Question

Calculate the percent by mass of the solute in each of the following aqueous solutions: (a) \(5.75 \mathrm{~g}\) of NaBr in \(67.9 \mathrm{~g}\) of solution, (b) \(24.6 \mathrm{~g}\) of \(\mathrm{KCl}\) in \(114 \mathrm{~g}\) of water, (c) \(4.8 \mathrm{~g}\) of toluene in \(39 \mathrm{~g}\) of benzene.

Short answer

(a) 8.47%, (b) 17.75%, (c) 10.96%

Step-by-step solution

Understand the formula

The percent by mass of a solute in a solution is calculated using the formula: \( \text{Percent by mass} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \% \). In cases where only the mass of the solvent is given, we add the solute's mass to find the total mass of the solution.

Calculate for NaBr in the solution (Part a)

Given: \( \text{Mass of NaBr} = 5.75 \text{ g} \), \( \text{Mass of solution} = 67.9 \text{ g} \). Substitute these values into the formula: \( \text{Percent by mass} = \left( \frac{5.75}{67.9} \right) \times 100 \% \). Calculate to get \( 8.47 \% \).

Calculate for KCl in the solution (Part b)

Given: \( \text{Mass of KCl} = 24.6 \text{ g} \), \( \text{Mass of water} = 114 \text{ g} \). First, find the mass of the solution: \( 114 + 24.6 = 138.6 \text{ g} \). Now use the formula: \( \text{Percent by mass} = \left( \frac{24.6}{138.6} \right) \times 100 \% \). Calculate to get \( 17.75 \% \).

Calculate for toluene in benzene (Part c)

Given: \( \text{Mass of toluene} = 4.8 \text{ g} \), \( \text{Mass of benzene} = 39 \text{ g} \). First, find the mass of the solution: \( 39 + 4.8 = 43.8 \text{ g} \). Now use the formula: \( \text{Percent by mass} = \left( \frac{4.8}{43.8} \right) \times 100 \% \). Calculate to get \( 10.96 \% \).

Key concepts

Mass of Solute

In chemistry, the term **solute** refers to the substance that is dissolved in a solvent to form a solution. This mass of solute is crucial when calculating the percent by mass, as it is the part of the total solution that we want to quantify.

To find the percent by mass, you'll first need to know the exact mass of the solute added. For instance, in the example exercise, we are given specific masses of substances like NaBr, KCl, and toluene. Each of these substances acts as the solute:

• NaBr with a mass of 5.75 g
• KCl with a mass of 24.6 g
• Toluene with a mass of 4.8 g

The mass of the solute impacts the overall properties of the solution, such as concentration. Thus, accurately measuring this mass is essential in calculations and scientific reactions.

Mass of Solution

The **mass of the solution** includes the total mass of both the solute and the solvent. For precise chemical calculations, understanding the mass of the entire solution is necessary. This metric helps chemists understand the concentration or strength of the solution.

For example, if only the solvent's mass is given, you must add the solute's mass to determine the mass of the full solution. In the steps provided:

• For NaBr, the mass of the solution was already known as 67.9 g.
• For KCl, we add its mass of 24.6 g to the 114 g of water, the solvent, to get a total solution mass of 138.6 g.
• For toluene, the addition to benzene yields a solution mass of 43.8 g.

The mass of the solution acts as a denominator in the percent by mass formula, and understanding how to compute it ensures accuracy in your chemistry work.

Percent Composition in Chemistry

**Percent composition** in chemistry is a calculation that shows the proportion of a particular component within a mixture. Specifically, the percent by mass describes the relative mass of the solute compared to the total mass of the solution. This is calculated using the following formula:

\[ \text{Percent by mass} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \% \]
Understanding this concept gives insight into the concentration and intensity of solutions. For instance, higher percent compositions suggest more concentrated solutions.

Using the exercise examples:

• The NaBr solution has a percent composition of 8.47%, meaning that about 8.47% of its mass is due to NaBr.
• The KCl solution has 17.75%, reflecting its higher concentration in terms of solute mass proportion.
• Lastly, toluene's percent composition is 10.96%, indicating a moderate concentration in benzene.

Such calculations are fundamental when formulating solutions for experiments and industrial processes, providing a standardized way to discuss and compare chemical solutions.