Problem 88 - Chemistry: An Atoms-Focused Approach

Question

How many moles of \(\mathrm{O}^{2-}\) ions are in \(0.55 \mathrm{mol} \mathrm{Al}_{2} \mathrm{O}_{3} ?\) What is the mass in grams of the \(\mathrm{O}^{2-}\) ions?

Step-by-Step Solution

Answer

Answer: There are 1.65 moles and 26.4 grams of \(O^{2-}\) ions in \(0.55\,\mathrm{mol}\,\mathrm{Al}_{2} \mathrm{O}_{3}\).

Step 1: Calculate moles of \(\mathrm{O}^{2-}\) ions

Since there are 3 moles of \(\mathrm{O}^{2-}\) ions per mole of \(\mathrm{Al}_{2} \mathrm{O}_{3}\), we can use the ratio of moles of \(\mathrm{O}^{2-}\) ions to moles of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) to find the moles of \(\mathrm{O}^{2-}\) ions in \(0.55\,\mathrm{mol}\,\mathrm{Al}_{2} \mathrm{O}_{3}\). To do this, we can multiply: Moles of \(\mathrm{O}^{2-}\) ions \(= 0.55\,\mathrm{mol}\,\mathrm{Al}_{2} \mathrm{O}_{3}\times \frac{3\,\mathrm{mol}\,\mathrm{O}^{2-}}{1\,\mathrm{mol}\,\mathrm{Al}_{2} \mathrm{O}_{3}}\)

Step 2: Calculate the mass of \(\mathrm{O}^{2-}\) ions in grams

Now that we have the moles of \(\mathrm{O}^{2-}\) ions, we can convert them to mass using the molar mass of oxygen (O), which is 16 g/mol: Mass of \(\mathrm{O}^{2-}\) ions \(= \text{(moles of O}^{2-} \text{ ions)} \times \text{(molar mass of O)}\) Now, let's perform the calculations.

Step 3: Perform the calculations

First, let's calculate the moles of \(\mathrm{O}^{2-}\) ions: Moles of \(\mathrm{O}^{2-}\) ions \(= 0.55\,\mathrm{mol}\,\mathrm{Al}_{2} \mathrm{O}_{3} \times \frac{3\,\mathrm{mol}\,\mathrm{O}^{2-}}{1\,\mathrm{mol}\,\mathrm{Al}_{2} \mathrm{O}_{3}} = 1.65\,\mathrm{mol}\,\mathrm{O}^{2-}\) Now, we can find the mass of \(\mathrm{O}^{2-}\) ions in grams: Mass of \(\mathrm{O}^{2-}\) ions \(= 1.65\,\mathrm{mol}\,\mathrm{O}^{2-} \times 16\,\mathrm{g/mol} = 26.4\,\mathrm{g}\) So, there are 1.65 moles and 26.4 grams of \(\mathrm{O}^{2-}\) ions in \(0.55\,\mathrm{mol}\,\mathrm{Al}_{2} \mathrm{O}_{3}\).

Key Concepts

Moles Calculation

In chemistry, calculations often revolve around the concept of moles. A mole is a unit used to represent a specific number of particles, such as atoms or molecules, equivalent to Avogadro's number which is approximately \(6.022 \times 10^{23}\). It provides a bridge between the atomic world and the macroscale world.
When calculating moles in a given reaction like the one in the original exercise, we use the relationship between the substances involved, often stated within the chemical formula. For instance, in \(\text{Al}_2\text{O}_3\), two aluminum atoms and three oxygen atoms form the compound.
Thus, knowing the formula, we calculate the moles of oxygen ions in any given amount of \(\text{Al}_2\text{O}_3\) by multiplying the moles of \(\text{Al}_2\text{O}_3\) by the stoichiometric factor from the formula:

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It's like a recipe in cooking but for chemical reactions, ensuring that the proportions of ingredients give the desired product.
In our example with \(\text{Al}_2\text{O}_3\), stoichiometry helps us understand how 3 moles of \(\mathrm{O}^{2-}\) ions relate to each mole of \(\text{Al}_2\text{O}_3\). By knowing this ratio, we can resolve how many \(\mathrm{O}^{2-}\) ions are present for a specific amount of \(\text{Al}_2\text{O}_3\):

• Moles of \(\mathrm{O}^{2-}\) = Moles of \(\text{Al}_2\text{O}_3\) \(\times \frac{3\text{ mol O}^{2-}}{\text{1 mol Al}_2\text{O}_3}\)

Stoichiometry offers the balance needed in reactions to know the right proportions and ensure everything reacts completely. Remember that balance is key to conserving mass in any chemical equation.

Molar Mass

Molar mass is the mass of one mole of a substance, and it's crucial for converting moles into grams. It is expressed in grams per mole (g/mol).
For elements, the molar mass is the atomic weight found on the periodic table. For compounds, like \(\text{Al}_2\text{O}_3\), you calculate the molar mass by adding up the molar masses of all atoms in the formula.
Given that the molar mass of oxygen (O) is 16 g/mol, it becomes quite straightforward to convert moles into mass:

• Mass (g) = Moles \(\times \) Molar Mass (g/mol)

If you had 1.65 moles of \(\mathrm{O}^{2-}\) ions, simply multiply by 16 g/mol to find the mass in grams. This conversion is essential for practical applications, allowing you to measure out reactants in lab settings effectively.