Verify that when \(10.0 \mathrm{~g}\) of sodium sulfate dissolves in water: a) there are \(7.04 \times 10^{-2}\) moles of sodium sulfate in the water. b) there are \(7.04 \times 10^{-2}\) moles of sulfate in the water. c) there are \(14.1 \times 10^{-2}\) moles of sodium in the water.

Understanding the molar mass of a compound is the cornerstone of many calculations in chemistry. Molar mass allows us to translate between the mass of a substance and the number of moles, which is a measure of the amount of substance in terms of particles, like atoms or molecules.

To calculate the molar mass, we sum the atomic masses of all the atoms that make up the compound. For example, sodium sulfate ((Na_2SO_4)) has two sodium atoms, one sulfur atom, and four oxygen atoms. Knowing that the atomic masses for sodium (Na), sulfur (S), and oxygen (O) are approximately 23 g/mol, 32 g/mol, and 16 g/mol respectively, we can calculate the molar mass of sodium sulfate by multiplying the number of each type of atom by its atomic mass and adding these values together. This gives us the molar mass of (Na_2SO_4) as (2 * 23 + 32 + 4 * 16 = 142 g/mol).

With this information, we can perform various calculations to understand the composition of a sample, including how many grams of the substance are in one mole, or conversely, how many moles are in a given mass of the substance.

Stoichiometry is essentially the mathematics of chemistry. It involves using the balanced chemical equation to understand the quantitative relationships between the reactants and products in a chemical reaction.

In stoichiometry, the coefficients in a balanced equation indicate the ratio of moles of each substance involved. For instance, in the dissolution of sodium sulfate in water, we deal with the stoichiometry of the dissolution process. Considering the molar ratios, we can infer how many moles of ions are produced when sodium sulfate dissolves.

Example:

If we dissolve one mole of sodium sulfate, we would end up with two moles of sodium ions (Na^+) because each formula unit of sodium sulfate ((Na_2SO_4)) yields two sodium ions upon dissolution. It is through stoichiometry that we can also confirm the number of moles of sodium and sulfate ions that result from this process.

Ionic compounds, such as sodium sulfate ((Na_2SO_4)), dissociate into ions when they dissolve in water due to water's polar nature. The process of dissolution involves the separation of the ions in the solid compound as they become solvated by water molecules.

During the dissolution, the ionic bonds holding the compound together are broken, allowing the individual cations and anions to disperse throughout the solution. For sodium sulfate, one unit of the compound separates into two sodium ions (Na^+) and one sulfate ion (SO_4^{2-}).

Thus, when calculating the amount of ions formed from a certain mass of ionic compound, it is important to consider not only the molar mass but also the ratio of the ions produced according to the chemical formula. This concept is crucial when determining the conductivity, the ability to form precipitates, and the chemical reactivity of the solution.