Question

Calculate the mass percent \((\mathrm{m} / \mathrm{m})\) for the solute in each of the following solutions: a. \(25 \mathrm{~g}\) of \(\mathrm{KCl}\) and \(125 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) b. \(12 \mathrm{~g}\) of sugar in \(225 \mathrm{~g}\) of tea solution with sugar c. \(8.0 \mathrm{~g}\) of \(\mathrm{CaCl}_{2}\) in \(80.0 \mathrm{~g}\) of \(\mathrm{CaCl}_{2}\) solution

Short answer

a. 16.67%, b. 5.33%, c. 10.0%

Step-by-step solution

Define the mass percent formula

The mass percent \((\mathrm{m} / \mathrm{m})\) of a solute in a solution can be calculated using the formula: \[ \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \% \]

Calculate mass percent for part (a)

For part (a): 1. Mass of solute (\(\mathrm{KCl}\)) = 25 g 2. Mass of solvent (\(\mathrm{H}_{2}\mathrm{O}\)) = 125 g 3. Total mass of solution = Mass of solute + Mass of solvent = 25 g + 125 g = 150 g Now, apply the formula: \[ \text{Mass percent} = \left( \frac{25}{150} \right) \times 100\% = 16.67\% \]

Calculate mass percent for part (b)

For part (b): 1. Mass of solute (sugar) = 12 g 2. Mass of solution = 225 g Now, apply the formula: \[ \text{Mass percent} = \left( \frac{12}{225} \right) \times 100\% = 5.33\% \]

Calculate mass percent for part (c)

For part (c): 1. Mass of solute (\(\mathrm{CaCl}_{2}\)) = 8.0 g 2. Mass of solution = 80.0 g Now, apply the formula: \[ \text{Mass percent} = \left( \frac{8.0}{80.0} \right) \times 100\% = 10.0\% \]

Key concepts

Solute and Solvent

In any solution, there are typically two main components: the solite and the solvent. The solute is the substance that is dissolved, while the solvent is the medium that does the dissolving. For example, in a saltwater solution, salt is the solute and water is the solvent.
When you mix them together, the solute particles become evenly distributed within the solvent, forming a homogeneous mixture. The amount and types of solutes and solvents can vary in different solutions.

• Solute: The component that is dissolved (e.g., salt, sugar).
• Solvent: The component that dissolves the solute (e.g., water, alcohol).

Understanding these roles is crucial in chemistry because it helps us to describe and calculate different properties of solutions, such as their concentrations.

Mass Percent Formula

The mass percent formula is a way to express the concentration of a solute in a solution. It tells us how much mass of the solute is present per 100 units of the total mass of the solution.
To calculate it, you can use the following formula:
\[ \text{Mass percent} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\text{%} \]
This formula gives a clear and consistent way to express and compare concentrations across different types of solutions. Here are the steps to find the mass percent in a given solution:

• Step 1: Find the mass of the solute.
• Step 2: Find the total mass of the solution (solute + solvent).
• Step 3: Insert these values into the mass percent formula.

It's a straightforward yet powerful tool widely used in lab settings, industry, and everyday applications.

Solution Concentration

Solution concentration is a measure of how much solute is present in a given quantity of solvent or solution. It can be expressed in various ways, such as molarity, molality, and mass percent.

In everyday terms, a highly concentrated solution has a lot of solute, while a diluted solution has very little solute. Concentrations are important in many fields, such as chemistry, biology, and medicine, because they affect the properties of the solution.
For mass percent concentration as shown in the exercise, we focus specifically on the relative mass of the solute compared to the solution. Higher mass percent means a more concentrated solution, and vice versa.