Problem 88 - Chemistry An Atoms First Approach

Question

Consider the reaction between oxygen \(\left(\mathrm{O}_{2}\right)\) gas and magnesium metal to form magnesium oxide. Using oxidation states, how many electrons would each oxygen atom gain, and how many electrons would each magnesium atom lose? How many magnesium atoms are needed to react with one oxygen molecule? Write a balanced equation for this reaction.

Step-by-Step Solution

Answer

In the reaction between oxygen gas \(\left(\mathrm{O}_{2}\right)\) and magnesium metal, each oxygen atom gains 2 electrons, and each magnesium atom loses 2 electrons. Two magnesium atoms are needed to react with one oxygen molecule. The balanced equation for this reaction is: \(2 \: \mathrm{Mg} \: + \: \mathrm{O}_{2} \rightarrow 2 \: \mathrm{MgO}\).

Step 1: Determine oxidation states

To determine the number of electrons gained or lost during the reaction, we must identify the initial and final oxidation states of magnesium and oxygen. The initial oxidation state of oxygen in molecular oxygen \(\left(\mathrm{O}_{2}\right)\) is 0, as it is the pure element. The initial oxidation state of magnesium (Mg) metal is also 0 because it is a pure element. In magnesium oxide, we have Mg bound to O. The oxidation state of oxygen in most compounds is \(-2\), and the oxidation state of magnesium is \(+2\).

Step 2: Determine electron transfers

Now we can determine the number of electrons gained or lost during the reaction. For Oxygen: Initial oxidation state = 0, Final oxidation state = -2, So, each oxygen atom gains 2 electrons (0 - (-2) = +2) For Magnesium: Initial oxidation state = 0, Final oxidation state = +2, So, each magnesium atom loses 2 electrons (0 - (+2) = -2)

Step 3: Determine the number of magnesium atoms needed

An oxygen molecule \(\left(\mathrm{O}_{2}\right)\) contains two oxygen atoms. Each oxygen atom gains 2 electrons during the reaction, meaning that a single oxygen molecule will gain a total of 4 electrons. Since a magnesium atom only loses 2 electrons during the reaction, we need 2 magnesium atoms to interact with one oxygen molecule (to balance the electron transfer).

Step 4: Write a balanced equation

We can now write the balanced equation for the reaction between oxygen gas and magnesium metal to form magnesium oxide: \(2 \: \mathrm{Mg} \: + \: \mathrm{O}_{2} \rightarrow 2 \: \mathrm{MgO}\) In this reaction, 2 magnesium atoms react with 1 oxygen molecule to form 2 magnesium oxide units, with each oxygen atom gaining 2 electrons and each magnesium atom losing 2 electrons.