Problem 72 - Chemistry The Science in Context

Question

What molality of a nonvolatile, nonelectrolyte solute is needed to raise the boiling point of water by \(7.60^{\circ} \mathrm{C}\) \(\left(K_{\mathrm{b}}=0.52^{\circ} \mathrm{C} / m\right) ?\)

Step-by-Step Solution

Answer

The molality of the nonvolatile, nonelectrolyte solute needed to raise the boiling point of water by 7.60°C is 14.62 m.

Step 1: Write down the boiling point elevation formula

We'll be using the boiling point elevation formula to find the molality of the solute needed to raise the boiling point of water by 7.60°C. The formula is: \(\Delta T_b = K_b \cdot m\)

Step 2: Substituting the given values

We are given the change in boiling point, \(\Delta T_b = 7.60^{\circ}\mathrm{C}\) and the boiling point elevation constant for water, \(K_b = 0.52^{\circ} \mathrm{C} / m\). Substitute these values into the equation: \(7.60^{\circ}\mathrm{C} = 0.52^{\circ} \mathrm{C} / m \cdot m\)

Step 3: Solve for molality, \(m\)

Now we have one equation with one unknown variable, \(m\). We can solve for \(m\) by dividing both sides of the equation by the boiling point elevation constant, \(K_b = 0.52^{\circ} \mathrm{C} / m\). That gives us: \(m = \frac{7.60^{\circ}\mathrm{C}}{0.52^{\circ} \mathrm{C} / m} = 14.62 \, m\)

Step 4: Report the answer

The molality of the nonvolatile, nonelectrolyte solute needed to raise the boiling point of water by 7.60°C is 14.62 m.

Key Concepts

Molality

Molality is a way to express the concentration of a solution, similar to molarity, but with a key difference. Instead of being based on volume, molality is based on the mass. This is important because it doesn’t change with temperature fluctuations or pressure changes. The formula for molality, denoted as \(m\), is:

• \(m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}\)

Molality is commonly used in boiling point elevation and freezing point depression calculations because it provides a more accurate measure of concentration for these colligative properties. These properties depend on the number of solute particles in the solution rather than the identity of the solute. Remember, molality is different from molarity, which is moles of solute per liter of solution.
Understanding molality helps us analyze how a solute influences the boiling and freezing points of a solvent.

Nonvolatile Solute

A nonvolatile solute is a substance that doesn’t easily vaporize, meaning it has a negligible vapor pressure. When added to a solvent like water, it influences the boiling point by causing it to elevate. This happens because nonvolatile solutes reduce the number of solvent molecules at the liquid surface, limiting their ability to escape into a vapor. Therefore, the solution requires a higher temperature to reach boiling point.
Boiling point elevation, denoted as \(\Delta T_b\), is directly proportional to the molality of the solution. The formula \(\Delta T_b = K_b \cdot m\) links the elevation to the concentration of solute molecules. This property doesn't depend on the type of nonvolatile solute, just the amount.
Other key points include:

• The boiling point of the pure solvent is increased by adding a nonvolatile solute.
• This increase is measured by the boiling point elevation constant (\(K_b\)).
• Typically used in problems involving cooking or industrial processes where precise boiling points are critical.

Nonelectrolyte

A nonelectrolyte is a solute that, when dissolved in a solvent, does not produce ions. This means it doesn't conduct electricity. Examples of nonelectrolytes include sugar and other organic compounds that don't dissociate in water.
When calculating properties like boiling point elevation, using nonelectrolytes simplifies the process since there are no additional particles beyond the original solute molecules. Each molecule remains intact in the solution and doesn't split into ions, making calculations straightforward.
In practice, the effect of a nonelectrolyte solute on boiling point elevation is solely due to the number of solute particles rather than any ionic dissociation.

• Nonelectrolytes don't affect the charge balance of a solution.
• They are frequently used in laboratory settings for accurate measurement of colligative properties since their behavior is predictable.
• Understanding nonelectrolytes is essential when working with solutions that need to maintain consistent electrical properties.