Problem 70 - Chemistry Matter and Change

Question

Calculate the percent by volume of a solution created by adding 75 \(\mathrm{mL}\) of acetic acid to 725 \(\mathrm{mL}\) of water.

Step-by-Step Solution

Answer

The percent by volume of acetic acid in the solution is 9.375%.

Step 1: Understand the Formula for Percent by Volume

The percent by volume of a solution is calculated using the formula: \( \text{Percent by Volume} = \left( \frac{\text{Volume of Solute}}{\text{Total Volume of Solution}} \right) \times 100 \% \). In this problem, the solute is acetic acid and the solvent is water.

Step 2: Determine the Volume of the Solute

The volume of the solute, which is acetic acid in this context, is given as 75 mL.

Step 3: Determine the Total Volume of the Solution

The total volume of the solution is the sum of the volumes of the solute and solvent. Here, it is calculated as follows: \( 75 \, \text{mL (acetic acid)} + 725 \, \text{mL (water)} = 800 \, \text{mL} \).

Step 4: Calculate the Percent by Volume

Substitute the volume of the solute and the total volume into the percent by volume formula: \( \text{Percent by Volume} = \left( \frac{75 \, \text{mL}}{800 \, \text{mL}} \right) \times 100 \% \). Simplifying the calculation gives \( 9.375 \% \).

Key Concepts

Understanding Acetic Acid

Acetic acid, also known by its chemical formula \( \text{CH}_3\text{COOH} \), is a simple carboxylic acid and is the main component of vinegar, aside from water. It is a colorless liquid with a distinctive sour taste and pungent smell that is widely used in both industrial and household applications. In chemistry, acetic acid is commonly used as a reagent to produce various chemical compounds.

It is important to understand that when working with acetic acid in solutions, its concentration is often expressed in terms of percent by volume, which allows us to understand the proportion of acetic acid compared to the entire solution. For instance, in our exercise, % by volume helped us determine the concentration of acetic acid when mixed with water. This is crucial for applications where specific solution concentrations are required, such as in food preservation or chemical reactions.

The Role of Solvent and Solute

In the context of solutions, the terms "solvent" and "solute" describe the components that make up a solution. A solution is a homogeneous mixture composed of a solute, which is the substance that gets dissolved, and a solvent, which is the substance that does the dissolving.

For the exercise we are looking at, acetic acid acts as the solute, because it is the substance being dissolved. Water acts as the solvent because it dissolves the acetic acid. Understanding the roles of these two components is central to grasping how solutions work both in nature and in experimental settings.

• Solute: The substance present in a smaller amount.
• Solvent: The substance present in a greater amount.

A clear understanding of these roles' difference helps when performing calculations or creating solutions for industrial or lab purposes.

Exploring Solution Concentration

Solution concentration is a term that refers to the amount of solute present in a given quantity of solvent or solution. Concentration can be expressed in several ways, such as molarity, molality, or percent by volume.

Percent by volume, in particular, is a useful measure in the context of liquid mixtures, involving the volume of the solute and the volume of the entire solution. It's calculated using the formula: \[ \text{Percent by Volume} = \left( \frac{\text{Volume of Solute}}{\text{Total Volume of Solution}} \right) \times 100 \% \]This gives a straightforward percentage that represents how much of the solution's total volume is made up by the solute.

In our exercise, accurately calculating the percent by volume was key in determining the concentration of acetic acid in the solution. Understanding how to calculate and interpret the concentration allows for accurate formulation of solutions required in many scientific and industrial applications.