Ocean water contains \(3.5 \% \mathrm{NaCl}\) by mass. What mass of ocean water in grams contains \(45.8 \mathrm{~g}\) of \(\mathrm{NaCl}\) ?

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the reactants and products in chemical reactions. It involves calculations that draw on the law of conservation of mass, which states that matter is neither created nor destroyed in chemical reactions. With this principle in mind, stoichiometry allows chemists to predict the amount of substances consumed and produced during a reaction.

For example, in our given exercise with ocean water and NaCl, stoichiometry comes into play when we calculate the mass of ocean water that will contain a specific mass of NaCl. Since the percentage by mass is given, stoichiometry helps us calculate the necessary quantity of ocean water to obtain 45.8 grams of NaCl. Inside this calculation lies the core principle of stoichiometry, which involves using the relationship between mass and moles to figure out what quantity of one substance is required to react with a given quantity of another substance.

Solution concentration is a measure of the quantity of a solute that is contained in a given quantity of solvent. Common ways to express solution concentration include molarity, molality, and percentage by mass. In our exercise, the concentration of NaCl in ocean water is given as a percentage by mass (3.5%).

This particular way of expressing concentration is especially useful when considering the physical properties of the solution that depend on the mass of the dissolved solute, such as boiling point elevation or freezing point depression. Understanding the concept of solution concentration is crucial when preparing solutions in a laboratory or industry setting, as well as when analyzing substances in environmental or biological contexts, like measuring salinity in ocean water.

Proportions in chemistry refer to the relationship of quantities and concentrations within a substance or reaction. They are the mathematical backbone to many chemical calculations, especially when discussing the relationships in stoichiometry or solution concentrations. A common application of proportions is the 'cross-multiplication' technique used to solve for an unknown quantity, a method also applied in our textbook example.

When chemists work with proportions, they can effectively relate different substances' quantities through the use of ratios. In our textbook example, the proportion we use is between the mass of NaCl and the mass of seawater. Understanding how to set up and solve these proportions is vital for students and professionals working in chemistry. Here, the proportion aids us in determining the total mass of ocean water based on the given percentage by mass of NaCl, directly applying the concept to a practical scenario.