Problem 123 - Chemistry Matter and Change

Question

You are given a liquid of unknown density. The mass of a graduated cylinder containing 2.00 \(\mathrm{mL}\) of the liquid is 34.68 \(\mathrm{g} .\) The mass of the empty graduated cylinder is 30.00 \(\mathrm{g} .\) Given this information, determine the density of the liquid. (Chapter 2\()\)

Step-by-Step Solution

Answer

The density of the liquid is 2.34 g/mL.

Step 1: Identify Known Values

First, we identify the known values from the problem. We know the mass of the graduated cylinder with the liquid is 34.68 g, the mass of the empty graduated cylinder is 30.00 g, and the volume of the liquid is 2.00 mL.

Step 2: Calculate Mass of the Liquid

Next, we need to find out the mass of just the liquid. We do this by subtracting the mass of the empty graduated cylinder from the mass of the cylinder with the liquid:\[\text{Mass of liquid} = 34.68\, \text{g} - 30.00\, \text{g} = 4.68\, \text{g}.\]

Step 3: Use the Density Formula

Density \((\rho)\) is defined as mass per unit volume. The formula for density is:\[\rho = \frac{\text{mass}}{\text{volume}}.\]

Step 4: Calculate the Density

Plug the values we have into the density formula. The mass of the liquid is 4.68 g, and the volume is 2.00 mL:\[\rho = \frac{4.68\, \text{g}}{2.00\, \text{mL}} = 2.34\, \text{g/mL}.\]

Key Concepts

Density Formula

Density is a fundamental property of matter that describes how much mass is contained in a given volume. Essentially, it tells you how "crowded" the matter is within a space. The density formula is a simple yet powerful tool expressed as: \[ \rho = \frac{\text{mass}}{\text{volume}} \]Where:

• \( \rho \) is the density, typically measured in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³).
• Mass is the amount of matter in the object or substance, usually in grams (g) or kilograms (kg).
• Volume is the space occupied by the mass, generally measured in milliliters (mL) or liters (L), or cubic centimeters (cm³) or cubic meters (m³).

Just plug the mass into the formula's numerator and the volume into the denominator to calculate density. It's super straightforward! This formula not only helps you in lab exercises but also in real-world applications such as material science and engineering.

Mass and Volume

Understanding the relationship between mass and volume is crucial for calculating density. Let's break it down:**Mass** is a measure of the amount of matter in an object. You can think of it as how much "stuff" makes up the object. In our exercise, to find the mass of the liquid, we need to subtract the mass of the empty container from the mass of the container with the liquid:\[\text{Mass of liquid} = \text{Mass with liquid} - \text{Mass of empty container}\]**Volume**, on the other hand, refers to the space that matter occupies. Volume measurements are usually done using tools like graduated cylinders. Remember, the same mass of different substances can occupy different volumes. In the exercise, once we have the mass of the liquid (4.68 g), we pair it with the volume (2.00 mL) to find its density. It's the relationship between these measurements that allows us to define density clearly.

Graduated Cylinder

A graduated cylinder is a common piece of laboratory equipment used for measuring the volume of a liquid. It’s called “graduated” because it has markings along its length that indicate volume. This allows for accurate volume measurements. To use:

• Place the graduated cylinder on a flat surface to avoid tilting errors.
• Pour the liquid carefully to avoid splashing.
• Read the volume at eye level at the bottom of the meniscus. The meniscus is the curve formed at the top surface of the liquid.

Graduated cylinders come in different sizes, and their precision can vary. For the liquid's density calculation, an accurate volume measurement is key, which is why using a graduated cylinder is very effective. Its transparency and graduations provide a clear way to observe the level of liquid.

Liquid Density Measurement

Measuring liquid density involves a few straightforward steps. This allows you to figure out how tightly packed the particles in your liquid are compared to the space it occupies.Step-by-step in practice:

• First, measure the mass of the empty container, such as a graduated cylinder.
• Next, add the liquid and re-measure. Subtract the empty container's mass from this to get the liquid's mass.
• Determine the volume of the liquid, usually directly from the graduated cylinder.
• Finally, use the density formula, \( \rho = \frac{\text{mass}}{\text{volume}} \), to calculate the density.

The resulting density can help identify the liquid, check its purity, or determine its concentration. Remember, precision in measuring mass and volume is key for accurate density calculation. This skill has applications in chemistry labs, cooking, and even in industries like oil and mineral exploration.