Question

You have \(250 .\) mL of \(0.136 \mathrm{M}\) HCl. Using a volumetric pipet, you take \(25.00 \mathrm{mL}\) of that solution and dilute it to \(100.00 \mathrm{mL}\) in a volumetric flask. Now you take \(10.00 \mathrm{mL}\) of that solution, using a volumetric pipet, and dilute it to \(100.00 \mathrm{mL}\) in a volumetric flask. What is the concentration of hydrochloric acid in the final solution?

Short answer

The final concentration of HCl is 0.0034 M.

Step-by-step solution

Calculate Moles of HCl in the Initial Solution

We start by calculating the moles of HCl in the initial 250 mL solution. The concentration is given by the formula \ \[ C = \frac{n}{V} \] where \( C \) is the concentration and \( n \) is the number of moles, and \( V \) is the volume in liters. Thus, \[ n = C \times V = 0.136 \times 0.250 = 0.034 \text{ mol} \] This is the amount of HCl present in the initial solution.

Calculate Concentration after First Dilution

Take 25.00 mL of the initial solution. Using the formula for dilution (\( C_1V_1 = C_2V_2\)), calculate the new concentration after dilution to 100.00 mL.\[ 0.136 \times 0.025 = C_2 \times 0.100 \]Solve for \( C_2 \):\[ C_2 = \frac{0.136 \times 0.025}{0.100} = 0.034 \, \text{M} \] Thus, the concentration after the first dilution is 0.034 M.

Calculate Concentration after Second Dilution

Now take 10.00 mL of the solution from the first dilution. Again, use the dilution formula to determine the new concentration after further diluting to 100.00 mL.\[ 0.034 \times 0.010 = C_3 \times 0.100 \]Solve for \( C_3 \):\[ C_3 = \frac{0.034 \times 0.010}{0.100} = 0.0034 \text{ M} \] Therefore, the final concentration of the HCl in the solution is 0.0034 M.

Key concepts

Molar Concentration

Molar concentration, often referred to as molarity, is a key concept in chemistry that describes the amount of a solute (in moles) present in a given volume of solution. It is represented by the formula \( C = \frac{n}{V} \), where \( C \) is the concentration, \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters. This measure helps chemists understand how much of a particular substance is present in a solution, which is critical for reactions and dilutions.
For instance, in the exercise, the hydrochloric acid has an initial molarity of 0.136 M, indicating that there are 0.136 moles of HCl in every liter of solution. Understanding molar concentration aids in knowing how to mix solutions correctly to achieve the desired reaction outcomes. It is crucial in laboratory settings where precision is a must.

Volumetric Analysis

Volumetric analysis is a method in which the volume of a solution required to react with a given quantity of an analyte is measured. This type of analysis is helpful in determining concentrations through titrations and other dilution processes. The exercise involves using volumetric tools like pipets and volumetric flasks that help ensure precise measurements of liquids.
A volumetric pipet is used to transfer a specific volume of solution accurately. In the given exercise, it was used to measure 25.00 mL and 10.00 mL of hydrochloric acid solution precisely. Meanwhile, a volumetric flask, which typically has a narrow neck and is designed to contain a precise volume, is used here to dilute the solution to the exact required mark of 100.00 mL. Such tools minimize errors, making volumetric analysis reliable for experiments requiring high accuracy.

Hydrochloric Acid Concentration

Hydrochloric acid (HCl) is a strong acid that dissociates completely in water, making it important to know its concentration in any given solution. This concentration determines how acidic the solution is and how it will behave in chemical reactions. In the exercise, we begin with a 250 mL solution of 0.136 M HCl. This information is essential for the subsequent dilutions.
Each step in the dilution process results in a new hydrochloric acid concentration, calculable using the dilution formula: \( C_1V_1 = C_2V_2 \). Knowing the original and final volumes as well as the initial concentration makes it possible to determine the concentration after each dilution step. This process allows us to safely handle acidic solutions by controlling their strengths.

Concentration Dilution Process

The concentration dilution process involves reducing the concentration of a solute in a solution. This is typically done by adding more solvent to the mixture. The formula for this process is \( C_1V_1 = C_2V_2 \), where \( C_1 \) and \( C_2 \) are the initial and final concentrations, and \( V_1 \) and \( V_2 \) are the initial and final volumes, respectively.
In our exercise, dilution is used to decrease the concentration of HCl step by step. First, 25.00 mL of the solution is diluted to 100.00 mL, and later 10.00 mL of this diluted solution is again diluted to 100.00 mL, ultimately leading to a final concentration of 0.0034 M. This technique is integral in preparing reagents for experiments, ensuring that solutions are at safe and optimal strengths for various applications in science.