Question Video: Recalling the Number of Atoms in 12 Grams of Carbon-12

How many moles of atoms are there in 12 g of carbon-12?

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Video Transcript

How many moles of atoms are there in 12 grams of carbon-12?

Carbon-12 is the name for a specific isotope of the element carbon. We can find the entry for carbon on the periodic table of elements, which tells us the symbol for carbon is C and that the atomic number for carbon is six. We can use this information to tell us a little bit more about what an atom of carbon looks like. As with all atoms, we have a nucleus surrounded by an electron cloud. The atomic number tells us the number of protons in atoms of carbon. So, in this nucleus, we have six protons.

By definition, an atom is neutral overall. So, we need six electrons to balance the charge of the six protons. However, there’s one bit of information we’re missing. An atom of carbon-12 contains a specific number of neutrons. When we label isotopes, we use the mass number. In this case, the mass number of carbon-12 is 12. The mass number of an isotope is simply the number of protons plus the number of neutrons to be found in nuclei of that isotope.

To work out the number of neutrons in our atom of carbon-12, we simply take the atomic number away from the mass number, giving us six, six neutrons in the nucleus. So, we now know what we’re talking about, neutral atoms of carbon-12 consisting of six protons, six neutrons, and six electrons each.

The question tells us that we have exactly 12 grams of carbon-12. To work out the absolute number of atoms, we could take our mass and divide it by the mass of each atom. However, this would be the amount of atoms we have. But the question is asking for the amount of atoms in moles. One mole of atoms is equivalent to an Avogadro’s number of atoms, which is an astonishingly big number, about six times 10 to the power of 23. So, to get the number of moles of atoms not simply the number of atoms, we have to divide our mass by the mass per mole for carbon-12.

You might see mass per mole referred to as molar mass. At this point, it’s very easy to make a mistake and use the atomic mass for the element on the periodic table. For an element, we can take the number in the periodic table and add the units, unified atomic mass units, to get the atomic mass and then convert that into the molar mass with units of grams per mole. However, this value is an average determined by the amount of each isotope and the mass of each isotope.

To find the molar mass of carbon-12, we need to do something different. For this, we need to recall the actual definition of a unified atomic mass unit, one twelfth of the mass of a carbon-12 atom. This means that the mass of a carbon-12 atom is exactly 12 unified atomic mass units. Therefore, the mass per mole of carbon-12 is 12 grams per mole, meaning moles of carbon-12 atoms. We can work out the number of moles of atoms in 12 grams of carbon-12 by taking the mass and dividing by the molar mass.

You might see this written as 𝑛 is equal to 𝑚 divided by capital 𝑀. So, our amount is 12 grams multiplied by one mole for every 12 grams, giving us our final answer of exactly one mole of carbon-12 atoms. Therefore, the number of moles of atoms in 12 grams of carbon-12 is one mole.

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