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 \(6.022 \times 10^{23}\) particles per mole, representing the number of atoms, ions, or molecules in one mole of a substance. A mole is the SI unit for measuring the amount of a substance, defined as the number of particles in 12 grams of carbon-12 isotope. (b) The relationship between the formula weight and the molar mass of a substance is: Molar Mass (g/mol) = Formula Weight (amu) × 1 g/mol They are numerically equal but have different units: formula weight in atomic mass units (amu) and molar mass in grams per mole (g/mol).

Step-by-step solution

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

Avogadro's number is a constant value representing the number of atoms, ions, or molecules in one mole of a substance. It is denoted by \(N_A\) and is approximately equal to \(6.022 \times 10^{23}\) particles per mole. A mole is the SI unit used to measure the amount of a substance, and it is defined as the number of particles (atoms, ions, or molecules) that are present in 12 grams of carbon-12 isotope. In other words, one mole of any substance contains \(6.022 \times 10^{23}\) particles (may it be atoms, ions, or molecules), and this number is referred to as Avogadro's number.

b) Relationship between Formula Weight and Molar Mass

The formula weight of a substance is the sum of the atomic weights of all the atoms present in the substance's chemical formula. The atomic weight of an atom is defined as the weighted average mass of all the naturally occurring isotopes of that element. Formula weight is a dimensionless quantity expressed in atomic mass units (amu). Molar mass, on the other hand, is the mass of one mole of a substance. It is expressed in grams per mole (g/mol). The molar mass of a substance is equal to its formula weight, but the units are different. To find the molar mass of a substance, we multiply the formula weight by the molar mass constant, which is 1 g/mol. In other words, the molar mass of a substance (in g/mol) is numerically equal to its formula weight (in amu). The relationship between the formula weight and the molar mass of a substance can be represented as: Molar Mass (g/mol) = Formula Weight (amu) × 1 g/mol In conclusion, the formula weight and the molar mass of a substance are numerically equal; however, they have different units. Formula weight is expressed in atomic mass units (amu), while molar mass is expressed in grams per mole (g/mol).

Key concepts

Understanding the Mole

The concept of the mole is fundamental in chemistry, especially when studying the amount of substances. Essentially, a mole is a unit of measurement used in chemistry to express amounts of a chemical substance. It allows chemists to count particles in a given sample by weighing it, rather than counting individual atoms or molecules, which would be impractical due to their minuscule size and sheer number.

The mole is defined by the number of atoms found in exactly 12 grams of the carbon-12 isotope, which is approximately Avogadro's number, or \(6.022 \times 10^{23}\) particles. Therefore, one mole of any element or compound contains approximately Avogadro's number of atoms, molecules, or ions, depending on the substance being measured.

A closer look at Avogadro's number reveals its role as a bridge between the micro world of atoms and the macro world we can measure. For example, if you have a mole of water, you have \(6.022 \times 10^{23}\) water molecules, a quantity that can be weighed on a scale, thereby connecting the atomic scale to the laboratory scale.

Decoding Molar Mass

Molar mass is another critical concept in chemistry, closely related to the mole. It represents the mass of one mole of a given substance and is expressed in grams per mole (g/mol). The molar mass is the link between the mass of a material and the amount (in moles) present in that sample.

To put it another way, if you know the molar mass of a substance, you can convert between the mass of a sample and the number of moles it contains by simple calculations. For instance, the molar mass of water (H2O) is approximately 18 g/mol, meaning that one mole of water weighs 18 grams.

This becomes particularly useful when you're performing reactions and need to know how much of each reactant to use, or when you're analyzing a compound and need to discern its composition. The knowledge of molar mass helps ensure that measurements and calculations are accurate, which is essential for all chemical procedures from the research lab to industrial processes.

Exploring Formula Weight

Formula weight is an extension of the molar mass concept but focuses more on the individual atoms or ions in a chemical formula. It is the sum of the atomic weights of all atoms in a compound's formula. This value is dimensionless and is expressed in atomic mass units (amu), which reflects the mass of individual atoms based on a relative scale.

For instance, if you have a compound such as sodium chloride (NaCl), its formula weight is the sum of the atomic weight of sodium (approximately 23 amu) and chlorine (approximately 35.5 amu), giving us a formula weight of about 58.5 amu. Understanding formula weight is critical when determining the proportions of elements in a compound and is especially useful in stoichiometry, where the relationships between the quantities of reactants and products in a chemical reaction are analyzed.

Interpreting Atomic Weight

Lastly, atomic weight serves as the foundation of both formula weight and molar mass. It is the average mass of the atoms of an element, accounting for the different isotopes and their abundance on Earth. The atomic weight is measured in atomic mass units, where one atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom.

Atomic weight is pivotal for understanding both the physical and chemical properties of an element. It plays a crucial role in a range of chemical calculations, from determining the relative proportions of elements in compounds to calculating the yield of a reaction. For each element on the periodic table, the atomic weight is an average that reflects the naturally occurring mixture of isotopes, providing a practical number that chemists can use in calculations.