Question

In Example \(2-1,\) we established that the mass ratio of magnesium to magnesium oxide is 0.455 g magnesium/ \(0.755 \mathrm{g}\) magnesium oxide. (a) What is the ratio of oxygen to magnesium oxide, by mass? (b) What is the mass ratio of oxygen to magnesium in magnesium oxide? (c) What is the percent by mass of magnesium in magnesium oxide?

Short answer

a) The ratio of oxygen to magnesium oxide, by mass, is 0.397. b) The mass ratio of oxygen to magnesium in magnesium oxide is 0.659. c) The percent by mass of magnesium in magnesium oxide is 60.26%.

Step-by-step solution

Find the Mass of Oxygen in Magnesium Oxide

The mass of oxygen in magnesium oxide can be determined by subtracting the mass of magnesium from the total mass of magnesium oxide: \[ \text{Mass of Oxygen in MgO} = \text{Total mass of MgO} - \text{Mass of Mg}\ \text{Mass of Oxygen in MgO} = 0.755 \text{ g} - 0.455 \text{ g} = 0.3 \text{ g}\]

The Ratio of Oxygen to Magnesium Oxide, by Mass

\[\text{Ratio of O to MgO} = \frac{0.3 \text{ g (mass of oxygen)}}{0.755 \text{ g (total mass of magnesium oxide)}} = 0.397\]

The Mass Ratio of Oxygen to Magnesium in Magnesium Oxide

This can be calculated as \[\text{Ratio of O to Mg} = \frac{0.3 \text{ g (mass of oxygen)}}{0.455 \text{ g (mass of magnesium)}} = 0.659\]

The Percent by Mass of Magnesium in Magnesium Oxide

Percentage by mass of magnesium in magnesium oxide can be calculated as follows: \[\text{Percentage of Mg in MgO} = \frac{\text{mass of Mg}}{\text{total mass of MgO}} \times 100 = \frac{0.455 \text{ g}}{0.755 \text{ g}} \times 100 = 60.26 \% \]

Key concepts

Mass Ratio

The concept of mass ratio is pivotal in stoichiometry, which is the part of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In our discussion, the mass ratio tells us how much of one element is present compared to another element or compound. This ratio is crucial when analyzing compounds to understand the relationship between their constituting parts.
Consider magnesium oxide (MgO), where we've determined specific mass ratios. First, we found that the ratio of magnesium to magnesium oxide is calculated by dividing the mass of magnesium by the total mass of magnesium oxide. In this specific case, it equals 0.455 g Mg per 0.755 g MgO, leading to a ratio of approximately 0.602. Such calculations help chemists determine the compound composition and its properties.
Understanding mass ratios allows us to identify not just the presence, but the proportion of elements in a compound, which can be crucial in both academic studies and practical applications like materials science or pharmaceuticals.

Magnesium Oxide

Magnesium oxide is a compound formed by the reaction of magnesium with oxygen. This compound is often abbreviated as MgO and is known for its high melting point and thermal conductivity, making it useful in various industries, including construction and medicine.
In a chemical context, magnesium oxide is the result of a stoichiometric reaction between magnesium and oxygen, typically following this balanced equation: \[2 ext{Mg} + ext{O}_2 ightarrow 2 ext{MgO}\]For our exercise, we calculated that when magnesium reacts completely with oxygen, the mass of the oxygen can be found by subtracting the mass of magnesium from the total mass of magnesium oxide. This is how we determined that in our example: \[0.755 ext{ g (MgO)} - 0.455 ext{ g (Mg)} = 0.3 ext{ g (O)}\]Learning how magnesium oxide is formed and calculated helps us not only in stoichiometric calculations but also in understanding its vast applications beyond the laboratory.

Percent Composition

Percent composition is a key concept that helps chemists understand the makeup of a compound in terms of the percentage of each element present. This is expressed in percent by mass, which tells us what portion of the total compound's mass is due to each element.
In the case of magnesium oxide, the percent composition of magnesium is calculated by dividing the mass of magnesium by the total mass of MgO and then multiplying by 100 to convert it into a percentage:\[\text{Percent of Mg in MgO} = \frac{0.455 \text{ g}}{0.755 \text{ g}} \times 100 = 60.26\%\]Such calculations help predict how a compound behaves chemically and physically. Moreover, understanding percent composition is critical for practical purposes, such as determining the yield of a reaction or the purity of a compound. It provides valuable insights into how an element contributes to the compound's overall properties and functionality.