Question

Magnesium metal, which burns in oxygen with an intensely bright white flame, has been used in photographic flash units. The balanced equation for this reaction is $$2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{MgO}(s)$$ How many grams of \(\mathrm{MgO}(s)\) are produced by complete reaction of \(1.25 \mathrm{g}\) of magnesium metal?

Short answer

The complete reaction of \(1.25\,\text{g}\) of magnesium metal will produce \(2.07\,\text{g}\) of magnesium oxide (MgO).

Step-by-step solution

Find the molar mass of magnesium and magnesium oxide

Consult the periodic table and find the molar mass of magnesium (Mg) and oxygen (O). Then, calculate the molar mass of magnesium oxide (MgO). Molar mass of Mg = \(24.305\,\text{g/mol}\) Molar mass of O = \(16.00\,\text{g/mol}\) Molar mass of MgO = \((24.305 + 16.00)\,\text{g/mol}\) = \(40.305\,\text{g/mol}\)

Calculate the moles of magnesium used

Given the mass of magnesium used, we can calculate the moles of magnesium using the molar mass: Moles of Mg = \( \frac{\text{Mass of Mg}}{\text{Molar mass of Mg}}\) Moles of Mg = \(\frac{1.25\,\text{g}}{24.305\,\text{g/mol}}\) = \(0.0514\,\text{moles}\)

Determine the amount of moles of MgO produced

Use the stoichiometry of the reaction to find the moles of MgO produced: From the balanced equation, we know that 2 moles of Mg react with 1 mole of O2 to form 2 moles of MgO. Given that 2 moles of Mg produce 2 moles of MgO, we can say that the amount of MgO produced is equal to the amount of Mg used. Moles of MgO = Moles of Mg = \(0.0514\,\text{moles}\)

Calculate the mass of magnesium oxide produced

Lastly, multiply the moles of MgO by the molar mass of MgO to get the mass of MgO produced: Mass of MgO = \( \text{Moles of MgO} \times \text{Molar mass of MgO}\) Mass of MgO = \(0.0514\,\text{moles} \times 40.305\,\text{g/mol}\) = \(2.07\,\text{g}\) So, complete reaction of 1.25 g of magnesium metal will produce 2.07 g of magnesium oxide (MgO).

Key concepts

Understanding Balanced Chemical Equations

At the heart of many chemistry problems lies the balanced chemical equation. It's a representation that shows exactly how reactants transform into products during chemical reactions. Establishing a balanced equation is crucial because it adheres to the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction.

The given equation for magnesium burning in oxygen, \[2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{MgO}(s)\], exemplifies this balance. In simple terms, it tells us that two atoms of magnesium (Mg) react with one molecule of oxygen (O2) to form two units of magnesium oxide (MgO). For every two moles of magnesium consumed, two moles of magnesium oxide are produced. Understanding this stoichiometric relationship is vital because it lays the groundwork for all subsequent calculations in the problem.

Molar Mass Calculation

The molar mass calculation enables us to convert between grams and moles, a fundamental concept in chemistry for quantifying substances. The periodic table provides the atomic weights of elements, which are the building blocks for computing the molar mass of compounds.

In our exercise, the molar mass of magnesium (\(24.305\,\text{g/mol}\)) and oxygen (\(16.00\,\text{g/mol}\)) are combined to determine the molar mass of magnesium oxide (MgO), summing up to \(40.305\,\text{g/mol}\). This calculation is essential for stoichiometry because it allows us to perform conversions and calculate the amounts of substances needed or produced in a chemical reaction.

Mastering Stoichiometric Calculations

Stoichiometric calculations form the bridge between chemical equations and practical applications like how much of a reactant is needed to produce a desired amount of product. In stoichiometry, the balanced chemical equation serves as a recipe that tells us the proportions in which substances react.

By understanding that the moles of magnesium oxide produced will be equal to the moles of magnesium reacted, based on the 1:1 ratio in the equation, we can calculate the mass of the product formed from a given mass of a reactant. This concept was applied to find that 1.25 g of magnesium will produce 2.07 g of magnesium oxide, using the relationship that the molar mass provides to transition between grams and moles. Learning to navigate through these calculations is crucial for many laboratory and industrial applications, where precision and accuracy in chemical recipes are imperative.