Question

If one mole of carbon atoms weighs 12 grams. What is the mass (in grams) of 1 atom of carbon?

Answer 1

We know that a mole is the term that defines the number of carbon (C) atoms in 12 g of pure carbon. After so many years of experiment, it has been proved that a mole of anything contains $6.022 \times {10^{23}}$representative particles.

Complete step by step answer:
We are given that the weight of one mole of carbon is 12 gram. We know that in one mole of anything, $6.022 \times {10^{23}}$representative particles present. So, it is clear that one mole of carbon atoms consist of $6.022 \times {10^{23}}$ carbon atoms. So, we can say that the mass of $6.022 \times {10^{23}}$atoms of carbon is 12 gram.
Now, we have to calculate the mass of one carbon atom using the unitary method. We have to divide the mass of one mole of atoms by the avogadro’s number. This calculation gives the mass of one carbon atom.

$6.022 \times {10^{23}}$atoms of carbon weighs=12 gram

Therefore, 1 atom of carbon weighs$= \dfrac{{12\,{\rm{g}}}}{{6.022 \times {{10}^{23}}}} = 1.99 \times {10^{ - 23}}\;{\rm{g}}$

So, the mass of one carbon atom is $1.99 \times {10^{ - 23}}\;{\rm{g}}$.

Additional Information:
Different kinds of particles, such as molecules, atoms, ions, electrons are representative particles. Mole is a unit of measurement of amount in a chemical substance. One mole of anything consists of $6.022 \times {10^{23}}$representative particles. For example, one mole of oxygen consists of $6.022 \times {10^{23}}$molecules of oxygen.Hence, the relation between mole and Avogadro’s number is $1\;{\rm{mol}} = 6.022 \times {10^{23}}\;{\rm{particles}}$.

Note:
Avogadro’s number$\left( {6.022 \times {{10}^{23}}} \right)$ is a special number that denotes the number of representative particles in 1 mole of substance. The number is named in honor of the Italian physicist Amedeo Avogadro. The Avogadro's number aids in counting very small particles.