Problem 48 - 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 of copper(II) sulfate in the diluted solution is 0.0100 M.

Step 1: Understand Dilution Formula

The dilution formula is given by: \[ C_1V_1 = C_2V_2 \] where \( C_1 \) is the initial concentration, \( V_1 \) is the initial volume, \( C_2 \) is the final concentration, and \( V_2 \) is the final volume.

Step 2: Identify Given Values

We know that \( C_1 = 0.0250 \mathrm{M} \), \( V_1 = 4.00 \mathrm{mL} \), and \( V_2 = 10.0 \mathrm{mL} \). We need to find \( C_2 \).

Step 3: Rearrange Dilution Formula

Rearrange the formula to solve for \( C_2 \): \[ C_2 = \frac{C_1V_1}{V_2} \]

Step 4: Substitute Values

Substitute the known values into the equation: \[ C_2 = \frac{0.0250 \times 4.00}{10.0} \]

Step 5: Calculate Final Concentration

Perform the calculation: \[ C_2 = \frac{0.100}{10.0} = 0.0100 \mathrm{M} \].

Key Concepts

Molar Concentration

Molar concentration, also known as molarity, is a measure of the concentration of a solute in a solution. It tells us how many moles of a substance are present in one liter of solution. The unit used for molarity is molar, represented by "M".

To calculate molarity, you can use the formula: \[M = \frac{n}{V}\]where:

• \(M\) is the molarity in moles per liter (M)
• \(n\) is the number of moles of solute
• \(V\) is the volume of the solution in liters

Molarity provides an easy way to discuss concentrations in chemistry that can be used in various calculations, such as determining the amount of reactant needed in a chemical reaction or analyzing dilution in solution preparation.

Copper(II) Sulfate

Copper(II) sulfate, commonly known by its chemical formula \(\text{CuSO}_4\), is a popular chemical compound in labs and industrial applications. It is known for its distinctive blue color when hydrated, as it commonly exists as a pentahydrate \(\text{CuSO}_4\cdot5\text{H}_2\text{O}\). This is the form that appears most often in chemistry laboratories.

Here are several important aspects of Copper(II) sulfate to understand:

• It is a highly soluble salt in water, making it ideal for various solutions.
• Frequently used in agriculture and industries for activities such as pest control and electroplating.
• In educational settings, it's often used to demonstrate chemical reactions and properties, such as conducting specific precipitation reactions.

These properties make copper(II) sulfate an essential component in experiments dealing with solutions and concentrations.

Solution Dilution

Solution dilution is a process whereby the concentration of a solute in a solution is decreased by adding more solvent. It helps chemists and students create solutions of desired concentrations for experiments and various applications.

The fundamental principle behind dilution is that the number of moles of solute remains constant before and after dilution. Consequently, the dilution formula \(C_1V_1 = C_2V_2\) is used to calculate how much solvent is needed or to find the new concentration.

The formula is interpreted as:

• \(C_1\) and \(V_1\) are the initial concentration and volume, respectively.
• \(C_2\) is the final concentration we want to find, and \(V_2\) is the final volume after dilution.

This formula allows for the practical application of dilutions in various fields, such as pharmaceuticals, food industry, and biochemistry. Understanding how to apply this concept is crucial for designing experiments and ensuring precise measurements in solution chemistry.