Question

Calculate the mass percent \((\mathrm{m} / \mathrm{m})\) of a solution containing \(15.5 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and \(75.5 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

The mass percent of the solution is approximately 17.03%.

Step-by-step solution

- Calculate the total mass of the solution

Add the mass of the solute, \(\text{Na}_2\text{SO}_4\), and the mass of the solvent, \(\text{H}_2\text{O}\): \[ \text{Total mass} = 15.5 \text{ g} + 75.5 \text{ g} = 91.0 \text{ g} \]

- Calculate the mass percent (\text{m}/\text{m}) of the solute

The mass percent is calculated using the formula: \[ \text{Mass percent} = \frac{\text{Mass of solute}}{\text{Total mass of solution}} \times 100\text{%} \] Substituting the given values: \[ \text{Mass percent} = \frac{15.5 \text{ g}}{91.0 \text{ g}} \times 100\text{%} \]

- Simplify the calculation

Perform the division and multiplication: \[ \text{Mass percent} = \frac{15.5}{91.0} \times 100\text{%} \] \[ \text{Mass percent} \approx 17.03\text{%} \]

Key concepts

Solution Chemistry

In chemistry, a solution is a homogeneous mixture composed of two or more substances.
The substance present in the largest amount is called the solvent. It dissolves the smaller amount of one or more substances called solutes.
For example, in a sugar-water solution, water is the solvent and sugar is the solute.

The process of making a solution involves physical interaction between the solute and solvent. The solute particles disperse uniformly, leading to a consistent composition throughout.
It's important to distinguish between solutions and other types of mixtures. Unlike suspensions or colloids, solutions do not separate over time, and the solute particles are too small to be seen or filtered out by ordinary means.

Mass Percent Formula

The mass percent formula is used to express the concentration of a solute in a solution. It's calculated using the following equation: To calculate mass percent, follow these steps:

• Add the mass of the solute and the solvent to find the total mass of the solution.
• Divide the mass of the solute by the total mass of the solution.
• Multiply the result by 100 to get the mass percent of the solute.

Let's use a specific example to illustrate this:
Given: 15.5 g of \(\text{Na}_2\text{SO}_4\) (solute) and 75.5 g of \(\text{H}_2\text{O}\) (solvent).
Step 1: Total mass of the solution: \(15.5 \text{ g} + 75.5 \text{ g} = 91.0 \text{ g}\)
Step 2: Mass percent: \[ \text{Mass percent}= \frac{15.5} {91.0}\times 100\left{% \right} \approx 17.03\% \] By following these steps, you've determined that the mass percent of \(\text{Na}_2\text{SO}_4\) in the solution is approximately 17.03%.

Solute and Solvent

Understanding the roles of solutes and solvents is essential in solution chemistry.

The solute is the substance that gets dissolved. Examples include salts in water, sugar in tea, or gases in liquids like oxygen in water.

The solvent is the substance that does the dissolving. It's usually present in larger amounts. Water is the most common solvent and is often called the 'universal solvent' due to its ability to dissolve many substances.

Solutions can exist in different states of matter:

• Solid: Alloys like brass (zinc in copper).
• Liquid: Vinegar (acetic acid in water).
• Gas: Air (oxygen and other gases in nitrogen).

Factors affecting solubility include temperature, pressure, and the nature of the solute and solvent.
Increased temperature usually increases solubility for solids and liquids but decreases it for gases.
By comprehensively understanding the properties and interactions of solutes and solvents, you can manipulate and use solutions more effectively in various chemical processes.