Question

A 1.546 -g sample of magnesium metal is heated in sufficient air at a high temperature so that all of the magnesium reacts. The reaction forms \(2.512 \mathrm{~g} \mathrm{MgO}\) and a small quantity of another magnesium-containing compound that is \(72.24 \%\) magnesium by mass. (a) Determine the formula of the other magnesiumcontaining compound. (b) Name this compound. (c) Calculate what fraction of the original \(\mathrm{Mg}\) is in this second compound.

Short answer

(a) The formula is Mg\(_3\)N\(_2\). (b) Magnesium Nitride. (c) 72.24% of original Mg is in this compound.

Step-by-step solution

Calculate the mass of oxygen in MgO

First, we need to calculate the mass of oxygen that reacted to form MgO. We subtract the initial mass of magnesium from the mass of MgO:\[m_{ ext{O}} = m_{ ext{MgO}} - m_{ ext{Mg}} = 2.512 ext{ g} - 1.546 ext{ g} = 0.966 ext{ g}\]

Determine mass of the other compound

Next, we calculate the mass of the other magnesium-containing compound. This is found by deducing it from the total mass of the products (2.512 g) and the mass of Mg:\[m_{ ext{other compound}} = m_{ ext{MgO}} - m_{ ext{O}} = 2.512 ext{ g} - 0.966 ext{ g} = 1.546 ext{ g}\]

Calculate mass of magnesium in other compound

Since the other compound is 72.24% magnesium by mass, we calculate the mass of magnesium in this compound:\[m_{ ext{Mg in other compound}} = m_{ ext{other compound}} \times \frac{72.24}{100} = 1.546 \text{ g} \times 0.7224 = 1.117 \text{ g}\]

Determine the formula of the other compound

Assume the compound contains magnesium and oxygen. Let the molar masses of Mg and O be 24.31 g/mol and 16.00 g/mol, respectively. Calculate moles:- Moles of Mg in the second compound: \((\frac{1.117 \text{ g}}{24.31 \text{ g/mol}}) = 0.046 \, \text{mol Mg}\)Since the compound is around 72.24% Mg, the rest is likely O:- Moles of O: \(\frac{m_{ ext{other compound}} - 1.117}{16.00 \, \text{g/mol}} = \frac{0.429}{16.00} \approx 0.0268 \, \text{mol O}\)The simplest mole ratio (dividing each by the smallest amount) gives:Mg:O = \(\dfrac{0.046}{0.0268} \approx 1.72\)This suggests the ratio is close to 3:2, so formula could be Mg\(\_3\)O\(\_2\), however the experimental compound is more likely Magnesium Nitride, Mg\(_3\)N\(_2\), due to nitrogen representations.

Calculate the fraction of original Mg in second compound

Calculate the fraction of the initial Mg in the second compound:\[fraction = \left(\frac{m_{\text{Mg in other compound}}}{m_{\text{initial Mg}}}\right) = \frac{1.117}{1.546} = 0.7224\]This confirms that approximately 72.24% of the original Mg is in the second compound.

Key concepts

Understanding Magnesium Reactions

Magnesium is a light, silvery-white metal (Mg) that is highly reactive, especially in the presence of oxygen. When magnesium is heated, it reacts vigorously with oxygen to form magnesium oxide (MgO). This reaction is highly exothermic, meaning it releases a significant amount of heat.
This property makes magnesium useful in applications such as flash powder, fireworks, and incendiary devices. When magnesium burns, it produces a bright white light, which is also utilized in military flares.
The general reaction for magnesium burning in air is:
- Magnesium reacts with oxygen to form magnesium oxide: \(2 ext{Mg} + ext{O}_2 ightarrow 2 ext{MgO}\).Understanding these reactions is crucial in predicting the outcomes of chemical processes involving magnesium and its compounds under various conditions.

Determining Compound Formulas

To determine the formula of an unknown compound, we often rely on the mass percentages of elements within it as well as known chemical laws.
In this exercise, the task is to find the formula of an unknown magnesium-containing compound besides magnesium oxide. A critical tool in this determination is the concept of molar mass, which allows us to convert between the mass of a substance and the amount in moles.
Using the data that the unknown compound is 72.24% magnesium by mass, we can calculate the mass of magnesium present in a sample of the unknown compound. Using this percentage and known molar masses (Mg: 24.31 g/mol, O: 16.00 g/mol), the formula can be deduced by calculating and comparing moles of magnesium and other elements present.
For example, if the known ratio of moles in the sample suggests a structure prevalent with a typical valency, such as Mg\(_3\)N\(_2\), it can indicate the presence of magnesium nitride rather than just magnesium oxide or another compound.

Performing Mole Calculations

Mole calculations serve as the backbone in determining how substances react and combine to form compounds. A mole, a unit used to measure the amount of a substance, is tied to Avogadro's number, which is approximately \(6.022 imes 10^{23}\) entities per mole.
When dealing with chemical reactions, it's critical to calculate the number of moles of reactants and products to understand the proportions in which substances combine.
For instance, using the given mass of magnesium in the unknown compound, we convert this mass to moles using the formula:

• For magnesium: \( ext{moles of Mg} = \frac{ ext{mass of Mg}}{ ext{molar mass of Mg}} \).

Similarly, once we know the moles of magnesium, we can find the moles of any other elements in the compound by using their mass and molar masses.
These calculations assist in determining the empirical formula of the compound, which is the simplest positive integer ratio of atoms present.