Question

Calculate the mass of \(0.750 \mathrm{~mol}\) of the following substances. (a) \(\mathrm{I}_{2}\) (c) \(\mathrm{SiO}_{2}\) (b) \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) (d) \(\mathrm{Na}_{3} \mathrm{PO}_{4}\)

Short answer

The masses of the substances are: \(190.3567 \thinspace g\) for \(\mathrm{I}_{2}\), \(45.0632 \thinspace g\) for \(\mathrm{SiO}_{2}\), \(111.2361 \thinspace g\) for \(\mathrm{Mg(NO_{3})_{2}}\), and \(122.9551 \thinspace g\) for \(\mathrm{Na}_{3}\mathrm{PO}_{4}\).

Step-by-step solution

Determination of Molar Masses

First, we need to determine the molar masses of all four compounds. We can use the periodic table to find the atomic masses of individual elements and add them together to find the molar mass of each compound. The molar mass of \(\mathrm{I}_{2}\) is \(253.8089 \, g/mol\). The molar mass of \(\mathrm{SiO}_{2}\) is \(60.0843 \, g/mol\). The molar mass of \(\mathrm{Mg(NO_{3})_{2}}\) is \(148.3148 \, g/mol\). The molar mass of \(\mathrm{Na}_{3}\mathrm{PO}_{4}\) is \(163.9401 \, g/mol\).

Calculate the Masses of the Substances

For each compound, multiply the number of moles \((0.750 \thinspace \text{mol})\) by the molar mass of the compound.\[(0.750 \thinspace \text{mol}) \times (253.8089 \thinspace g/mol) = 190.3567 \thinspace g\] for \(\mathrm{I}_{2}\).\[(0.750 \thinspace \text{mol}) \times (60.0843 \thinspace g/mol) = 45.0632 \thinspace g\] for \(\mathrm{SiO}_{2}\).\[(0.750 \thinspace \text{mol}) \times (148.3148 \thinspace g/mol) = 111.2361 \thinspace g\] for \(\mathrm{Mg(NO_{3})_{2}}\).\[(0.750 \thinspace \text{mol}) \times (163.9401 \thinspace g/mol) = 122.9551 \thinspace g\] for \(\mathrm{Na}_{3}\mathrm{PO}_{4}\).

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that involves using relationships between reactants and products in a chemical reaction to determine desired quantitative data. In basic terms, stoichiometry can be thought of as the 'math' of chemistry. It allows us to predict the amounts of substances consumed and produced in a given reaction.

When solving problems involving stoichiometry, the first step is often to balance the chemical equation, which ensures that the same number of each type of atom is present on both sides of the equation. Next, using the balanced equation, the stoichiometric coefficients can guide us in converting between moles of reactants and products.

Key to stoichiometry is the concept of the mole, which is a unit for counting particles, just like a dozen is for counting eggs. The exercise of converting moles of a substance to grams further showcases the practical application of stoichiometry, as we can precisely calculate how much of a substance will react or be produced, crucial for both laboratory and industrial chemical reactions.

Mole Concept

The mole concept is a fundamental aspect of chemistry that allows chemists to work with the submicroscopic world of atoms and molecules on a macroscopic scale. A mole can be defined as exactly 6.02214076 × 10²³ (Avogadro's number) representative particles of that substance. Representative particles can refer to atoms, molecules, or ions, depending on the context.

The mole provides a bridge between the atomic world and the world we can measure, as we often deal with counting atoms and molecules, which are extraordinarily small, and a mole allows us to count them in reasonable, measurable quantities. For instance, if we're told to calculate the mass of 0.750 mol of a substance, as in the given exercise, we can use the mole concept linked with molar mass to find the mass in grams.

Atomic Mass

Atomic mass, often confused with atomic weight, is the mass of a single atom of a chemical element. It is usually measured in atomic mass units (amu), where one amu is defined as one-twelfth the mass of a carbon-12 atom. The atomic masses of all elements are listed in the periodic table and represent the average mass of all the isotopes of that element, taking into account their relative abundance.

In the context of molar mass calculations, we use the atomic mass of each element to calculate the total molar mass of a compound. This is done by adding together the atomic masses of each element in the compound, multiplied by the number of atoms of that element present in the compound's chemical formula, as seen in the provided exercise solution.

Chemical Formula

A chemical formula represents the composition of a substance using the symbols for the chemical elements and numerical subscripts. These symbols and subscripts indicate the types and numbers of atoms present in a single unit of the substance, which can be a molecule or a formula unit, depending on whether the material is molecular or ionic.

The chemical formula is essential for determining the molar mass of a compound because it allows us to see exactly how many atoms of each element are in the compound. For example, in the chemical formula \( Mg(NO_{3})_{2} \), the subscript '2' outside the parentheses means there are two nitrate groups, each composed of one nitrogen atom and three oxygen atoms. Knowing these quantities, we can calculate the molar mass by summing each atom's atomic mass for the entire compound. This calculation enables us to tackle stoichiometry problems, such as finding the mass corresponding to a given number of moles, as exhibited in the example problem.