Question

If one mole of carbon atom weighs 12 g, then what is the mass in grams of 1 atom of carbon?
A. \[1.993 \times {10^{ - 23}}\]
B. \[1.993 \times {10^{23}}\]
C. \[1.993 \times {10^{ - 24}}\]
D. \[1.993 \times {10^{24}}\]

Answer 1

Hint: To solve this question, we must first derive a relation between the number of moles and number of atoms/ molecules of a substance. Then we must derive a relation between the number of moles and molar mass of a substance. From these two relations, we must correlate the number of atoms/molecules to the molar mass of the substance.

Complete Step-by-Step Answer:
Before we move forward with the solution of this question, let us first understand some important basic concepts.
Mole concept: Moles are used to measure the amount of matter present in a given sample of a substance. To be more specific, it helps in measuring the number of atoms or molecules present in the given sample of the substance. One mole of any substance contains \[6.022 \times {10^{23}}\] atoms or molecules.
Now, due to the variation in the number of protons, neutrons and electrons present in the atoms of different elements, the weight of these atoms also varies. Because of this, one mole of different substances may have different weight.
Now, moving back to the question, we have been given that one mole of carbon weighs 12 g, and we are supposed to find the mass of 1 atom of carbon.
We know that,
1 mole = \[6.022 \times {10^{23}}\] atoms
Now, the weight of 1 mole of carbon is 12 grams
Hence,
12 g = \[6.022 \times {10^{23}}\] atoms
12 g = \[(6.022 \times {10^{23}})\] (1 atom)
1 atom = \[\dfrac{{12}}{{6.022 \times {{10}^{23}}}}\] g
1 atom = \[1.993 \times {10^{ - 23}}\] g
Hence, 1 atom of carbon weighs \[1.993 \times {10^{ - 23}}\] g
Hence, Option A is the correct option

Note: One mole of any substance has an equivalent number of atoms or molecules of the corresponding substance. These constant numbers of atoms or molecules in one of a substance are assigned a specific constant value. This constant is known as Avogadro’s constant. The value of this constant is given as \[6.022 \times {10^{23}}\] molecules/mole.