How many milliliters of \(0.10 \mathrm{M} \mathrm{HCl}\) must be added to \(50.0 \mathrm{~mL}\) of \(0.40 \mathrm{M} \mathrm{HCl}\) to give a final solution that has a molarity of \(0.25 M ?\)

The concept of dilution in chemistry refers to the process of reducing the concentration of a solute in a solution by adding more solvent. This procedure is crucial in various laboratory applications, including preparing solutions for experimentation and achieving desired concentrations for reactions.

Understanding dilution is fundamental for working with chemical solutions because it allows the laboratory technician or chemist to manipulate the concentration without changing the solute's amount. The formula typically used for dilution is expressed as \( C_1V_1 = C_2V_2 \), where \( C_1 \) and \( C_2 \) are the molar concentrations of the original and diluted solutions, while \( V_1 \) and \( V_2 \) represent their respective volumes.

To improve the ease of understanding for students, the dilution concept can be likened to adding water to a concentrated fruit juice to lessen its intensity, without altering the actual amount of juice being served. The principle remains the same; more solvent leads to a lower concentration of the solute, thereby diluting the solution.

Molarity, denoted as \( M \), is a commonly used unit for expressing the concentration of a solution in chemistry. It is defined as the amount of solute (usually measured in moles) present in one liter of solution.

The formula for molarity is given by \( M = \frac{n}{V} \), with 'n' representing the number of moles of the solute and 'V' the volume of the solution in liters. This measurement allows chemists to conduct precise calculations for reactions, as molarity directly correlates to the number of reactive particles in a given volume.

Importance of Molarity in Dilution

When performing a dilution, molarity acts as a bridge between the solute's concentration and the total volume of the solution. Precise molarity calculations ensure that reactions proceed correctly, especially when exact concentrations are needed, as in the case of the provided exercise.

Acid-base titration is a quantitative analytical technique used to determine the concentration of an unknown acid or base by neutralizing it with a base or acid of known concentration. The point at which neutralization occurs is known as the equivalence point and is often indicated by a color change due to an indicator added to the solution.

The relationship between the volume and concentration of the titrant (the solution of known concentration) and the analyte (the solution of unknown concentration) is described by the titration formula: \( C_aV_a = C_bV_b \), where \( C_a \) and \( C_b \) are the concentrations of the acid and base, and \( V_a \) and \( V_b \) are the respective volumes. By knowing three of these values, you can calculate the fourth, which is a vital aspect of this analytical method.

Dilution's Role in Titration

Dilutions are often performed in the preparatory phases of a titration to reach a desired concentration level that will allow precise determination of an unknown concentration upon reaching the equivalence point. Mastering both dilution calculations and titration techniques is essential for students in the field of chemistry, especially when dealing with acid-base reactions.