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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

Expert verified
The density of bromine is approximately 3.117 g/mL.

Step by step solution

01

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.
02

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.
03

Substitute Values into the Density Formula

Substitute \( m = 586 \mathrm{~g} \) and \( V = 188 \mathrm{~mL} \) into the density formula: \[ \rho = \frac{586 \mathrm{~g}}{188 \mathrm{~mL}} \]
04

Perform the Calculation

Using a calculator, divide the mass by the volume: \( 586 \div 188 = 3.117 \) (rounded to three decimal places).
05

State the Density

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

A chemist mixes two liquids \(\mathrm{A}\) and \(\mathrm{B}\) to form a homogeneous mixture. The densities of the liquids are \(2.0514 \mathrm{~g} / \mathrm{mL}\) for \(\mathrm{A}\) and \(2.6678 \mathrm{~g} / \mathrm{mL}\) for \(\mathrm{B}\). When she drops a small object into the mixture, she finds that the object becomes suspended in the liquid; that is, it neither sinks nor floats. If the mixture is made of 41.37 percent \(\mathrm{A}\) and 58.63 percent \(\mathrm{B}\) by volume, what is the density of the object? Can this procedure be used in general to determine the densities of solids? What assumptions must be made in applying this method?

The thin outer layer of Earth, called the crust, contains only 0.50 percent of Earth's total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon (Si) is the second most abundant element in Earth's crust ( 27.2 percent by mass). Calculate the mass of silicon in kilograms in Earth's crust (mass of Earth \(=5.9 \times 10^{21}\) tons; 1 ton \(=2000 \mathrm{lb}\); \(1 \mathrm{lb}=453.6 \mathrm{~g})\).

Pheromones are compounds secreted by females of many insect species to attract mates. Typically, \(1.0 \times 10^{-8} \mathrm{~g}\) of a pheromone is sufficient to reach all targeted males within a radius of \(0.50 \mathrm{mi}\). Calculate the density of the pheromone (in grams per liter) in a cylindrical air space having a radius of \(0.50 \mathrm{mi}\) and a height of \(40 \mathrm{ft}\) (volume of a cylinder of radius \(r\) and height \(h\) is \(\pi r^{2} h\) ).

Comment on whether each of the following statements represents an exact number: (a) 50,247 tickets were sold at a sporting event. (b) \(509.2 \mathrm{~mL}\) of water was used to make a birthday cake, (c) 3 dozen eggs were used to make a breakfast, (d) \(0.41 \mathrm{~g}\) of oxygen was inhaled in each breath, (e) Earth orbits the sun every 365.2564 days.

A cylindrical glass tube \(12.7 \mathrm{~cm}\) in length is filled with mercury (density \(=13.6 \mathrm{~g} / \mathrm{mL}\) ). The mass of mercury needed to fill the tube is \(105.5 \mathrm{~g}\). Calculate the inner diameter of the tube (volume of a cylinder of radius \(r\) and length \(h\) is \(V=\pi r^{2} h\) ).

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