Question

Determine (a) the mass of 0.429 mol of gold. (b) the number of atoms in \(0.715 \mathrm{~g}\) of gold. (c) the number of moles of electrons in \(0.336 \mathrm{~g}\) of gold.

Short answer

Answer: (a) The mass of 0.429 mol of gold is 84.513 g. (b) There are approximately \(2.184 \times 10^{21}\) atoms in 0.715 g of gold. (c) There are approximately 0.134795 moles of electrons in 0.336 g of gold.

Step-by-step solution

(a) Finding the mass of gold

To find the mass of 0.429 mol of gold, we will use the molar mass of gold, which is 197.0 g/mol. We can use the following formula: Mass (g) = number of moles × molar mass (g/mol) So, Mass of gold = 0.429 mol × 197.0 g/mol = 84.513 g

(b) Finding the number of atoms in gold

To find the number of atoms in 0.715 g of gold, we need first to find the number of moles of gold. We can use the following formula: Number of moles = mass (g) / molar mass (g/mol) Number of moles of gold = 0.715 g / 197.0 g/mol = 0.00363 mol Next, we can find the number of atoms using Avogadro's number: Number of atoms = number of moles × Avogadro's number Number of atoms = 0.00363 mol × \(6.022 \times 10^{23}\) atoms/mol ≈ \(2.184 \times 10^{21}\) atoms

(c) Finding the number of moles of electrons in gold

First, we need to find the number of moles of gold in 0.336 g. We can use the formula we used earlier: Number of moles of gold = 0.336 g / 197.0 g/mol = 0.001705 mol Since each gold atom has 79 electrons, we can find the total number of moles of electrons as follows: Number of moles of electrons = number of moles of gold × number of electrons per gold atom Number of moles of electrons = 0.001705 mol × 79 ≈ 0.134795 mol

Key concepts

Molar Mass

Understanding the molar mass of a substance is crucial when solving chemistry problems. Molar mass, represented in grams per mole (g/mol), is the mass of one mole of a particular substance. A mole is a basic chemical unit that denotes the amount of a substance.

For example, gold has a molar mass of 197.0 g/mol. This implies that one mole of gold atoms weighs 197.0 grams. When dealing with exercises like calculating the mass of a certain number of moles of an element, we multiply the number of moles by its molar mass to arrive at the total mass.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, representing the number of constituent particles, usually atoms or molecules, in one mole of a substance. The value of Avogadro's number is approximately 6.022 x 10^23 particles per mole.

When given a mass in grams and asked to find out the number of atoms, as with our gold example, you would first convert grams to moles, then use Avogadro's number to find the number of atoms or molecules. This makes Avogadro's number indispensable for converting between microscopic and macroscopic quantities.

Moles to Grams Calculation

To interconvert moles and grams, a two-step calculation is often used: first, determine the number of moles from the mass and vice versa, and then use Avogadro's number for particle counts if necessary.

The formula for converting moles to grams is:
Mass (g) = number of moles × molar mass (g/mol). Conversely, to find the number of moles from the mass, you would divide the mass by the molar mass of the substance. These conversions are fundamental in stoichiometry, allowing chemists to weigh out exact amounts of reactants for reactions.

Atoms and Molecules

Atoms are the basic units of matter and the defining structure of elements. A molecule, on the other hand, is a chemical combination of two or more atoms bonded together. Stoichiometry often requires us to count atoms and molecules when reacting substances to understand how they will interact.

For solid elements like gold, counting individual atoms is based on their division into moles—a group of Avogadro's number of atoms, which then can be weighed as molar mass. In chemical reactions, understanding the mole relationships between reactants and products is key to predicting the amounts of substances produced or consumed.