Problem 52 - Chemistry and Chemical Reactivity

Question

If \(4.00 \mathrm{mL}\) of \(0.0250 \mathrm{M} \mathrm{CuSO}_{4}\) is diluted to \(10.0 \mathrm{mL}\) with pure water, what is the molar concentration of copper(II) sulfate in the diluted solution?

Step-by-Step Solution

Answer

The molar concentration after dilution is 0.0100 M.

Step 1: Identify Initial Variables

To solve this problem, first identify the initial volume and concentration of the copper(II) sulfate solution: the initial volume is 4.00 mL and the initial concentration is 0.0250 M.

Step 2: Determine Dilution Formula

The formula used for dilution is \( C_1V_1 = C_2V_2 \), where \( C_1 \) and \( V_1 \) are the initial concentration and volume, and \( C_2 \) and \( V_2 \) are the final concentration and volume after dilution.

Step 3: Apply Given Values

Plug in the given values into the dilution formula: \( C_1 = 0.0250 \, M \), \( V_1 = 4.00 \, mL \), and the final volume \( V_2 = 10.0 \, mL \).

Step 4: Solve for Final Concentration

Reformulate the equation to isolate \( C_2 \): \( C_2 = \frac{C_1V_1}{V_2} \). Substitute the known values to find \( C_2 \):\[ C_2 = \frac{0.0250 \, M \times 4.00 \, mL}{10.0 \, mL} \].

Step 5: Simplify the Calculation

Perform the calculation:\( C_2 = \frac{0.100 \, mL}{10.0 \, mL} = 0.0100 \, M \).

Step 6: Conclusion

The molar concentration of copper(II) sulfate in the diluted solution is 0.0100 M.

Key Concepts

Dilution Calculations

Dilution calculations are essential when dealing with chemical solutions. They help determine how concentrations change when a solution is diluted, i.e., when additional solvent is added. In chemistry, we often use the formula \( C_1V_1 = C_2V_2 \) for such calculations.
This formula states that the product of the initial concentration \( (C_1) \) and the initial volume \( (V_1) \) equals the product of the final concentration \( (C_2) \) and the final volume \( (V_2) \). The logic behind this is that the amount of solute remains constant during dilution, even though its concentration in the solution decreases.

• \( C_1 \) and \( V_1 \) represent the concentration and the volume before dilution.
• \( C_2 \) and \( V_2 \) denote the concentration and the volume after dilution.

By rearranging this equation, you can solve for any one of the four variables if the other three are known. This method simplifies how we calculate the concentration changes without direct measurement of solute mass.

Copper(II) Sulfate

Copper(II) sulfate is a common chemical compound used in these exercises. It's often seen as a blue crystalline solid in its hydrated form, known as copper(II) sulfate pentahydrate. Its chemical formula is \( \mathrm{CuSO}_4 \cdot 5H_2O \) for the pentahydrate form, but in solutions, we usually deal with the anhydrous form \( \mathrm{CuSO}_4 \).

• It plays a significant role in different chemical and industrial applications.
• It is used in agriculture, manufacturing, and chemistry labs.
• In laboratories, it's commonly used to prepare chemical solutions and conduct experiments.

When dissolved in water, copper(II) sulfate disassociates to form copper and sulfate ions, giving the solution its characteristic blue color. Understanding the behavior of copper(II) sulfate in solutions, including its concentration changes upon dilution, is essential for accurate experimental results.

Molarity

Molarity, denoted by the symbol \( M \), is a way of expressing the concentration of a solution. It represents the number of moles of a solute per liter of solution.
Molarity is an essential concept because it helps chemists to:

• Quantify how much of a solute is in a solution.
• Make accurate and precise mixtures in both laboratory and industrial settings.
• Perform various chemical calculations such as stoichiometry, titration, and equilibrium analysis.

The formula for molarity is: \[ Molarity (M) = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]
In practical applications, such as the concentration of copper(II) sulfate post-dilution, molarity allows us to determine how a certain volume adjustment influences solute concentration. It is key to ensuring desired concentrations in reactions and other chemical processes.

Chemical Solutions

Chemical solutions are homogeneous mixtures comprised of solutes and solvents. They are integral to numerous scientific and industrial processes. Understanding solutions involves knowing the basic components:

• A solute is the substance dissolved in the solvent (e.g., copper(II) sulfate in water).
• A solvent is the medium in which the solute is dissolved, typically a liquid like water in chemical solutions.

When preparing solutions, achieving the right concentrations is crucial. Precise concentrations enable accurate predictions of chemical reactions and expected outcomes.
Dilution is one of the methods used to modify the concentration of a solution. By adding more solvent, the concentration of the solute decreases, enabling changes in the solution's properties. Knowing how to properly dilute solutions, such as using copper(II) sulfate, is a fundamental skill in chemistry and various applications of this science.