Question

Bromine is a reddish-brown liquid. Calculate its density (in \(\mathrm{g} / \mathrm{mL}\) ) if \(586 \mathrm{~g}\) of the substance occupies \(188 \mathrm{~mL}\).

Short answer

The density of bromine is approximately 3.117 g/mL.

Step-by-step solution

Understand the Formula for Density

Density is defined as mass per unit volume. The formula to calculate density \( \rho \) is given by \( \rho = \frac{m}{V} \), where \( m \) is the mass of the substance and \( V \) is its volume.

Identify Given Values

From the problem statement, we have the mass \( m = 586 \mathrm{~g} \) and the volume \( V = 188 \mathrm{~mL} \). These are the values we will substitute into the density formula.

Substitute Values into the Density Formula

Substitute \( m = 586 \mathrm{~g} \) and \( V = 188 \mathrm{~mL} \) into the density formula: \[ \rho = \frac{586 \mathrm{~g}}{188 \mathrm{~mL}} \]

Perform the Calculation

Using a calculator, divide the mass by the volume: \( 586 \div 188 = 3.117 \) (rounded to three decimal places).

State the Density

The density of bromine is \( 3.117 \mathrm{~g/mL} \).

Key concepts

Mass and Volume Relationship

The concept of the mass and volume relationship is central to understanding how density is calculated. Density represents how much mass of a substance is contained in a given volume. It is the measure of how "packed" the substance's particles are. To find the density, we use the formula:\[\rho = \frac{m}{V}\] Where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume. This formula shows that density is directly proportional to mass and inversely proportional to volume.
More mass in the same volume means higher density, while more volume with the same mass means lower density. This relationship helps to understand why heavy objects sink and lighter objects float in fluids, as their densities relative to the fluid determine their buoyancy. When calculating density, make sure to keep the units consistent, usually grams for mass and milliliters or cubic centimeters for volume.

Bromine Properties

Bromine is an interesting and unique element with distinctive properties that are important in chemistry. It is one of the few elements that is a liquid at room temperature, known for its reddish-brown color. Here are some key properties of bromine:

• Appearance: Reddish-brown liquid
• State at Room Temperature: Liquid
• Density: From the exercise, its calculated density is 3.117 g/mL
• Reactivity: Bromine is a halogen, which makes it highly reactive with metals and organic compounds.
• Toxicity: It has a strong odor and is toxic, requiring careful handling.

The unique characteristics of bromine, like its state and reactivity, make it useful in applications such as chemical synthesis and water purification. Understanding these properties can help explain its behavior in different chemical reactions and environmental conditions.

Unit Conversion in Calculations

Unit conversion is an essential skill in chemistry, helping to translate measurements into different units according to the requirement of each calculation. In our exercise, mass and volume are already provided in common units for density calculation: grams (g) for mass and milliliters (mL) for volume. In some problems, however, you might encounter different units, and the process of conversion ensures that you are comparing "apples to apples." Here are some common conversions that might be useful:

• 1 liter (L): Equals 1000 milliliters (mL)
• 1 kilogram (kg): Equals 1000 grams (g)
• Volume in cubic centimeters (cm³): Equivalent to milliliters (1 cm³ = 1 mL)

To perform unit conversions, remember to multiply by conversion factors that equal one so that units cancel appropriately, leaving you with your desired unit. Understanding and proficiency in unit conversion are crucial in ensuring accurate and meaningful calculations in a variety of scientific contexts.