Video Transcript
How many grams of oxygen gas are necessary to react completely with 2.93 times 10 of the 21st power atoms of magnesium to yield magnesium oxide? Give your answer to two decimal places in scientific notation. The molar mass of oxygen is 16 grams per mole, and magnesium is 24 grams per mole.
When reading the first sentence in the question, we see the keywords “to yield.” Substances that appear before “to yield” in the sentence are the reactants of the chemical reaction, while substances that appear after “to yield” are the products. Let’s write a basic word equation for this reaction. Oxygen gas is reacting with magnesium metal. We would expect magnesium metal to be a solid at standard conditions. We’ll need to put a plus sign between magnesium solid and oxygen gas because these are two different reactants.
The keywords “to yield” represent the reaction arrow of our equation. Magnesium oxide appears after the words “to yield” in the sentence, so it is the product of the reaction. Magnesium oxide is an ionic compound, so we would expect it to be a solid at standard conditions. In this question, we are asked to find the mass in grams of one substance, oxygen gas. And we are given the amount of atoms of a second substance, magnesium solid. We need to figure out the relationship between oxygen and magnesium before we can solve this problem. To do so, we need to write a balanced chemical equation for the reaction. Let’s start by writing the chemical formula of each substance under its name.
The chemical symbol for magnesium metal is Mg. And since it is a solid, we’ll use the state symbol s. The chemical formula for oxygen gas is O2 followed by the state symbol g. Finally, the chemical formula for magnesium oxide solid is MgO followed by the state symbol s. Now, we’re ready to balance the chemical equation. First, let’s count up how many of each type of atom we have on either side of the equation.
On the left side of the equation, there is one magnesium atom, and on the right side, there is also one magnesium atom. Now, let’s look at the oxygen atoms. On the left side of the equation, there are two oxygen atoms. And on the right side of the equation, there is one oxygen atom. We’ll need to use a coefficient of two in front of magnesium oxide to balance the oxygen atoms. But this means that we now also have two magnesium atoms on the product side of the equation. We’ll need to go back to the reactant side and balance the magnesium atoms. A coefficient of two is required in front of magnesium to fully balance the equation.
Now that we have a balanced chemical equation, let’s write the data provided in the question under the correct substance in the equation. We know that 2.93 times 10 to the 21st atoms of magnesium are reacting. So, let’s write this under magnesium in the chemical equation. We aren’t given any other data, but we do know that we must find the mass in grams of oxygen that will react with this specific amount of magnesium atoms. We cannot directly relate atoms of one substance to grams of another substance in a balanced chemical equation. However, we can directly relate the amount in moles of magnesium to the amount in moles of oxygen using the balanced chemical equation.
The stoichiometric coefficients that we used to balance the chemical equation represent the amount in moles of each substance needed for a complete reaction. We typically don’t write a coefficient of one, but let’s go ahead and include it in front of oxygen gas to help us solve the problem. According to our balanced equation, one mole of oxygen gas is necessary to completely react with two moles of magnesium. When we write this relationship as a ratio, it’s called the molar ratio. It can be used as a conversion factor to help us convert between magnesium and oxygen.
In this problem, we are given the number of magnesium atoms, not moles. In order to convert from atoms of magnesium to moles of magnesium, we’ll need to make use of the following equation. In this equation, lowercase 𝑛 represents the amount in moles of magnesium, which is what we are trying to find. Uppercase 𝑁 represents the given amount of magnesium atoms. And 𝑁 𝐴 is Avogadro’s constant. For this problem, we’ll use the truncated form, which is 6.022 times 10 to the 23 entities per mole. For this type of problem, we don’t need to use such a precise value.
After substituting in the amount of magnesium atoms and Avogadro’s constant into the equation, we get 2.93 times 10 to the 21st power divided by 6.022 times 10 to the 23rd power entities per mole. After performing the division, we get an answer of 0.00487 moles of magnesium. Let’s wait to round our answer until the final step of the problem.
Now, we’ll need to multiply by the molar ratio from the balanced chemical equation in order to convert moles of magnesium to moles of oxygen. In our conversion factor for the molar ratio, we’ll want to put one mole of O2 in the numerator since these are the desired units for this calculation and two moles of magnesium in the denominator since these are the undesired units or the units that we wish to cancel. When performing the calculation, the units moles of magnesium cancel, and our answer is 0.00243 moles of O2. We’ll wait to round because we still have one final step.
In order to convert our answer with the units moles of O2 to the units grams of O2, we’ll need to make use of the following equation. In this equation, lowercase 𝑚 represents the mass in grams, which is what we are trying to find. Lowercase 𝑛 is the amount in moles of O2, which is 0.00243. Uppercase 𝑀 is the molar mass of O2. The molar mass for oxygen given in the problem is 16 grams per mole. This means that the molar mass of O2 would be twice as much or 32 grams per mole.
Let’s substitute our values for the amount of moles of O2 and the molar mass of O2 into the equation. Here, we’ve expanded the units of molar mass to show that 32 grams of O2 is the mass of one mole of O2. When we perform the calculation, the units of moles of O2 cancel. After multiplying 0.00243 by 32, we get an answer of 0.077848 grams of O2.
To finish up, we need to round our answer to two decimal places and express it in scientific notation. Our final answer is 7.78 times 10 to the negative second power grams of O2, which is the amount in grams of oxygen gas necessary to completely react with the atoms of magnesium.
