Question

If \(25.0 \mathrm{mL}\) of \(0.104 \mathrm{M} \mathrm{BaCl}_{2}\) solution is pipetted into a 100 -mL volumetric flask, and water added to the calibration mark, what is the concentration of the resulting dilute solution?

Short answer

The final concentration of the resulting dilute BaCl₂ solution after diluting with water is \(0.026 M\).

Step-by-step solution

List down the given information

We are given the following information: - Initial Volume (V₁) = 25.0 mL - Initial Concentration (C₁) = 0.104 M (Moles per Liter) - Final Volume (V₂) = 100 mL (after dilution) Our goal is to find the final concentration (C₂).

Use the dilution formula to solve for C₂

We will use the dilution formula C₁V₁ = C₂V₂ to solve for the final concentration (C₂). First, we'll plugin the given values into the formula: \(C₁V₁ = C₂V₂\) \((0.104 M)(25.0 mL) = C₂(100 mL)\)

Solve for the final concentration (C₂)

Now solve for C₂: \(C₂ = \frac{(0.104 M)(25.0 mL)}{100 mL}\) \(C₂ = \frac{2.6 M·mL}{100 mL}\) \(C₂ = 0.026 M\)

Write the final answer

The final concentration of the resulting dilute BaCl₂ solution after diluting with water is 0.026 M.

Key concepts

Molarity

Molarity, denoted by the symbol 'M', is an essential concept in chemistry that stands for molar concentration. It is a measure of the number of moles of a substance per liter of solution. Here, a mole corresponds to Avogadro's number (approximately 6.022 x 10²³) of particles, whether they are atoms, molecules, ions, or electrons.

In the context of dilutions, understanding molarity is crucial as it allows us to express the concentration of a solute in a solution before and after dilution. For instance, in our exercise, the initial concentration of the BaCl₂ solution was given as 0.104 M, indicating that we have 0.104 moles of barium chloride for every liter of solution.

To better grasp molarity, one can consider it as the 'strength' of a solution. A high molarity implies a high concentration of solute, while a low molarity indicates a more dilute solution. When solutions are diluted by adding more solvent, the molarity decreases, but the total number of moles of the solute remains unchanged.

Concentration of Solutions

The concentration of a solution refers to the amount of solute that is dissolved in a given volume of solvent. It is a fundamental concept in chemistry because it influences the rate of chemical reactions, the effectiveness of a chemical in its function, and how a given chemical should be dosed or applied. Concentrations can be expressed in various ways, such as molarity, percentage concentration, parts per million (ppm), and mole fraction.

In our exercise, the concentration of the barium chloride solution is changing because the volume of the solution is increased by adding water up to the 100-mL mark on the volumetric flask. This process dilutes the solution, spreading the same amount of solute over a larger volume, thereby reducing its concentration. The concept of conservation of mass applies here; we have the same amount of barium chloride before and after the dilution, but it's now present in a larger volume, leading to a lower concentration of the solution.

Volumetric Analysis

Volumetric analysis, also known as titrimetry, involves measuring the volume of a solution of known concentration (a titrant) which is used to determine the concentration of an analyte (the substance being analyzed) in a sample. While our original exercise doesn't involve an actual titration, it encompasses important principles of volumetric analysis, such as precise measurement of volume and understanding the relationships between concentration and volume.

In the process described, we use a 100-mL volumetric flask to make a dilution. Volumetric flasks are designed for precise volume measurements, making them indispensable in volumetric analysis. The exactitude of volumetric devices ensures the accuracy of dilutions and the reliability of subsequent calculations. Also, by employing the molarity concept, students learn the stoichiometry of solutions which is a pillar of volumetric analyses in determining the concentration of unknown solutions through various titration methods.