Problem 131 - General Chemistry

Question

Vinegar contains acetic acid (about \(5 \%\) by mass). Pure acetic acid has a strong vinegar smell but is corrosive to the skin. What volume of pure acetic acid has a mass of \(35.00 \mathrm{~g} ?\) The density of acetic acid is \(1.053 \mathrm{~g} / \mathrm{mL}\).

Step-by-Step Solution

Answer

The volume of pure acetic acid is approximately 33.23 mL.

Step 1: Understand the problem

We need to find the volume of pure acetic acid that has a mass of 35.00 grams. We know that density relates mass and volume, and we are given the density of acetic acid as 1.053 g/mL.

Step 2: Recall the formula for density

Density is defined as mass divided by volume. Mathematically, it can be expressed as \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). We can rearrange this formula to solve for volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Step 3: Insert the given values

We use the rearranged formula for volume, substituting the mass (35.00 g) and the density (1.053 g/mL):\[ \text{Volume} = \frac{35.00 \text{ g}}{1.053 \text{ g/mL}} \].

Step 4: Calculate the volume

Perform the division: \( \frac{35.00}{1.053} \approx 33.23 \). Thus, the volume is approximately 33.23 mL.

Key Concepts

Density Calculation

Understanding density is key to solving problems related to mass and volume. In the case of acetic acid, density provides insight into how much mass is contained within a unit volume. Density is a measure of how tightly the molecules of a substance are packed together. It is expressed in terms of mass per volume, such as grams per milliliter (g/mL).

To calculate density, use the formula:

• Density = Mass / Volume

The closer the molecules are packed, the higher the density. For acetic acid, with a density of 1.053 g/mL, every milliliter weighs 1.053 grams. This understanding allows us to determine changes in volume given a certain mass or vice versa.

Volume Calculation

Finding the volume of a substance like acetic acid involves using the formula that relates volume, mass, and density. Volume is the amount of space that an object occupies. When given the mass and density, you can calculate volume using the rearranged formula:

• Volume = Mass / Density

This formula requires you to divide the mass of the substance by its density. For our problem, substituting 35.00 grams of mass and a density of 1.053 g/mL, the calculation becomes:

• Volume = 35.00 g / 1.053 g/mL

After performing the division, you find that the volume is approximately 33.23 mL. This means 35 grams of pure acetic acid will take up about 33.23 milliliters of space.

Mass-Volume Relationship

The relationship between mass and volume is a fundamental concept in understanding density. Mass refers to the amount of matter within a substance, measured in grams or kilograms, whereas volume measures the space taken up by the substance, in liters or milliliters.

This relationship can be quantified through density, which acts as a bridge between mass and volume. More specifically:

• If you know the density and volume, you can find mass: Mass = Density x Volume.
• If you know mass and density, you can find volume: Volume = Mass / Density.

By understanding how these quantities relate, you can manipulate and solve for any of these variables, depending on what information is given. For instance, to determine how much space 35 grams of acetic acid would occupy, you apply the density to find the corresponding volume. This relationship is critical in chemistry and physics for working with substances and mixtures.