If a student weighs \(18 \mathrm{~g}\) of aluminum and needs twice as many atoms of magnesium as she has of aluminum, how many grams of Mg does she need?

To understand stoichiometry problems, you first need to grasp the concept of molar mass calculations. The molar mass of a substance is the mass of one mole of its atoms or molecules. It's expressed in grams per mole (g/mol). For example, the molar mass of aluminum (Al) is approximately 27 g/mol. This means one mole of Al atoms weighs 27 grams. To find the number of moles from a given mass, you use the formula:

\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]

In our example, with 18 grams of aluminum, we would calculate the moles as follows:

• Given mass of Al = 18 g
• Molar mass of Al = 27 g/mol

\[ \text{moles of Al} = \frac{18 \text{ g}}{27 \text{ g/mol}} = 0.6667 \text{ moles} \]

This is the crucial first step in solving any stoichiometry problem; without knowing the moles, you can't proceed to the next calculations.

Mole conversions are essential in chemistry, especially when dealing with stoichiometric calculations. Once you have the moles, you can easily convert between different substances using molar ratios. In this problem, the student needs twice as many atoms of magnesium (Mg) as they have of aluminum (Al). Because the number of atoms is directly proportional to the number of moles, you multiply the moles of Al by 2 to get the moles of Mg:

\[ \text{moles of Mg} = 2 \times \text{moles of Al} \]

Using the moles we calculated earlier:

• Moles of Al = 0.6667
• Moles of Mg needed = 2 \times 0.6667 = 1.3334 moles

Mole conversions are a straightforward yet vital step to solving most stoichiometry problems and bridge the gap between different chemical substances. This understanding helps in the calculation of required reactants and products in chemical reactions.

Chemical quantities involve converting between moles, mass, and number of atoms or molecules. After finding the number of moles using molar mass calculations and mole conversions, you often need to express this in grams for practical use. We use the formula:

\[ \text{mass} = \text{moles} \times \text{molar mass} \]

In our example problem, the student requires 1.3334 moles of Mg. Given the molar mass of magnesium is 24 g/mol, the mass is calculated as:

• Moles of Mg = 1.3334
• Molar mass of Mg = 24 g/mol

\[ \text{mass of Mg} = 1.3334 \text{ moles} \times 24 \text{ g/mol} = 32 \text{ g} \]

Knowing how to efficiently convert these chemical quantities ensures accuracy in preparing solutions, conducting experiments, and understanding reactions. Mastery of these conversions ultimately illuminates the relationships between different chemical substances and their quantities.