Question

At room temperature the element bromine, \(\mathrm{Br}_{2},\) is a liquid with a density of 3.12 \(\mathrm{g} / \mathrm{cm}^{3} .\) Calculate the mass of 125 \(\mathrm{mL}\) of bromine. What volume does 85.0 \(\mathrm{g}\) of bromine occupy?

Short answer

The mass of 125 mL of bromine is 390 g, and the volume occupied by 85.0 g of bromine is approximately 27.2 cm³.

Step-by-step solution

Convert volume to an appropriate unit.

The given volume is in mL, but the units for density are g/cm³. So, the volume should also be in cm³. We can convert the volume to cm³ using the conversion factor 1 cm³ = 1 mL: \(V = 125\,\text{mL} \times \frac{1\,\text{cm}^{3}}{1\,\text{mL}} = 125\,\text{cm}^3\)

Calculate the mass of bromine.

Using the given density and volume, we can calculate the mass using the formula: Mass = Density × Volume \(m = 3.12\,\frac{\text{g}}{\text{cm}^3} \times 125\,\text{cm}^3\) \(m = 390\,\text{g}\) So, the mass of 125 mL of bromine is 390 g.

Calculate the volume of 85.0 g of bromine.

Using the given density and mass, we can calculate the volume using the formula: Volume = Mass / Density \(V = \frac{85.0\,\text{g}}{3.12\,\frac{\text{g}}{\text{cm}^{3}}}\) \(V \approx 27.2\,\text{cm}^{3}\) So, the volume occupied by 85.0 g of bromine is approximately 27.2 cm³.

Key concepts

Volume Conversions

When dealing with measurements in science, different units are often used to express volume. It's essential to convert between these units properly to ensure calculations are accurate. In chemistry, you might frequently encounter milliliters (mL) and cubic centimeters (cm³), especially since these are common units for liquids. Thankfully, these two units are equivalent:

• 1 mL = 1 cm³

This equivalence makes conversions straightforward. Simply remember, if you have a volume in milliliters, it's the same number in cubic centimeters.
For example, consider converting 125 mL of bromine to cm³. Since 1 mL equals 1 cm³, the calculation is simple:

• 125 mL × \( \frac{1 \, \text{cm}^3}{1 \, \text{mL}} = 125 \, \text{cm}^3 \)

Whether you're dealing with liquids or gases, understanding how to convert volumes between units efficiently is a foundational skill in chemistry.

Mass Calculation

Calculating the mass of a substance involves using the concept of density, which is defined as mass per unit volume. The formula you need is:

• Mass = Density × Volume

This formula is a fundamental relationship in chemistry that helps you find how much a substance weighs based on its density and volume.
Let's take bromine as an example. If you have a density of 3.12 g/cm³, and you want to find the mass of 125 cm³ of bromine:

• Mass = \( 3.12 \frac{\text{g}}{\text{cm}^3} \times 125 \text{ cm}^3 = 390 \, \text{g} \)

The mass of 125 mL (or cm³) of bromine is 390 grams. Calculating mass using density and volume is straightforward as long as you ensure the units are compatible.

Chemical Elements

Understanding chemical elements, like bromine, involves recognizing their properties, such as density and state of matter at room temperature. Bromine, for example, is a unique element:

• It appears as a reddish-brown liquid at room temperature.
• The symbol for bromine is \( \mathrm{Br} \).
• Its molecular form is \( \mathrm{Br}_{2} \), meaning it's diatomic.

Familiarizing yourself with the properties of elements is crucial when performing chemical calculations. For instance, knowing bromine has a density of 3.12 g/cm³ allows you to compute how much space a specific mass of bromine will occupy.
Consider how to determine the volume of 85.0 grams of bromine using its density:

• Volume = \( \frac{85.0 \, \text{g}}{3.12 \, \frac{\text{g}}{\text{cm}^{3}}} \approx 27.2 \, \text{cm}^3 \)

This understanding bridges the gap between theoretical knowledge of chemical properties and practical applications in laboratory settings.