Question

Describe the steps to take in diluting a solution of \(0.500 \mathrm{M}\) \(\mathrm{HCl}\) to make \(250 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\)

Short answer

To make 250 mL of 0.100 M HCl from 0.500 M HCl, measure 50 mL of the concentrated HCl and add water until the final volume is 250 mL.

Step-by-step solution

Understand the Dilution Concept

Dilution involves adding more solvent to a solution to decrease its concentration. The amount of solute in the solution remains the same before and after dilution. This is expressed by the formula: \(C_1V_1 = C_2V_2\), where \(C_1\) and \(C_2\) are the initial and final concentrations, and \(V_1\) and \(V_2\) are the initial and final volumes.

Identify Known Values

We know the initial concentration (\(C_1\)) is 0.500 M, the final concentration (\(C_2\)) we want to obtain is 0.100 M, and the final volume (\(V_2\)) of the solution is 250 mL. Our goal is to find the volume of the initial concentrated solution (\(V_1\)) needed for dilution.

Insert Known Values into the Dilution Formula

Using the relation \(C_1V_1 = C_2V_2\), we can set up our equation: \(0.500 \text{ M} \times V_1 = 0.100 \text{ M} \times 250 \text{ mL}\).

Solve for the Unknown Volume \(V_1\)

To solve for \(V_1\), we rearrange the equation: \(V_1 = \frac{C_2V_2}{C_1}\). Plugging in the values, we get \(V_1 = \frac{0.100 \text{ M} \times 250 \text{ mL}}{0.500 \text{ M}}\).

Calculate the Initial Volume \(V_1\) Needed

Perform the calculation to find \(V_1\): \(V_1 = \frac{0.100 \text{ M} \times 250 \text{ mL}}{0.500 \text{ M}} = 50 \text{ mL}\).

Dilute the Solution

To prepare the desired dilution, you measure 50 mL of the 0.500 M \(HCl\) solution and then add enough water to reach a final volume of 250 mL.

Key concepts

Molarity

Molarity is a fundamental concept in chemistry used to describe the concentration of a solution. It is denoted by the symbol 'M' and is defined as the number of moles of solute per liter of solution. To calculate molarity, you divide the number of moles of the solute by the volume of the solution in liters:
\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
Molarity is particularly important when preparing solutions in a laboratory and executing chemical reactions that require precise concentrations. For instance, if a chemist needs to prepare a solution with a specific molarity, they need to carefully measure the amount of solute and the total volume of the solution to ensure accuracy.

Dilution Formula

The dilution formula is a simple yet powerful tool in chemistry for calculating the volume or concentration changes when diluting a solution. The fundamental idea is that the amount of solute in the solution remains the same before and after dilution, which allows us to relate initial and final concentrations and volumes through the equation:
\[ C_1V_1 = C_2V_2 \]
In this equation, \(C_1\) and \(V_1\) represent the initial concentration and volume, while \(C_2\) and \(V_2\) are the final concentration and volume after dilution. This relationship shows that if you know any three of the values, you can solve for the fourth. It's essential for accurately creating solutions with desired concentrations from stock solutions in both academic and industrial settings.

Exercise Improvement Advice:

• Always make sure to start with a stock solution that has a higher concentration than the desired dilution.
• It is crucial to mix the solution thoroughly after adding solvent to ensure even distribution of the solute throughout the new solution volume.

Concentration-Volume Calculation

Concentration-volume calculation involves manipulating the molarity of solutions and their respective volumes during dilutions or concentrations. In the exercise presented, we employed this principle to figure out how much of the higher concentration 0.500 M HCl solution was required to obtain 250 mL of a 0.100 M HCl solution.
To solve such problems, we depend on the dilution formula:
\[ V_1 = \frac{C_2V_2}{C_1} \]
Here, we solve for \(V_1\) by rearranging the equation to find the initial volume of concentrated solution needed. Once \(V_1\) is calculated, the procedure is straightforward: measure \(V_1\) of the concentrated solution and add enough solvent to achieve the final volume \(V_2\). This process is critical in many scientific applications including creating solutions for biological assays, chemical reactions, and calibrating instruments.
Following these methods ensures proper preparation of a diluted solution, crucial for the accuracy and reproducibility of experimental results.