Question

Concentrated hydrochloric acid is \(12 \mathrm{M}\). What is the molarity of an \(\mathrm{HCl}\) solution prepared by diluting \(10.0 \mathrm{~mL}\) of concentrated acid to a total volume of \(250.0 \mathrm{~mL}\) ?

Short answer

The molarity of the diluted solution is \(0.48 \mathrm{M}\).

Step-by-step solution

Identify the Given Information

The problem states that the concentration of the initial hydrochloric acid (HCl) solution is \(12 \mathrm{M}\), and we have \(10.0 \mathrm{~mL}\) of this solution. The final volume after dilution is \(250.0 \mathrm{~mL}\).

Use the Dilution Formula

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

Insert Given Values into the Formula

Insert the given values: \(C_1 = 12 \mathrm{M}\), \(V_1 = 10.0 \mathrm{~mL}\), and \(V_2 = 250.0 \mathrm{~mL}\). The equation becomes \(12 \times 10.0 = C_2 \times 250.0\).

Solve for the Unknown Molarity

Rearrange the equation to solve for \(C_2\), the molarity of the diluted solution. Divide both sides by \(250.0\): \(C_2 = \frac{12 \times 10.0}{250.0}\).

Calculate the Final Molarity

Calculate \(C_2\): \(C_2 = \frac{120}{250} = 0.48 \mathrm{M}\). Thus, the molarity of the diluted HCl solution is \(0.48 \mathrm{M}\).

Key concepts

Understanding Molarity

Molarity is a key concept in chemistry referring to the concentration of a solution. It is expressed as moles of solute per liter of solution, denoted by the unit mol/L, or simply M. Consider molarity as a way to describe "how much" of a substance is present in a given solution.
In the case of hydrochloric acid (HCl), if we have a solution that is 12 M, it means there are 12 moles of HCl dissolved in every liter of that solution. This concentration level is quite high, indicating a strong or concentrated solution.
To ensure accuracy, especially in chemical reactions and experiments, knowing the molarity helps in determining how much of a chemical is available for interaction. This is crucial when precise amounts of reagents are necessary for reactions to occur as expected.

Chemical Dilution Basics

Chemical dilution involves reducing the concentration of a solution by adding more solvent, while keeping the amount of solute the same. Think of dilution as spreading a small amount of coloring in more water; the color becomes faint, just like how the concentration decreases.
In the dilution process, the initial solution, often concentrated, is mixed with additional solvent, such as water, to achieve a desired concentration level. The amount of solute stays unchanged, only the solution volume increases.
For dilution calculations, the relationship between the initial and final concentrations and volumes can be captured with the formula: \[ C_1V_1 = C_2V_2 \]
Here:

• \( C_1 \) is the initial concentration.
• \( V_1 \) is the initial volume.
• \( C_2 \) is the final concentration.
• \( V_2 \) is the final volume.

This equation ensures that the product of the initial concentration and volume equals the product of the final concentration and volume, maintaining the total amount of solute.

Properties of Hydrochloric Acid

Hydrochloric acid (HCl) is a strong acid, commonly encountered in both industrial and laboratory settings. Known for its strong acidic properties, it fully dissociates into hydrogen ions (H\(^+\)) and chloride ions (Cl\(^-\)) in water.
The potency of hydrochloric acid makes it a valuable tool in various chemical processes. It's used in applications such as cleaning metals, fabricating materials, and as a chemical reagent to prepare other compounds.
Despite its usefulness, HCl requires careful handling due to its corrosive nature. Even dilute solutions can be hazardous, which highlights the importance of using protective equipment and measures when working with this substance.
In educational contexts, understanding and safely handling acids like HCl expands knowledge of chemical behavior and reactions, fostering responsible and knowledgeable chemists.