Question

The average mass of one gold atom in a sample of naturally occurring gold is 3.27$\times {10^{ - 22}}$ g. Calculate the molar mass of gold.

Answer 1

We simply know that molar mass is weight of the substance multiplied by the number of atoms and every mole or gram equivalent contains equal number of atoms that is 6.022$\times {10^{23}}$.

Complete answer:

From Avogadro’s law we understand that equal volumes of all gases contain equal numbers of molecules under similar conditions. Now since one mole of molecules of all gases contain the same number (6.022$\times {10^{23}}$ ) of molecules, therefore they occupy the same volume under similar pressure and temperature. The mass of one mole of atoms is exactly equal to the atomic mass in grams of that element. Therefore
Molar mass of gold = 3.27$\times {10^{ - 22}}$ $\times$ ${N_A}$ (Avogadro’s number)
${M_{Ag}} = 3.27 \times {10^{ - 22}} \times 6.022 \times {10^{23}} = 196.2\;g/mole$

Hence the molar mass of gold is 196.2 g.

Additional Information: We know that one atomic mass unit is defined as exactly 1/12th mass of an atom of carbon - 12. We know experimentally that the mass of an atom carbon 12 is 1.992$\times{10^{ - 23}}$ g. The mass of another type of atom in grams can be expressed in an atomic mass unit by using this relation as a conversion factor. It follows that the number of atoms in exactly 12 gm of carbon-12 is
$\dfrac{{12}}{{1.9926 \times {{10}^{ - 23}}}} = 6.023 \times {10^{23}}$
This relationship of number of objects to the atom is also true for ions or molecules.

Note: Every mole or gram equivalent has the same number of atoms defined as Avogadro’s number. It is important to know that the question revolves around mole and molar volume. i.e. the molar volume of all gases at STP 22.4 L and also the mass of one mole of atoms of any element is equal to the atomic mass in grams of that element.