Question

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

Short answer

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

Step-by-step solution

Calculate the initial moles of CaCl₂

First, we need to find the initial moles of CaCl₂ using the initial concentration and volume of the solution. The formula for calculating moles is: Moles = Concentration × Volume Here, the initial concentration of CaCl₂ is 0.275 M, and the initial volume is 230 mL. We will convert the volume to liters: 230 mL × (1 L / 1000 mL) = 0.230 L Now, we can calculate the initial moles of CaCl₂: Moles of CaCl₂ = 0.275 M × 0.230 L = 0.06325 mol

Calculate the final moles of CaCl₂

Since the moles of CaCl₂ remain constant after the evaporation of water, the final moles of CaCl₂ are the same as the initial moles: Final moles of CaCl₂ = 0.06325 mol

Calculate the final volume of the solution

Next, we will find the final volume of the CaCl₂ solution using the final concentration and the final moles of CaCl₂. The formula to calculate the volume is: Volume = Moles / Concentration The final concentration of CaCl₂ is given as 1.10 M. We can now calculate the final volume of the solution: Final volume = 0.06325 mol / 1.10 M = 0.0575 L

Calculate the volume of water that evaporated

Now, we can calculate the volume of water that evaporated from the initial solution by comparing the initial and final volumes of the solution: Initial volume - Final volume = Volume of water evaporated 0.230 L - 0.0575 L = 0.1725 L

Convert the volume to milliliters

Finally, we will convert the volume of evaporated water to milliliters: 0.1725 L × (1000 mL / 1 L) = 172.5 mL So, 172.5 mL of water evaporated from the 0.275 M CaCl₂ solution.

Key concepts

Molarity

Molarity is a way to express the concentration of a solution. It indicates how many moles of a solute are present in one liter of solution. Understanding molarity is crucial in chemistry, especially when preparing or diluting solutions. Let's break down the key points:

• Molarity (\( M \)) is determined using the formula: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).
• This measurement allows you to easily calculate how much of a substance is in a given quantity of water or solvent."
• In the original exercise, the molarity of the calcium chloride (\( \text{CaCl}_2 \)) solution changes from \( 0.275 M \) to \( 1.10 M \) due to evaporation.

Molarity helps quickly determine how the removal of the solvent affects the concentration of the solution. It depicts why solutions become more concentrated as they lose a solvent, such as water.

Volume Change

Volume change occurs when the amount of solvent in a solution changes, while the amount of solute remains the same. This is a crucial concept when studying the effects of evaporation on a solution:

• Initially, we have a solution with a specific volume — in this case, 230 mL.
• After the water evaporates, the volume of the solution decreases, even though the solute amount remains unchanged.
• This decrease in volume results in an increase in solution concentration.

In our exercise, as the water evaporates, the total volume reduces significantly, causing the solution's concentration to increase from \( 0.275 M \) to \( 1.10 M \). Understanding volume change is essential to predict how the solution's concentration adjusts over time due to evaporation or other processes.

Evaporation

Evaporation is a process where liquid turns into vapor without boiling. It's a natural way for a liquid phase to lose solvent molecules, leading to a concentrated solution. Here's how evaporation impacts a solution:

• The amount of solute does not alter, but the solvent quantity decreases.
• This loss of water molecules results in a smaller volume and a higher concentration of the solution.
• In our problem, leaving the \( \text{CaCl}_2 \) solution on the hot plate overnight led to the evaporation of 172.5 mL of water.

Evaporation is common in everyday scenarios where water bodies lose moisture to the atmosphere. Understanding its effect helps in practical and laboratory settings where precise concentrations are necessary.

Calculation of Moles

Calculating moles is an essential component in solution chemistry. Moles are a standard unit for measuring the amount of substance. Here's a simple guide:

• To find the number of moles, multiply the concentration by the volume (in liters) of the solution.
• Use the formula: \( \text{Moles} = \text{Concentration} \times \text{Volume} \).
• In the exercise, the initial moles of \( \text{CaCl}_2 \) were found using \( 0.275 M \times 0.230 L = 0.06325 \ ext{mol} \).

Accurate calculation of moles is crucial. It ensures that chemical reactions achieve the desired outcomes, as moles determine the proportions in which substances react. Recognizing how initial and final moles remain constant, independent of evaporation, underpins many solution-based problems in chemistry.