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Chapter 12: Problem 7

How many moles of aluminum are present in 5 mol of \(\mathrm{MgAl}_{2} \mathrm{O}_{4} ?\)

Short Answer

Expert verified
There are 10 moles of aluminum in 5 moles of \(\text{MgAl}_{2}\text{O}_{4}\).

Step by step solution

01

Identify the compound composition

The compound \(\text{MgAl}_{2}\text{O}_{4}\) contains magnesium (Mg), aluminum (Al), and oxygen (O) atoms.
02

Determine the aluminum atoms per formula unit

In \(\text{MgAl}_{2}\text{O}_{4}\), there are 2 aluminum atoms in each formula unit of the compound.
03

Relate moles of compound to moles of aluminum

Since 1 mole of \(\text{MgAl}_{2}\text{O}_{4}\) contains 2 moles of aluminum atoms, use this ratio to find the number of moles of aluminum.
04

Calculate the total moles of aluminum

Given 5 moles of \(\text{MgAl}_{2}\text{O}_{4}\), multiply by 2 to find the moles of aluminum: \[\text{Moles of Al} = 5 \text{ mol } \times 2 = 10 \text{ mol}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

chemical composition
Understanding the chemical composition of a compound is an essential part of chemistry. A compound is made up of different elements bonded together in fixed proportions. For instance, in the compound \(\text{MgAl}_{2}\text{O}_{4}\), you'll find magnesium (Mg), aluminum (Al), and oxygen (O) atoms. These are bound in a specific ratio: one magnesium atom, two aluminum atoms, and four oxygen atoms per formula unit. This specific arrangement and ratio form the unique properties of the compound. By breaking down a compound's chemical composition, we can understand its properties and reactions better.
molar ratio
A molar ratio is a proportion between the amounts in moles of any two compounds involved in a chemical reaction. It is useful in stoichiometry to convert between different substances. For example, in the compound \(\text{MgAl}_{2}\text{O}_{4}\), the molar ratio of aluminum to the compound is crucial. One formula unit of \(\text{MgAl}_{2}\text{O}_{4}\) contains 2 moles of aluminum atoms. This gives us a molar ratio of 1:2 between \(\text{MgAl}_{2}\text{O}_{4}\) and aluminum. Molar ratios make it easier to calculate how much of one substance will react with or be produced from another in a chemical reaction.
aluminum atoms
Atoms are the building blocks of all matter. An aluminum atom (Al) is a single unit of the element aluminum with a specific atomic structure. In our compound, \(\text{MgAl}_{2}\text{O}_{4}\), there are 2 aluminum atoms per formula unit. So, if you have a mole of this compound, you have 2 moles of aluminum atoms. Remembering that aluminum atoms are repeated in each formula unit helps in calculating the total number of moles of aluminum when given a certain number of moles of the compound. This simple multiplication is a core part of mole calculations in chemistry.
stoichiometry
Stoichiometry is the area of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In simpler terms, it helps us calculate how much of one chemical you'll need to react with a given amount of another. In our exercise, if you have 5 moles of \(\text{MgAl}_{2}\text{O}_{4}\), using stoichiometry, you multiply this by the molar ratio of aluminum, i.e., 2. Hence, \(5 \text{ mol } \times 2 = 10 \text{ mol}\) of aluminum atoms. By understanding stoichiometry, you can predict and measure the outcomes of reactions with precision.

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