Two solutions of a substance (non-electrolyte) are mixed in the following manner. \(480 \mathrm{~mL}\) of \(1.5 \mathrm{M}\) first solution \(+520 \mathrm{~mL}\) of \(1.2 \mathrm{M}\) second solution. What is the molarity of the final mixture? (a) \(1.344 \mathrm{M}\) (b) \(2.70 \mathrm{M}\) (c) \(1.50 \mathrm{M}\) (d) \(1.20 \mathrm{M}\)

Understanding solution concentration is fundamental when working with chemical solutions. Concentration refers to the amount of a substance, known as the solute, dissolved in a specific volume of solvent. The measure of concentration in chemistry often comes in the form of molarity (M), which indicates the moles of solute per liter of solution.

When combining two solutions with known molarities, the resulting mixture will have a concentration that reflects the combined volume and the total moles of solute. To solve problems involving the mixture of solutions, as seen in our exercise, recognizing the relationship between solute, solvent, and concentration is critical. A higher volume of solvent would typically dilute the solute, reducing concentration, whereas adding more solute would increase it, presuming the volume remains constant.

This concept is the backbone of many operations in the scientific field, especially when preparing solutions for reactions, dilutions, or titrations. The ability to accurately calculate and understand the concentration of solutions ensures precise and effective experimentation and analysis.

The term moles of solute is a key concept in chemistry that corresponds to the quantity of substance in a given solution. A mole is a unit that measures the amount of a chemical substance and is defined by Avogadro's number, which is approximately 6.022 × 10²³ entities (atoms, molecules, ions, etc.).

To perform molarity calculations, as demonstrated in the problem, we first need to determine the moles of solute in each solution. This is achieved through the formula:
Moles = Molarity × Volume in liters.
In practical terms, knowing the moles of solute helps quantitatively describe the amount of a substance in a reaction or solution. Whether you are diluting a solution or reacting substances to form new products, the number of moles involved provides a clear way to measure and predict the outcomes based on stoichiometric ratios and principles.

In the context of the given exercise, volumetric analysis refers to the technique used to determine the concentration of a solute in a solution through volume measurements. This analytical method is crucial when we mix solutions of different volumes and concentrations and want to determine the resulting mixture's molarity.

Volumetric analysis typically involves a series of steps including measuring volumes precisely with a graduated cylinder or a volumetric flask, and manipulating these volumes mathematically as we have seen in the step by step solution above. The final aim is often to derive concentration values or other related quantities such as purity or formula weight of a substance.

Application in the Exercise

When we follow the steps of volumetric analysis, we begin by precisely measuring the volume of the solutions we are working with. Then, through the molarity calculations we performed, the total number of moles of solute is obtained. Finally, by combining the total volume with the total moles, we are able to find the concentration of the new mixture, adhering to the principles of volumetric analysis.