Chapter 2: The Mole

Section 2-1: Introduction to Avogadro's Number and the Mole

Section 2-3: Converting Between Mass and Number of Atoms or Molecules

Chapter 2 Practice Exercises and Review Quizzes

Section 2-1: Introduction to Avogadro's Number and the Mole

The unit mole (mol) is used to describe the amount of a substance:

1 mol = 6.02 x 10²³ atoms or molecules (more than one bonded atom)

The number 6.02 x 10²³ is known as Avogadro's number and will be given the symbol N_A in calculations throughout this textbook. The following problem will demonstrate how to convert back and forth between an amount in moles and the number of atoms or molecules using dimensional analysis:

Sample Exercise 2A:

Convert the following:

(a) 3.00 moles of silver to number of silver atoms

(b) 1.2 x 10²¹ gold atoms to moles of gold

(d) 5.42 x 10²² water molecules to moles of water

Solution:

Section 2-2: Molar Mass

The mass of one mole of an element or compound in the unit grams per mole (g/mol) is known as the molar mass (M) and can be obtained from the periodic table. Note that the molar masses found on different periodic tables may differ slightly. Throughout this textbook, we will round all molar mass values to 4 sig. fig.s. The following table shows some examples:

Element or Compound	M (g/mol)
Cu	63.55
Cl₂	2(35.45) = 70.90
C₆H₁₂O₆	6(12.01) + 12 (1.008) + 6(16.00) = 180.2
(NH₂)₂CO	2(14.01) + 4(1.008) + 12.01 + 16.00 = 60.06

Once we have obtained the molar mass of an element or compound, we can convert back and forth between an amount in moles and the mass using dimensional analysis as demonstrated in the following problem:

Sample Exercise 2B:

Convert the following:

(a) 0.03 moles of copper to grams

(b) 14.2 grams of Cl₂ to moles

(d) 0.360 kilograms of (NH₂)₂CO to moles

Solution:

Section 2-3: Converting Between Mass and Number of Atoms or Molecules

We can combine the methods used in the previous two sections to convert back and forth between mass and the number of atoms or molecules using dimensional analysis and one of the following strategies:

The following problem will demonstrate each of the strategies above:

Sample Exercise 2C:

Convert the following:

(a) 0.080 grams of I₂ to number of I₂ molecules

(b) 2.29 x 10²⁴ CS₂ molecules to kilograms of CS₂

Solution:

(a) M of I₂ = 2(126.9) = 253.8 g/mol

(b) M of CS₂ = 12.01 + 2(32.07) = 76.15 g/mol

Note that it was not necessary to stop and actually calculate the moles along the way to finding the final answer.

If we know the number of molecules in a sample, we can calculate the number of atoms of any element present in the sample as follows:

Sample Exercise 2D:

A sample contains 8.40 x 10²⁵molecules C₆H₄(NO₂)₂. How many oxygen atoms are in the sample?

Solution:

We see from the chemical formula that one molecule contains 4 oxygen atoms, so we simply multiply the number of molecules by a conversion factor representing the number of oxygen atoms per one molecule: