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Chapter 1: Problem 82

A vessel contains \(4.67 \mathrm{~L}\) of bromine, whose density is \(3.10 \mathrm{~g} / \mathrm{cm}^{3}\). What is the mass of the bromine in the vessel (in kilograms)?

Short Answer

Expert verified
The mass of the bromine is 14.477 kilograms.

Step by step solution

01

Convert volume from liters to cubic centimeters

We start by understanding that the density is given in grams per cubic centimeter. Therefore, we need to convert the volume of bromine from liters to cubic centimeters. We know that 1 liter equals 1000 cubic centimeters, so we multiply the given volume in liters by 1000: \[ 4.67 ext{ L} = 4.67 imes 1000 ext{ cm}^3 = 4670 ext{ cm}^3 \]
02

Use the density to find the mass in grams

Now, we use the density of bromine to find the mass in grams. The formula for mass using density is: \[ ext{mass} = ext{density} imes ext{volume} \] Using the given density, \(3.10 ext{ g/cm}^3\), and the volume, \(4670 ext{ cm}^3\), we get: \[ ext{mass} = 3.10 ext{ g/cm}^3 imes 4670 ext{ cm}^3 = 14477 ext{ grams} \]
03

Convert mass from grams to kilograms

Finally, we'll convert the mass from grams to kilograms, since the problem asks for the mass in kilograms. Knowing that 1 kilogram is equal to 1000 grams, we divide the mass in grams by 1000: \[ 14477 ext{ grams} = 14.477 ext{ kilograms} \]

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Key Concepts

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

Mass Conversion
When solving problems involving mass, understanding how to convert between units is crucial. Mass is often measured in grams or kilograms in chemistry. For conversion:
  • 1 kilogram (kg) = 1000 grams (g).
  • To convert grams to kilograms, divide by 1000.
  • To convert kilograms to grams, multiply by 1000.
For example, if you have a mass of 14477 g and need to convert it to kilograms, you divide by 1000 to get 14.477 kg. This conversion is essential in chemistry for accurate calculations and understanding of measurements.
Volume Conversion
In many chemistry problems, understanding volume and its conversion between units is necessary. Volume can be measured in different units such as liters (L) and cubic centimeters (cm鲁). Here's how to convert:
  • 1 liter (L) = 1000 cubic centimeters (cm鲁).
  • To convert liters to cubic centimeters, multiply the volume in liters by 1000.
  • To convert cubic centimeters to liters, divide the volume in cm鲁 by 1000.
For instance, if you have a volume of 4.67 L, converting it into cm鲁 involves multiplying by 1000, resulting in 4670 cm鲁. Grasping these conversions ensures proper analysis and comprehension of chemistry exercises.
Chemistry Problem Solving
Solving chemistry problems often involves using a step-by-step approach by understanding and applying fundamental concepts. Here's how to tackle such problems:
  • Identify what is given and what needs to be found. This problem provides volume and density, asking for mass.
  • Ensure all units match, often requiring conversions. For example, density given in g/cm鲁 means volume should be in cm鲁.
  • Utilize known formulas, like mass = density 脳 volume, to find unknown quantities.
  • Carry out calculations carefully, double-checking each step to avoid errors.
  • Finally, present your answer in the correct units, making conversions as necessary.
By following these guidelines, you can systematically approach and solve complex chemistry problems, ensuring clarity and accuracy.

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Most popular questions from this chapter

Assume that you have two graduated cylinders, one with a capacity of \(5 \mathrm{~mL}\) (a) and the other with a capacity of \(50 \mathrm{~mL}\) (b). Draw a line in each, showing how much liquid you would add if you needed to measure \(2.64 \mathrm{~mL}\) of water. Which cylinder will give the more accurate measurement? Explain.

Vinaigrette salad dressing consists mainly of oil and vinegar. The density of olive oil is \(0.918 \mathrm{~g} / \mathrm{cm}^{3}\), the density of vinegar is \(1.006 \mathrm{~g} / \mathrm{cm}^{3}\), and the two do not mix. If a certain mixture of olive oil and vinegar has a total mass of \(397.8 \mathrm{~g}\) and a total volume of \(422.8 \mathrm{~cm}^{3}\), what is the volume of oil and what is the volume of vinegar in the mixture?

A Big Mac hamburger from McDonald's contains 540 Calories. (a) How many kilojoules does a Big Mac contain? (b) For how many hours could the amount of energy in a Big Mac light a 100 watt lightbulb? \((1\) watt \(=1 \mathrm{~J} / \mathrm{s})\)

Of the 90 or so naturally occurring elements, only four are liquid near room temperature: mercury (melting point = \(\left.-38.87^{\circ} \mathrm{C}\right)\), bromine \(\left(\right.\) melting point \(\left.=-7.2{ }^{\circ} \mathrm{C}\right)\), cesium (melting point \(\left.=28.40^{\circ} \mathrm{C}\right)\), and gallium (melting point \(=\) \(\left.29.78{ }^{\circ} \mathrm{C}\right)\). Convert these melting points to degrees Fahrenheit.

Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of \(-117.3^{\circ} \mathrm{C}\) and a boiling point of \(78.5^{\circ} \mathrm{C}\), but on your new scale calibrated in units of degrees ethanol, \({ }^{\circ} \mathrm{E}\), you define ethanol to melt at \(0{ }^{\circ} \mathrm{E}\) and boil at \(200^{\circ} \mathrm{E}\). (a) How does your ethanol degree compare in size with a Celsius degree? (b) How does an ethanol degree compare in size with a Fahrenheit degree? (c) What are the melting and boiling points of water on the ethanol scale? (d) What is normal human body temperature \(\left(98.6^{\circ} \mathrm{F}\right)\) on the ethanol scale? (e) If the outside thermometer reads \(130{ }^{\circ} \mathrm{E}\), how would you dress to go out?
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