How many oxygen atoms are there in 224 grams of O2? Give your answer to two decimal places. Oxygen equals 16 grams per mole.
The mass of a substance and the number of entities of that substance cannot be directly related to one another. However, the mass of a substance can be related to the amount of that substance in moles, which can then be related to the number of entities of that substance. Mass and amount can be related via the key equation 𝑛 equals lowercase 𝑚 divided by capital 𝑀, where 𝑛 represents the amount in moles, lowercase 𝑚 is the mass in grams, and capital 𝑀 is the molar mass in grams per mole.
The mass of oxygen gas was provided in the question, as was the molar mass of oxygen. But we need to be careful here. The molar mass provided is the molar mass of one mole of oxygen. But what we need is the molar mass of oxygen gas. To calculate the molar mass of oxygen gas, we simply multiply the molar mass of oxygen by two. This gives us a molar mass of 32 grams per mole. We can then substitute the mass and molar mass into the key equation. We perform the calculation and determine the number of moles of oxygen gas to be seven moles.
Now that we know the amount in moles, we can use this value to determine the number of entities using the key equation capital 𝑁 equals capital 𝑁 subscript A times lowercase 𝑛, where capital 𝑁 represents the number of entities. Lowercase 𝑛 is the amount in moles and capital 𝑁 subscript A is Avogadro’s constant, a value equal to 6.22 times 10 to the 23rd per mole. As we already calculated the amount in moles, we can substitute the seven moles and Avogadro’s constant into the key equation. We perform the calculation and determine the number of entities to be 4.2154 times 10 to the 24th entities.
But what was the entity being determined? Looking back at our previous work, we used the mass of oxygen gas and the molar mass of oxygen gas in the first key equation. This means that we must have solved for the amount of oxygen gas in moles. We then used the amount of oxygen gas in moles in the second key equation. This means that we should be able to replace the unit entities with molecules of oxygen gas. Looking back at the question, we were asked to determine the number of oxygen atoms, not the number of oxygen molecules.
Looking at the chemical formula of oxygen gas, we see that one molecule of oxygen gas contains two atoms of oxygen. We can then multiply the number of molecules of oxygen gas by this relationship written as a fraction with molecules of oxygen gas in the denominator so that the units cancel. We perform the calculation and determine the number of atoms of oxygen to be 8.4308 times 10 to the 24th atoms. But the question asked us to give our answer to two decimal places. Rounding appropriately, we have determined that 224 grams of oxygen gas contains 8.43 times 10 to the 24th atoms of oxygen.