Question

What mass of solute is dissolved in the following solutions? (a) \(10.0 \mathrm{~g}\) of \(2.50 \% \mathrm{~K}_{2} \mathrm{CO}_{3}\) solution (b) \(50.0 \mathrm{~g}\) of \(5.00 \% \mathrm{Li}_{2} \mathrm{SO}_{4}\) solution

Short answer

(a) 0.25 g of K2CO3; (b) 2.50 g of Li2SO4.

Step-by-step solution

Understand the Problem

The problem asks for the mass of solute in different solutions. We are given a percentage concentration by mass for each solution, which tells us how many grams of solute are present in 100 grams of solution.

Set Up the Calculation for Part (a)

For the solution with concentration \(2.50\%\), this means there are 2.50 grams of solute for every 100 grams of solution. We have 10.0 grams of solution, so we calculate the mass of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) as follows: \[ \text{mass of solute} = \left(10.0 \text{ g of solution} \right) \times \left(\frac{2.50 \text{ g of solute}}{100 \text{ g of solution}}\right) \]

Perform the Calculation for Part (a)

Calculate the mass of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) in the solution: \[ \text{mass of solute} = \left(10.0 \right) \times \left(\frac{2.50}{100}\right) = 0.25 \text{ g} \]

Set Up the Calculation for Part (b)

For the solution with concentration \(5.00\%\), this means there are 5.00 grams of solute for every 100 grams of solution. We have 50.0 grams of solution, so we calculate the mass of \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) as follows: \[ \text{mass of solute} = \left(50.0 \text{ g of solution} \right) \times \left(\frac{5.00 \text{ g of solute}}{100 \text{ g of solution}}\right) \]

Perform the Calculation for Part (b)

Calculate the mass of \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) in the solution: \[ \text{mass of solute} = \left(50.0 \right) \times \left(\frac{5.00}{100}\right) = 2.50 \text{ g} \]

Key concepts

The Basics of Solution Chemistry

In solution chemistry, understanding how different substances interact when mixed together is crucial. A solution is a type of homogeneous mixture 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, often a liquid like water.
Think of a simple example: sugar dissolved in water. Here, sugar is the solute, and water is the solvent. When they mix, the molecules of sugar disperse throughout the water, resulting in a uniform solution.
Key points to remember about solutions:

• Solutions are homogeneous, meaning their composition is consistent throughout.
• The solute is present in a smaller amount, while the solvent is generally larger.
• Concentration describes how much solute is present in a given amount of solution.

To analyze solutions, we often consider their concentration, which can be expressed in various ways including mass percent concentration, molarity, and molality. Here, we'll focus on percentage by mass."

Calculating Mass of Solute

Knowing how to calculate the mass of solute in a solution is fundamental in chemistry. Let's break this down with a simple method, using the formula related to percentage by mass.
Percentage by mass tells us how much solute is present in a certain amount of solution. This can be expressed as a percentage because it provides an easy comparison. If a solution is 2% solute, this means there are 2 grams of solute in 100 grams of solution.
The formula to calculate the mass of a solute is:

• Mass of Solute = (Mass of Solution) \( \times \left( \frac{\text{Percent Concentration}}{100} \right) \)

For example, if you have a 10 g solution that is 2.5% solute, distribute this percentage:

• Calculate mass: \( 10 \text{ g} \times \left( \frac{2.5}{100} \right) = 0.25 \text{ g} \)

This lets us know that there are 0.25 grams of solute in the solution. Knowing how to extract these kinds of values from solutions prepares you for practical laboratory work.

Understanding Percentage by Mass

Percentage by mass, sometimes called mass percent concentration, is a straightforward way to express concentration. It signifies what portion of the solution's total mass is attributed to the solute.
The formula for percentage by mass is:

• Percentage by Mass = \( \left( \frac{\text{Mass of Solute}}{\text{Total Mass of Solution}} \right) \times 100 \)

This form of concentration is particularly helpful when you need to quickly understand how concentrated a solution is.
Example:

• If you dissolve 5 grams of salt in 95 grams of water, the total mass of the solution is 100 grams. The percentage by mass of the salt is \( \left( \frac{5}{100} \right) \times 100 = 5\% \).

This method is widely applicable in real-world scenarios, such as in the formulation of chemical solutions or when diluting or concentrating compounds. It gives an easy visual of the solute's relative mass in the solution.