent in the solution. Here, decane (C_{10}H_{22}) is the solute, and chloroform (CHCl_{3}) is the solvent.

Calculate the molality (m) of the solution using the formula: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). First, find the moles of decane by dividing its mass by its molar mass.

Use the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor (which is 1 for non-electrolytes like decane), \( K_f \) is the freezing point depression constant for chloroform, and \( m \) is the molality calculated in the previous step.

Calculate the new freezing point by subtracting \( \Delta T_f \) from the normal freezing point of chloroform.

Use the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( K_b \) is the boiling point elevation constant for chloroform. Calculate the new boiling point by adding \( \Delta T_b \) to the normal boiling point of chloroform.

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Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation and freezing point depression, which are crucial for understanding how the addition of a solute, like decane, affects the phase changes of the solvent, in this case, chloroform.

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01:26

Colligative Properties

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a non-volatile solute is added. The extent of this elevation can be calculated using the formula ΔT_b = i * K_b * m, where ΔT_b is the change in boiling point, K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution. Understanding this concept is essential for calculating the new boiling point of the chloroform solution.

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03:05

Boiling Point Elevation

Freezing Point Depression

Freezing point depression is another colligative property that indicates how the freezing point of a solvent decreases when a solute is added. This can be calculated using the formula ΔT_f = i * K_f * m, where ΔT_f is the change in freezing point, K_f is the cryoscopic constant of the solvent, and m is the molality. This concept is vital for determining how the addition of decane will lower the freezing point of chloroform.

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01:59

Freezing Point Depression

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Using data from Table 13.3, calculate the freezing and boiling points of each of the following solutions: (a) 0.25 m glucose in ethanol; (b) 20.0 g of decane, C10H22, in 50.0 g CHCl3; (c) 3.50 g NaOH in 175 g of water, (d) 0.45 mol ethylene glycol and 0.15 mol KBr in 150 g H2O.

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Colligative Properties

Boiling Point Elevation

Freezing Point Depression

Using data from Table 13.3, calculate the freezing and boiling points of each of the following solutions: (a) 0.25 m glucose in ethanol; (b) 20.0 g of decane, C₁₀H₂₂, in 50.0 g CHCl₃; (c) 3.50 g NaOH in 175 g of water, (d) 0.45 mol ethylene glycol and 0.15 mol KBr in 150 g H₂O.