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?

Short answer

(a) Avogadro's number (\(N_A\)) is approximately \(6.022 \times 10^{23} \: entities/mol\) and represents the number of atoms, ions, or molecules in one mole of any substance. A mole is a unit of measurement in chemistry that indicates the amount of particles in a substance, and Avogadro's number relates the number of particles to the quantity of substance in moles. (b) Both formula weight and molar mass have the same numerical value but are expressed in different units. The formula weight is the sum of the atomic weights (masses) of all the atoms present in a substance's chemical formula and is expressed in atomic mass units (amu). Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). For example, the formula weight of water (H₂O) is 18 amu, while its molar mass is 18 g/mol.

Step-by-step solution

(a) Define Avogadro's number and its relation to the mole

Avogadro's number, denoted by \(N_A\) or simply \(N\), is a constant that represents the number of atoms, ions, or molecules in one mole of any substance. Its value is approximately equal to \(6.022\:\times 10^{23} \: entities/mol\). A mole is a unit of measurement used in chemistry that indicates the amount of particles in a substance. Avogadro's number relates the number of particles to the quantity of substance in moles. When there is one mole of a substance, it contains Avogadro's number of particles.

(b) Define formula weight and molar mass

The formula weight of a substance is the sum of the atomic weights (masses) of all the atoms present in its chemical formula. It is generally expressed in atomic mass units (amu). Molar mass is defined as the mass of one mole of a substance, and it is expressed in grams per mole (g/mol).

(b) Relationship between formula weight and molar mass

The relation between formula weight and molar mass is that they have the same numerical value; however, they are expressed in different units. The molar mass is the formula weight expressed in grams per mole, whereas the formula weight is the sum of the atomic weights in atomic mass units (amu). For example, let's consider water (H₂O). The atomic weight of one hydrogen atom is approximately 1 amu, and we have two hydrogen atoms in water. The atomic weight of one oxygen atom is about 16 amu. Thus, the formula weight of water is calculated by adding the atomic weights of all the atoms in its chemical formula: Formula weight of H₂O = 2 × (Atomic weight of H) + 1 × (Atomic weight of O) = (2 × 1) + 16 = 18 amu, which is the same numerical value as the molar mass of water, 18 g/mol.

Key concepts

Mole

In chemistry, the mole is a fundamental unit used to quantify an amount of substance. Essentially, it represents a specific number of particles, whether they are atoms, molecules, ions, or electrons. The term "mole" becomes especially significant because it links the microscopic world of atoms and molecules to the macroscopic world we observe and manipulate in the lab.

• A mole contains exactly Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\) particles/mole. This massive number allows chemists to count atoms and molecules in grams, a unit we can measure easily.
• Using the mole to measure substances means you can compare the number of particles between different materials since a mole of any substance contains the same number of entities.

Understanding the mole is essential for stoichiometry, which involves calculating relationships in chemical reactions where substances need to be measured accurately by the number of particles involved.

Formula Weight

Formula weight is a term used to express the sum of the atomic weights of all atoms in a chemical formula. It is essential for understanding the weight of a substance on the atomic scale and provides insight into the composition of compounds.

• Formula weight is often measured in atomic mass units (amu), which accounts for the average mass of atoms based on naturally occurring isotopes.
• For example, to calculate the formula weight of sulfuric acid \( \text{H}_2\text{SO}_4 \), add the atomic weights: 2 (H atoms) × 1 amu + 1 (S atom) × 32 amu + 4 (O atoms) × 16 amu = 98 amu.
• Recognizing formula weight aids in identifying the composition of a compound, assisting in writings of chemical equations and reactions.

Hence, formula weight helps in analyzing and predicting chemical behavior based on the compound's atomic components.

Molar Mass

Molar mass tells us the mass of one mole of any substance. It serves the practical purpose of relating the mass of a substance to a quantity of matter in moles, which can be weighed with laboratory balances.

• While formula weight operates on an atomic scale (amu), molar mass uses the same numerical value but in grams per mole (g/mol), making it applicable for laboratory work.
• For example, if a compound has a formula weight of 44 amu, then its molar mass is 44 g/mol.
• Molar mass is vital for converting between grams and moles, allowing chemists to measure the precise amount of a substance needed for reactions.

In essence, knowing the molar mass enables you to assess chemical reactions in practical terms, as it connects the molecular scale to the real-world scale of grams and moles in laboratory measurements.