Question

A 230.-mL sample of a \(0.275 \mathrm{M} \mathrm{CaCl}_{2}\) solution is left on a hot plate overnight; the following morning, the solution is \(1.10 \mathrm{M}\). What volume of water evaporated from the \(0.275 \mathrm{M} \mathrm{CaCl}_{2}\) solution?

Short answer

172.5 mL of water evaporated from the 0.275 M CaCl2 solution.

Step-by-step solution

Calculate the initial amount of solute in the solution.

First, calculate the initial amount (in moles) of the calcium chloride in the 230 mL solution by using the formula: moles = concentration x volume. Initial moles of CaCl2 = \( 0.275 \mathrm{M} \times 230 \mathrm{mL} \) Please note that it's essential to convert the volume from milliliters to liters: Initial moles of CaCl2 = \( 0.275 \mathrm{M} \times 0.230 \mathrm{L} \) Initial moles of CaCl2 = \( 0.06325 \mathrm{mol} \)

Calculate the final volume of the solution after water evaporation.

Since the amount of solute (calcium chloride) is conserved during the evaporation process, we can now calculate the final volume of the 1.10 M solution. We will use the formula: moles = concentration x volume. Rearranging it for volume: Final volume = moles / concentration Final volume = \( 0.06325 \mathrm{mol} \div 1.10 \mathrm{M} \) Final volume = \( 0.0575 \mathrm{L} \)

Calculate the volume of water evaporated from the original solution.

Now, subtract the final volume from the initial volume to get the volume of water evaporated: Volume of water evaporated = Initial volume - Final volume Volume of water evaporated = \( 0.230 \mathrm{L} - 0.0575 \mathrm{L} \) Volume of water evaporated = \( 0.1725 \mathrm{L} \) Finally, convert the volume of water evaporated from liters to milliliters: Volume of water evaporated = \( 0.1725 \mathrm{L} \times 1000 \mathrm{mL/L} \) Volume of water evaporated = \( 172.5 \mathrm{mL} \) So, 172.5 mL of water evaporated from the 0.275 M CaCl2 solution.

Key concepts

Understanding Calcium Chloride

Calcium chloride (CaCl₂) is a salt and an important compound with wide-ranging uses. It is composed of one calcium ion (Ca²⁺) and two chloride ions (Cl⁻). This means for every molecule of calcium chloride, there is one calcium atom and two chlorine atoms bonded together.
In solutions, calcium chloride dissociates into its individual ions, which allows it to interact with water molecules effectively.

• Calcium ions help in hardening substances and are integral in many industries.
• Chloride ions are key in de-icing solutions and preserving food.

Its ability to absorb water effectively makes it an excellent humectant. When dealing with calcium chloride in solutions, understand that it will completely dissociate, which is why it is used in the exercise to calculate concentrations.

Evaporation of Water

Evaporation is a process where liquid turns into vapor and escapes into the air. It is an important aspect in various natural and industrial processes. In this context, water evaporation increases the concentration of solutes in a solution. As water molecules leave the solution, the same amount of solute occupies a smaller volume. This is what increases the calcium chloride concentration when the solution is left on a hot plate overnight.

• Factors like heat increase the rate of evaporation.
• Less water in a solution means higher concentrations of solutes.

This principle is crucial in the textbook exercise to determine how much water has been lost from the solution.

Exploring Molarity

Molarity is a measure of the concentration of solute in a solution. It is defined as moles of solute per liter of solution. The formula \[ \text{Molarity} (M) = \frac{\text{moles of solute}}{\text{liters of solution}} \]is used to determine the concentration of a solution.

• It allows comparison of strengths of solutions based on the quantity of solute.
• In the exercise, we started with an initial and final molarity to find the volume change due to evaporation.

A good understanding of molarity enables us to precisely quantify the concentration changes in a solution as it undergoes processes like evaporation.

Concept of Solute Conservation

Solute conservation is a key aspect of solution chemistry. It dictates that the amount of solute in a solution does not change unless solute is added or removed. In the exercise given, calcium chloride is our solute. During evaporation, the water volume decreases, yet the solute amount remains the same. This is why the concentration changes; it's a result of a reduced water volume, not a change in the amount of solute.

• The principle helps us solve problems involving changes in solution concentration.
• Understanding solute conservation allows for accurate calculations such as determining volumes and concentrations when solution conditions change.

Thus, solute conservation is essential in ensuring accurate results in chemical calculations and reactions.