Question

(a) The world population is estimated to be approximately 7 billion people. How many moles of people are there? (b) What units are typically used to express formula weight? (c) What units are typically used to express molar mass?

Short answer

(a) There are approximately \(1.162 \times 10^{-14}\) moles of people in the world. (b) Formula weight is typically expressed in atomic mass units (amu). (c) Molar mass is typically expressed in grams per mole (g/mol).

Step-by-step solution

Convert the world population into moles of people

To convert the world population into moles, simply divide the population (7 billion) by Avogadro's Number (6.022 x 10^23). Moles of people = \(\frac{7 \times 10^9}{6.022 \times 10^{23}}\)

Calculate the moles of people

Divide the population by Avogadro's Number: Moles of people = \(1.162 \times 10^{-14}\) moles. So, there are approximately \(1.162 \times 10^{-14}\) moles of people in the world.

Identify the units for formula weight

The units typically used to express formula weight are atomic mass units (amu). One atomic mass unit is defined as one twelfth the mass of one carbon-12 atom.

Identify the units for molar mass

Molar mass is expressed in grams per mole (g/mol). It represents the mass of one mole of a substance in grams. In conclusion: (a) There are approximately \(1.162 \times 10^{-14}\) moles of people in the world. (b) Formula weight is typically expressed in atomic mass units (amu). (c) Molar mass is typically expressed in grams per mole (g/mol).

Key concepts

Avogadro's Number

Understanding Avogadro's Number is key to grasping the concept of moles in chemistry. Avogadro's Number, represented by the symbol N_A, is the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. The value of N_A is approximately 6.022 x 10²³. This incredibly large number is a fundamental constant in chemistry and serves as a bridge between the microscopic scale of atoms and the macroscopic world we observe.

For example, if we consider the world's population of 7 billion people and wanted to find how many moles of people that would be, we would divide the population number by Avogadro's Number. This leads us to the quirky but illustrative calculation showing that the world's population is a minuscule fraction of a mole, emphasizing just how large Avogadro's Number really is.

It's perhaps easier to understand when applied to atoms: 1 mole of carbon atoms, for instance, contains exactly 6.022 x 10²³ carbon atoms. This connects the concept of moles to measurable quantities of a substance when we discuss chemical reactions and stoichiometry.

Atomic Mass Unit (amu)

The atomic mass unit, or amu, is a standard unit of mass that quantifies mass on an atomic or molecular scale. Defined as one twelfth the mass of a carbon-12 atom, an amu allows chemists to express the mass of atoms and subatomic particles with a more practical figure than kilograms or grams, which are too large to be convenient for such tiny entities.

In the context of formula weight, which is the sum of the atomic mass units of each atom in a chemical formula, amu plays a critical role. For instance, the formula weight of water (H₂O) is calculated by adding the atomic masses of two hydrogen atoms (approximately 1 amu each) and one oxygen atom (approximately 16 amu), which gives us about 18 amu.

Breaking Down the Formula Weight

As a measure of formula weight, amu helps chemists understand the mass of different molecules relative to each other, providing a basis for comparing substances at the atomic level. It also simplifies complex calculations in the realm of chemical reactions and stoichiometry.

Formula Weight

Formula weight is a term often used in chemistry that represents the sum of the atomic mass units (amu) for all the atoms in a chemical formula. To be precise, the formula weight is the term applied to ionic compounds, while the similar term 'molecular weight' is used for molecular substances.

For example, sodium chloride (NaCl) has a formula weight that is the sum of the atomic weight of sodium (approximately 23 amu) and chlorine (approximately 35.5 amu), totaling about 58.5 amu. Calculate the formula weight by identifying each element in the formula, determining how many atoms of each are present, and then multiplying the atomic weight of each element by the number of times that element occurs in the formula, and finally adding all of those values together.

Understanding formula weight is essential for converting between moles and grams in chemical equations and for determining the proportions of elements within a compound. This quantity gives chemists the ability to determine how much of a substance is needed or produced in a chemical reaction, a fundamental aspect of lab work and industrial processes.