Question

How many atoms (or ions) of each element are in \(140.0 \mathrm{~g}\) of the following substances? (a) \(\mathrm{BaSO}_{4}\) (c) \(\mathrm{O}_{2}\) (b) \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) (d) \(\mathrm{KBr}\)

Short answer

The answer will be the number of atoms (or ions) of each element in 140g of \(\mathrm{BaSO}_{4}\), \(\mathrm{O}_{2}\), \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\), \(\mathrm{KBr}\). Each will be specific depending on the molar mass of each compound and the atomic composition of the compound. Therefore, a specific numerical answer cannot be given without knowing these factors.

Step-by-step solution

Determine the molar mass of each compound

Start by determining the molar mass of \(\mathrm{BaSO}_{4}\), \(\mathrm{O}_{2}\), \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\), \(\mathrm{KBr}\). The molar mass is the sum of all the atomic masses in a molecule, in units of grams/mol. We can use the atomic weights from the periodic table to find the molar vectors of elements.

Convert mass to moles

Next, convert the given mass (140g) of each compound into moles. This can be accomplished by dividing the mass by the molar mass.

Convert moles to atoms (or ions)

Once you have the number of moles, we must convert this into the number of atoms (or ions) using Avogadro's number which tells there are \(6.022 \times 10^{23}\) entities in a mole.

Key concepts

Molar Mass Calculation

Understanding the concept of molar mass is crucial for students delving into the world of chemistry. The molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, we sum the atomic masses of all the atoms in a single molecule of that compound. These atomic masses can be found on the periodic table and usually represent the average mass of all isotopes of that element as they occur naturally.

For example, in the compound \textbf{Barium Sulfate} (\textbf{BaSO}\(_4\)), the molar mass would be calculated by adding the atomic masses of one Barium (Ba), one Sulfur (S), and four Oxygen (O) atoms. This requires us to multiply the atomic mass of Oxygen by four because there are four Oxygen atoms in the compound. Calculating molar mass accurately is the first step in understanding the relationship between mass and moles in a chemical substance, which is foundational for stoichiometry.

Mole to Mass Conversion

Once the molar mass is determined, converting between moles and mass is a straightforward process but is a common point of confusion for many students. To convert mass to moles, you divide the given mass of the compound by its molar mass. This gives the number of moles present in that mass. Conversely, to convert from moles to mass, you multiply the number of moles by the molar mass.

For instance, suppose we have 140.0 grams of \textbf{Magnesium Phosphate} (\textbf{Mg}\(_3\)(\textbf{PO}\(_4\))\(_2\)), and we've already calculated its molar mass. We divide 140.0 g by the molar mass to find out how many moles are present in this particular mass of the compound. This step is vital in stoichiometry, as it allows chemists to quantify the amount of substance and reactants or products in a chemical reaction.

Avogadro's Number

In the realm of chemistry, \textbf{Avogadro's number} is a fundamental constant that represents the number of particles, such as atoms or molecules, in one mole of a substance. This value is a cornerstone in stoichiometry and has been experimentally determined to be approximately \(6.022 \times 10^{23}\) entities per mole.

With Avogadro's number, converting moles to particles becomes feasible. If we know the number of moles of a compound, we can simply multiply it by Avogadro's number to find the number of atoms or ions present. For example, if we have 1 mole of \textbf{Potassium Bromide} (\textbf{KBr}), this means we have \(6.022 \times 10^{23}\) formula units of KBr. Each formula unit contains one atom of potassium (K) and one atom of bromine (Br), which means there are also \(6.022 \times 10^{23}\) atoms of K and Br each. Understanding Avogadro's number is essential for translating between the macroscopic world of grams and kilograms and the microscopic world of atoms and molecules.