Question

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

Short answer

The percent by volume (\(\% v/v\)) of acetic acid in the solution created by adding 75 mL of acetic acid to 725 mL of water is approximately 9.375%.

Step-by-step solution

Determine the total volume of the solution

Since we're adding 75 mL of acetic acid to 725 mL of water, we can find the total volume of the solution by adding the two volumes together: Total volume of solution = Volume of acetic acid + Volume of water

Calculate the total volume of the solution

Now, we can substitute the given values into the equation to find the total volume of the solution: Total volume of solution = 75 mL (acetic acid) + 725 mL (water) Total volume of solution = 800 mL

Calculate the percent by volume of acetic acid

Now that we have the total volume of the solution, we can use the percent by volume formula to calculate the \(\% v/v\) of acetic acid in the solution: Percent by volume (\( \% v/v\)) = \(\frac{Volume\, of\, solute (acetic\, acid)}{Total\, volume\, of\, solution}\) × 100 Percent by volume (\( \% v/v\)) = \(\frac{75\, mL}{800\, mL}\) × 100

Calculate the final value

Now, we can perform the calculation to find the percent by volume of acetic acid in the solution: Percent by volume (\( \% v/v\)) = \(\frac{75}{800}\) × 100 Percent by volume (\( \% v/v\)) ≈ 9.375 % Therefore, the percent by volume of acetic acid in the solution is approximately 9.375%.

Key concepts

Acetic Acid

Acetic acid is a colorless liquid with a distinct sour smell, commonly found in vinegar. It is a well-known carboxylic acid often used in chemical laboratories and industries. Understanding the properties of acetic acid is crucial when preparing solutions because it influences the overall reaction and outcome of the experiment.
When we talk about acetic acid in the context of solutions, it's the substance being dissolved in a solvent, like water, to form a homogeneous mixture. This mixture is often referred to as a solution and can be used to conduct various experiments or processes.
Acetic acid has many applications, such as in the food industry as a preservative, or in the chemical industry for producing different chemicals. Its concentration in the solution can affect the acidity, taste, and reaction rates, which is why calculating its concentration accurately is vital.

Solution Preparation

Solution preparation is a key skill in chemistry, especially when working with acids like acetic acid. Preparing a solution involves dissolving a solute, such as acetic acid, in a solvent like water.
There are a few key steps to keep in mind when preparing a solution:

• Measure the exact volume of the solute, which is the acetic acid in this context.
• Measure the volume of the solvent, often water, into which the solute will be dissolved.
• Add the solute to the solvent gradually, ensuring that it is evenly mixed to form a homogeneous solution.
• Ensure accurate measurements to achieve the desired concentration of the solution.

Proper solution preparation ensures that the desired chemical properties and reactions are achieved, which is especially crucial in experimental and industrial settings.

Volume Calculation

Calculating volumes accurately is essential in preparing chemical solutions. The percent by volume is a common method for expressing concentrations, key in quantifying solute proportions like acetic acid in a mixture.
To find the percent by volume, you first need to calculate the total volume of the solution by adding the volumes of the solute and solvent together. In the example exercise, adding 75 mL of acetic acid to 725 mL of water gives a total solution volume of 800 mL.
Once the total volume is known, use the formula for percent by volume:

• The formula is: \( \% \, v/v = \frac{\text{Volume of solute}}{\text{Total volume of solution}} \times 100\)

Substitute the values into the formula. For instance, with 75 mL of acetic acid in 800 mL total solution volume, divide 75 by 800 and multiply by 100 to get approximately 9.375%.
This computation provides a precise understanding of how much of the solution is composed of the solute, which is crucial for consistent and repeatable results.