Problem 50 - 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 is 0.0100 M.

Step 1: Identify Initial Parameters

We begin with an initial volume of the copper(II) sulfate solution, which is \( V_1 = 4.00 \text{ mL} \), and an initial concentration \( C_1 = 0.0250 \text{ M} \). The solution is then diluted to a final volume \( V_2 = 10.0 \text{ mL} \).

Step 2: Understand the Dilution Formula

The dilution formula is given by \( C_1 \times V_1 = C_2 \times V_2 \), where \( C_2 \) is the concentration of the diluted solution. This formula shows that the amount of solute remains constant before and after dilution.

Step 3: Convert Volumes to Liters

To use the formula, ensure the volumes are in consistent units. Convert milliliters to liters: \( V_1 = 4.00 \text{ mL} = 0.00400 \text{ L} \), \( V_2 = 10.0 \text{ mL} = 0.0100 \text{ L} \).

Step 4: Apply the Dilution Formula

Substitute the known values into the dilution formula: \( (0.0250 \text{ M}) \times (0.00400 \text{ L}) = C_2 \times (0.0100 \text{ L}) \).

Step 5: Solve for the Diluted Concentration

To find \( C_2 \), rearrange the equation to \( C_2 = \frac{(0.0250 \text{ M}) \times (0.00400 \text{ L})}{0.0100 \text{ L}} \). Compute \( C_2 \): \( C_2 = \frac{0.000100 \text{ mol}}{0.0100 \text{ L}} = 0.0100 \text{ M} \).

Key Concepts

Molar Concentration

Molar concentration, often referred to as molarity, is a way to express how much of a substance is present in a solution. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution. A helpful formula for calculating molarity is:

• \( M = \frac{n}{V} \)

where \( M \) is the molarity, \( n \) is the number of moles of solute, and \( V \) is the volume of the solution in liters.

To find the molarity, ensure the volume is always in liters. This is important for accurate calculations. Molar concentration is crucial in chemical experiments and solutions because it helps in determining how substances will react together. Using molarity, chemists can predict the outcome of reactions and prepare solutions with precise concentrations needed for various applications.

Copper(II) Sulfate

Copper(II) sulfate, often denoted as \( \text{CuSO}_4 \), is a blue crystalline solid commonly used in chemistry. It is a salt formed from copper and sulfate ions. In laboratories and industries, copper(II) sulfate plays several roles:

• It is used in agriculture as a fungicide.
• In analytical chemistry, it acts as a reagent.
• It serves in the electroplating of metals.

Copper(II) sulfate solutions exhibit a clear blue color, which helps in visually confirming the presence and concentration of the substance. The molar concentration of copper(II) sulfate in a solution is significant because it determines its effectiveness in various reactions and applications.

When dealing with solutions and dilutions of copper(II) sulfate, it's important to consider its impact on the final reaction outcome. Accurate dilutions ensure proper functioning in its intended use.

Dilution Formula

The dilution formula is a simple yet powerful tool in chemistry. It is used to determine the concentration of a solute in a diluted solution. The formula is expressed as:

• \( C_1 \times V_1 = C_2 \times V_2 \)

This equation shows that the total amount of solute remains unchanged despite the change in volume. Here, \( C_1 \) and \( V_1 \) are the initial concentration and volume, respectively, while \( C_2 \) and \( V_2 \) are their counterparts after dilution.

When you apply the dilution formula, keep these points in mind:

• Ensure all volumes are in the same unit before performing calculations.
• The formula assumes no solute is lost during the dilution process.

By understanding and using the dilution formula, you can easily find the new concentration after changing the volume of the solvent. This is especially useful in preparing solutions for experiments and industrial processes where precise concentrations are necessary.