Question

Determine (a) the mass of \(0.357\) mol of gold. (b) the number of atoms in \(0.357 \mathrm{~g}\) of gold. (c) the number of moles of electrons in \(0.357 \mathrm{~g}\) of gold.

Short answer

Answer: In a 0.357 g sample of gold, the mass is 70.33 g, the number of atoms is \(1.088 \times 10^{21}\) atoms, and the number of moles of electrons is 0.143 moles.

Step-by-step solution

Part (a): Determine the mass of 0.357 mol of gold.

To find the mass of 0.357 mol of gold, we need to know the molar mass of gold. Gold has a molar mass of 196.97 g/mol. We can compute the mass of 0.357 mol of gold using the following formula: Mass = Moles × Molar mass So, the mass of 0.357 mol of gold would be: Mass = 0.357 mol × 196.97 g/mol = 70.33 g

Part (b): Determine the number of atoms in 0.357 g of gold.

To find the number of atoms in 0.357 g of gold, we first need to find out how many moles of gold are in this mass. We can use the formula: Moles = Mass / Molar mass Which gives us: Moles = 0.357 g / 196.97 g/mol = 0.00181 mol Now, we can use Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol) to find the number of atoms in 0.00181 mol of gold: Number of atoms = Moles × Avogadro's number So, the number of atoms in 0.357 g of gold would be: Number of atoms = 0.00181 mol × \(6.022 \times 10^{23}\) atoms/mol = \(1.088 \times 10^{21}\) atoms

Part (c): Determine the number of moles of electrons in 0.357 g of gold.

To find the number of moles of electrons in 0.357 g of gold, we first need to determine the number of electrons in one gold atom. Gold has an atomic number of 79, which means it has 79 electrons. Next, we'll use the moles of gold we calculated in Part (b) to find the total number of moles of electrons: Moles of electrons = Moles of gold × Number of electrons per gold atom So, the number of moles of electrons in 0.357 g of gold would be: Moles of electrons = 0.00181 mol × 79 = 0.143 moles

Key concepts

Avogadro's Number

Often mentioned in chemistry, Avogadro's number, named after the scientist Amedeo Avogadro, is a fundamental constant that provides a link between the macroscopic world we can see and the microscopic world of atoms and molecules. This number, approximately \( 6.022 \times 10^{23} \), tells us how many units of any substance there are in one mole. This is incredibly useful when converting moles, a unit of chemical amount, into something tangible like the count of discrete atoms or molecules.

When performing calculations like determining the number of atoms in a particular mass of a substance, you first convert the mass to moles and then use Avogadro's number to switch to the actual number of atoms or molecules. It's a cornerstone of chemical quantification and stoichiometry, facilitating the transition from the weight of a substance to its constituent particles.

Chemical Molar Mass

The chemical molar mass is an essential concept in chemistry that relates to the mass of one mole of a substance. It is typically measured in grams per mole (g/mol). In simple terms, it's the mass of a given substance that Avogadro's number of particles (atoms, molecules, ions, etc.) would have.

To calculate it for an element, like gold in our exercise, we look at the atomic mass found on the periodic table. For compounds, the molar mass is the sum of the atomic masses of all the atoms in the molecule. Knowing the molar mass of a substance allows us to convert back and forth between the mass of a sample and the number of moles it represents, a critical step in performing stoichiometry and understanding the proportion of elements in compounds.

Gold Atomic Properties

Symbol and Atomic Number

Gold is represented by the symbol 'Au' (from the Latin 'aurum') and has an atomic number of 79. This implies that a gold atom has 79 protons in its nucleus.

Electrons

Corresponding to its atomic number, gold also has 79 electrons. These electrons are arranged in shells around the nucleus, with the outermost shell determining many of the chemical properties of the element, such as valency and the ability to form certain types of bonds.

Molar Mass

The molar mass of gold is 196.97 g/mol, a value used to convert between mass and moles of gold in calculations, as was seen in the provided exercise.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's based on the conservation of mass and the concept of moles. Simply put, it tells us how much of a substance is needed or produced in a reaction.

Stoichiometry relies on balanced chemical equations, where the coefficients represent the ratio of moles of each substance involved. With this knowledge, chemists can scale reactions up or down, make predictions about the outcomes of reactions, and calculate yields. Essential to stoichiometry is the understanding of molar masses and Avogadro's number, which are used to translate between masses and moles, enabling the precise measurement of chemical substances participating in a reaction.