Problem 74 - General Chemistry

Question

A flask contains a \(30.0 \mathrm{~mL}\) sample of acetone (nail polish remover) that weighs 23.6 grams. What is the density of the acetone?

Step-by-Step Solution

Answer

The density of the acetone is approximately \(0.787 \text{ g/mL}\).

Step 1: Identify Given Information

We are given the volume of the acetone sample as \(30.0 \text{ mL}\) and its mass as \(23.6 \text{ g}\).

Step 2: Recall the Formula for Density

Density is defined as the mass per unit volume of a substance. The formula to calculate density is:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]

Step 3: Substitute Given Values into the Density Formula

Using the values provided, substitute the mass and volume into the formula:\[\text{Density} = \frac{23.6 \text{ g}}{30.0 \text{ mL}}\]

Step 4: Calculate the Density

Perform the division to find the density:\[\text{Density} = 0.7867 \text{ g/mL}\]

Step 5: Interpret the Result

The density of the acetone is calculated to be approximately \(0.787 \text{ g/mL}\) when rounded to three significant figures.

Key Concepts

Mass and Volume

To understand density, we first need to grasp two essential concepts: mass and volume. Mass is the amount of matter present in an object, often measured in grams (g) or kilograms (kg). If you imagine picking up a brick, the force you feel is due to its mass. Volume, on the other hand, is the space an object occupies. It can be measured in milliliters (mL), liters (L), cubic centimeters (cm³), etc. Think of volume as the amount of space required for an object or substance to exist.

• Mass = "How much stuff" is there.
• Volume = "How much space" does it take up.

In the original exercise, the acetone's mass is 23.6 grams, and its volume is 30.0 mL. These values are crucial for calculating density.

Density Formula

Density is a fundamental concept in physics and chemistry, representing how densely matter is packed in a substance. It's defined as the mass of an object divided by its volume. The formula for density is expressed as:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]This means density provides a ratio of an object’s mass relative to its volume. If you think of a room packed with people (high density) versus a sparsely filled room (low density), that's akin to comparing high and low density substances.

• High density = lots of mass in a small volume.
• Low density = less mass in a greater volume.

By using the formula and plugging in the mass and volume for acetone, we calculated a density of approximately 0.787 g/mL, giving insight into how tightly the molecules are packed in acetone.

Significant Figures

When dealing with measurements, significant figures are important. They tell us about the precision of the measurement. For instance, in our exercise, both the mass (23.6 g) and the volume (30.0 mL) are given with three significant figures. This indicates a certain level of precision inherent in the data provided and affects how we present our final results. Significant figures include all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal part. When we calculated the density, the result was initially 0.7867 g/mL. However, respecting the significant figures of the measured values, we round off the density to 0.787 g/mL. This ensures our result remains consistent with the precision of the initial measurements. Always remember to adjust your final answer based on the significant figures of the input data.