Question

Calculate the percent by mass of solute in each of the following solutions. a. \(2.14 \mathrm{~g}\) of potassium chloride dissolved in \(12.5 \mathrm{~g}\) of water b. \(2.14 \mathrm{~g}\) of potassium chloride dissolved in \(25.0 \mathrm{~g}\) of water c. \(2.14 \mathrm{~g}\) of potassium chloride dissolved in \(37.5 \mathrm{~g}\) of water d. \(2.14 \mathrm{~g}\) of potassium chloride dissolved in \(50.0 \mathrm{~g}\) of water

Short answer

The percent by mass of potassium chloride in each solution is: a. \(14.61\%\) b. \(7.88\%\) c. \(5.40\%\) d. \(4.10\%\)

Step-by-step solution

Identify the Mass of Solute and Solvent in Each Solution

In each solution, the mass of solute (potassium chloride) is given as \(2.14 \mathrm{~g}\). The mass of solvent (water) is different in each solution and is provided in the exercise.

Calculate the Total Mass of Each Solution

To find the total mass of each solution, add the mass of solute (potassium chloride) to the mass of solvent (water) for each respective solution. a. \(2.14 \mathrm{~g} + 12.5 \mathrm{~g} = 14.64 \mathrm{~g}\) b. \(2.14 \mathrm{~g} + 25.0 \mathrm{~g} = 27.14 \mathrm{~g}\) c. \(2.14 \mathrm{~g} + 37.5 \mathrm{~g} = 39.64 \mathrm{~g}\) d. \(2.14 \mathrm{~g} + 50.0 \mathrm{~g} = 52.14 \mathrm{~g}\)

Calculate the Percent by Mass of Potassium Chloride in Each Solution

To find the percent by mass of potassium chloride in each solution, divide the mass of solute (potassium chloride) by the total mass of the solution and multiply by 100. a. \(\frac{2.14 \mathrm{~g}}{14.64 \mathrm{~g}} \times 100 = 14.61\% \) b. \(\frac{2.14 \mathrm{~g}}{27.14 \mathrm{~g}} \times 100 = 7.88\% \) c. \(\frac{2.14 \mathrm{~g}}{39.64 \mathrm{~g}} \times 100 = 5.40\% \) d. \(\frac{2.14 \mathrm{~g}}{52.14 \mathrm{~g}} \times 100 = 4.10\% \) So, the percent by mass of potassium chloride in each solution is: a. \(14.61\%\) b. \(7.88\%\) c. \(5.40\%\) d. \(4.10\%\)

Key concepts

Percent Composition

Percent composition is a key concept in chemistry that refers to the percentage by mass of each element within a compound or a component within a mixture. When relating it to solutions, it often involves determining the mass percentage of a solute in a solution. To put it simply, this concept is used to express the proportion of a substance within a mixture.

For example, if you dissolve sugar in water to make a sweet solution, the percent composition will tell you how much sugar is present compared to the total mass of the solution. This can be particularly helpful for understanding the concentration of solutions, which is a measure of how much solute exists within a solvent. So when you're enjoying that sweet tea, the percent by mass of sugar is what determines just how sweet it is.

In the exercise provided, finding the percent by mass of potassium chloride in various water solutions involved dividing the mass of potassium chloride (the solute) by the total mass of the solution (the sum of the mass of potassium chloride and the mass of water), and then multiplying the result by 100 to get a percentage. This provides a clear picture of how concentrated the solute is in each solution.

Concentration of Solutions

Concentration of solutions is a fundamental concept in chemistry that describes the amount of a substance (solute) present in a mixture, relative to the volume or mass of the solvent or total solution. Concentration can be expressed in various ways, including molarity, molality, normality, and percent by mass or volume. The latter, which was the focus of our exercise, is particularly intuitive as it involves simple ratios and multiplication.

In everyday terms, the concentration of a substance can dictate its strength or intensity. Think about making lemonade: adding more lemon juice (solute) to the water (solvent) increases the concentration, resulting in a stronger taste. Similarly, diluting the lemonade with more water reduces the concentration, making it less potent.

The exercise provided is an excellent example of how the concentration of a solution changes with the addition of more solvent. As more water was added to the potassium chloride, the percent by mass of potassium chloride decreased, indicating a lower concentration of the solute in each solution.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's like a recipe in cooking: stoichiometry tells you how much of each reactant you need to produce a desired amount of product. This involves calculations based on the balanced chemical equation and includes concepts such as the mole, molar mass, and Avogadro's number.

While stoichiometry wasn't directly used in our exercise, understanding the stoichiometric coefficients in a balanced reaction would allow you to predict how much reactant is necessary to create a certain amount of product. In the context of solution chemistry, stoichiometry can also be applied to calculate concentrations when reactants are mixed or when products are formed in a reaction.

In a broader sense, the principles of stoichiometry are essential for creating solutions with specific properties, such as the desired concentration of a solute. This is crucial in fields ranging from culinary arts, where recipes are followed meticulously, to pharmacology, where drug concentrations must be accurate for efficacy and safety.