Question

Calculate the number of moles in \(100.0 \mathrm{~g}\) of each of the following compounds. (a) \(\mathrm{SO}_{2}\) (c) \(\mathrm{BaSO}_{4}\) (b) \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) (d) \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2}\)

Short answer

The number of moles in 100.0 g of each compound is approximately: (a) 1.56 for SO2 (b) 0.39 for BaSO4 (c) 0.70 for Na2SO4 (d) 0.37 for KAl(SO4)2.

Step-by-step solution

Calculate Molar Mass

Use the periodic table to find the atomic mass of each element in the compound. Sum these atomic masses to find the molar mass of the compound. For SO2, the molar mass is \(32.1 \: g/mol (S) + 2 \times 16.0 \: g/mol(O) = 64.1 \: g/mol\) . Calculate this way for all compounds

Compute the Number of Moles

Use the given mass of each compound and its molar mass to calculate the number of moles using the formula: moles = mass / molar mass. For SO2, the number of moles = \(100.0\, g / 64.1\, g/mol = 1.56\, moles\). Proceed similarly for all compounds.

Repeat for All Compounds

Repeat steps 1 and 2 above for each of the four compounds. The calculations for each compound are independent of each other.

Key concepts

Molar Mass Calculation

The first step in solving many chemistry problems, including the one above, is determining the molar mass of a compound. This calculation involves using atomic masses from the periodic table. Each element has a specific atomic mass, expressed in grams per mole (g/mol). To find the molar mass of a compound:

• Identify the elements and the number of each element in the chemical formula.
• Find the atomic mass of each element on the periodic table.
• Multiply the atomic mass by the number of atoms of that element in the formula.
• Add the results for all elements in the compound.

Let's consider sulfur dioxide, \(\text{SO}_2\). Sulfur (S) has an atomic mass of 32.1 g/mol, and oxygen (O) has an atomic mass of 16.0 g/mol. For SO₂, \(\text{Molar Mass} = 32.1 \text{ g/mol} + 2 \times 16.0 \text{ g/mol} = 64.1 \text{ g/mol}\). This approach will help you find the molar mass of any compound you encounter.

Number of Moles

After calculating the molar mass, the next step is finding out the number of moles of the compound in a given mass. The number of moles represents the quantity of substance, a critical concept in chemistry, as reactions happen on a mole-to-mole basis. Here's how to calculate it:
To find the number of moles, use the formula:\[\text{number of moles} = \frac{\text{mass of the compound (g)}}{\text{molar mass of the compound (g/mol)}}\]Using sulfur dioxide (\(\text{SO}_2\)) again as an example, if you have 100 g of \(\text{SO}_2\), then:

• The number of moles = \(\frac{100.0 \text{ g}}{64.1 \text{ g/mol}} = 1.56 \text{ moles}\).

This calculation allows you to determine how much of the compound is present to participate in a reaction.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's a vital tool that allows you to predict the amounts of substances consumed and produced in a reaction.
To make the best use of stoichiometry:

• First, write the balanced chemical equation for the reaction. This shows the proportions in which substances react and are formed.
• Use molar ratios from the balanced equation to convert moles of one substance to moles of another.
• The moles information calculated from the previous steps (like the number of moles from given mass) aligns excellently here.

For example, if \(a\) moles of \(\text{A}\) react with \(b\) moles of \(\text{B}\) to form \(c\) moles of \(\text{C}\), understanding these relationships helps predict how much \(\text{B}\) is needed for a given \(\text{A}\) or how much \(\text{C}\) will be produced. Mastery of these concepts is key to solving complex chemistry problems successfully.