Calculate the percent by mass of the solute in each of the following aqueous solutions: (a) \(5.50 \mathrm{~g}\) of \(\mathrm{NaBr}\) in \(78.2 \mathrm{~g}\) of solution, (b) \(31.0 \mathrm{~g}\) of \(\mathrm{KCl}\) in \(152 \mathrm{~g}\) of water, (c) \(4.5 \mathrm{~g}\) of toluene in \(29 \mathrm{~g}\) of benzene.

Understanding solution concentration is a fundamental aspect of chemistry and can be quite practical in various scientific applications. Solutions are mixtures composed of two or more substances, where at least one substance, the solute, is dissolved in another, the solvent, resulting in a homogeneous mixture.

To quantify the concentration of a solution, there are several methods, and percent by mass is one of the simplest. This measure expresses the mass of the solute as a percentage of the total mass of the solution. The formula to calculate percent by mass is given by \( \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\% \) .

Using this formula allows us to understand the relative amount of solute in a given volume of solvent, which is crucial when the balance between solute and solvent determines the effectiveness of a solution, such as in medical solutions or chemical reactions. This simple yet powerful concept aids students and chemists alike in standardizing solutions for various experiments and applications.

Aqueous solutions play an essential role in chemistry, biology, and our daily lives. When we speak of aqueous solutions, we refer to a solution in which water is the solvent. This characteristic is what makes such solutions 'aqueous'. Water is called the 'universal solvent' because it can dissolve a wide range of substances, making it incredibly versatile.

Aqueous solutions can be found everywhere, from the oceans, where salt is dissolved in water, to the human body, where various salts and sugars are dissolved in the blood. Understanding the behavior of solutes in aqueous solutions is fundamental to fields such as biochemistry and environmental science. For instance, the solubility of a gas in water can determine the habitability of environments for aquatic life.

Every solution is composed of a solute and a solvent. The solute is the substance that gets dissolved, while the solvent is the substance that does the dissolving. In the context of our examples with aqueous solutions, water acts as the solvent, and substances like NaBr, KCl, or toluene serve as solutes.

The distinction between solute and solvent is crucial when preparing solutions. A solute's solubility in a specific solvent can vary widely, which influences how substances interact in a solution. For instance, salt (NaCl) is highly soluble in water but would not dissolve as readily in a solvent like benzene.

Moreover, the ratio of solute to solvent influences the solution's properties, such as boiling point, freezing point, and vapor pressure. Hence, understanding the interplay between solute and solvent is not just academic—it's vital for practical applications like antifreeze formulations or pharmaceuticals.