Ch.2 - Atoms & Elements

Tro - Chemistry: A Molecular Approach 4th Edition

Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Not the one you use?Change textbook

Tro 4th Edition

Ch.2 - Atoms & Elements

Problem 90

Chapter 2, Problem 90

Calculate the mass, in kg, of each sample. a. 7.55×10²⁶ cadmium atoms b. 8.15×10²⁷ nickel atoms c. 1.22×10²⁷ manganese atoms d. 5.48×10²⁹ lithium atoms

Verified step by step guidance

1. To calculate the mass of a sample, we first need to know the number of moles. We can find this by using Avogadro's number, which is approximately \(6.022 * 10^{23}\) atoms per mole. So, divide the given number of atoms by Avogadro's number to find the number of moles.

2. For example, for cadmium atoms, the calculation would be \(7.55 * 10^{26}\) atoms divided by \(6.022 * 10^{23}\) atoms/mole.

3. Once we have the number of moles, we can find the mass by multiplying the number of moles by the molar mass of the element. The molar mass of an element can be found on the periodic table. For cadmium, the molar mass is approximately 112.41 g/mole.

4. So, for cadmium, multiply the number of moles calculated in step 2 by 112.41 g/mole. This will give you the mass in grams.

5. To convert the mass from grams to kilograms, divide by 1000 since there are 1000 grams in a kilogram. Repeat these steps for each of the other elements, using the appropriate molar mass for each.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. For example, the molar mass of cadmium (Cd) is approximately 112.41 g/mol, which is essential for converting between the number of atoms and mass.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms, ions, or molecules in one mole of a substance. This constant allows chemists to relate the macroscopic scale of substances to the microscopic scale of individual particles, enabling calculations involving the number of atoms in a sample.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, it involves converting the number of atoms to moles using Avogadro's number and then to mass using the molar mass. Understanding how to perform these conversions is crucial for accurately calculating the mass of the samples in kilograms.

Recommended video:

Guided course

01:56

Conversion Factors

Related Practice

Textbook Question

How many helium atoms are there in a helium blimp containing 536 kg of helium?

408

views

Textbook Question

Calculate the mass, in grams, of each sample. c. 1.8×10²³ lead atoms

739

views

Textbook Question

Using scanning tunneling microscopy, scientists at IBM wrote the initials of their company with 35 individual xenon atoms (as shown below). Calculate the total mass of these letters in grams.

413

views

Textbook Question

Calculate the average mass, in grams, of one platinum atom.

1331

views

Textbook Question

Calculate the mass, in grams, of each sample. a. 1.1×10²³ gold atoms b. 2.82×10²² helium atoms

1317

views

Textbook Question

Calculate the mass, in grams, of each sample. d. 7.9×10²¹ uranium atoms