Problem 82 - Chemistry

Question

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)?

Step-by-Step Solution

Answer

The mass of the bromine is 14.477 kilograms.

Step 1: 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: \[ 4.67 ext{ L} = 4.67 imes 1000 ext{ cm}^3 = 4670 ext{ cm}^3 \]

Step 2: 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: \[ ext{mass} = 3.10 ext{ g/cm}^3 imes 4670 ext{ cm}^3 = 14477 ext{ grams} \]

Step 3: 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: \[ 14477 ext{ grams} = 14.477 ext{ kilograms} \]

Key Concepts

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 (cm³). Here's how to convert:

• 1 liter (L) = 1000 cubic centimeters (cm³).
• To convert liters to cubic centimeters, multiply the volume in liters by 1000.
• To convert cubic centimeters to liters, divide the volume in cm³ by 1000.

For instance, if you have a volume of 4.67 L, converting it into cm³ involves multiplying by 1000, resulting in 4670 cm³. 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/cm³ means volume should be in cm³.
• Utilize known formulas, like mass = density × 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.