Problem 27 - Chemistry: The Central Science

Question

(a) What is Avogadro's number, and how is it related to the mole? (b) What is the relationship between the formula weight of a substance and its molar mass?

Step-by-Step Solution

Answer

(a) Avogadro's number (\(N_A\)) is approximately \(6.022 \times 10^{23}\) particles per mole and relates the number of particles in a sample to the mass of the sample using the mole concept. (b) The formula weight of a substance, in atomic mass units (amu), is equal to its molar mass, expressed in grams per mole (g/mol). The relationship between them is: Formula Weight (amu) = Molar Mass (g/mol)

Step 1: Define Avogadro's Number

Avogadro's number, denoted as \(N_A\), is the number of representative particles (such as atoms, ions, or molecules) in one mole of a substance. It is a fixed value, approximately equal to \( 6.022 \times 10^{23} \) particles per mole.

Step 2: Connect Avogadro's Number to the Mole

The mole is a unit for expressing the amount of a substance. It relates the number of particles in a sample to the mass of the sample. By knowing the molecular weight of a substance, we can determine the number of moles and hence the number of particles in a given mass of the substance using Avogadro's number.

Step 3: Define Formula Weight and Molar Mass

The formula weight (also known as molecular weight) of a substance is the sum of the atomic weights of all the atoms in a chemical formula. It is represented in atomic mass units (amu). Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). Since 1 amu is almost equal to 1 g/mol, you can consider the formula weight of a substance to be numerically equal to its molar mass.

Step 4: Relate Formula Weight to Molar Mass

The relationship between the formula weight of a substance and its molar mass lies in the fact that they have the same numerical value. The formula weight (in amu) represents the mass of one particle of a substance, whereas the molar mass (in g/mol) represents the mass of one mole of a substance, containing Avogadro's number of particles. Thus, the formula weight of a substance is equal to the molar mass, or: Formula Weight (amu) = Molar Mass (g/mol)