Question

If you are given $2.13 \times {10^{24}}$ atoms $Au$, how do you determine the moles in the sample and the mass of the sample?

Answer 1

Hint:In order to solve this question we must first divide the given number of atoms by the Avogadro's number to obtain the number of moles in the sample and then we can multiply this number which is the number of moles of gold obtained in the previous step by the molar mass of gold to determine the mass of the sample.

Complete step-by-step answer: Now as given in the question first we have to find out the number of moles in the sample for that we first have to divide the number of atoms which is given in the question by avogadro’s number.
As we know the Avogadro’s number is \[6.022 \times {10^{23}}\]
The equation is given as
$Moles{\text{ of gold atom = }}\dfrac{{2.13 \times {{10}^{24}}gold{\text{ atoms}}}}{{6.022 \times {{10}^{23}}gold{\text{ atoms}} \cdot mo{l^{ - 1}}}} = 3.5mol$
Then to find out the mass of the sample we multiply the number of moles which is we got above with the molar mass of gold which is $197g/mol$
$3.5mol \times 197g/mol = 700g$
Therefore the moles in the sample is $3.5mol$ and the mass of the sample is $700g$

Note:We must note that one mole is equal to \[6.022 \times {10^{23}}\] molecular entities which is commonly known as the Avogadro’s number, and each element has a different molar mass which depends on the weight of \[6.022 \times {10^{23}}\] of its atoms which is one mole. The molar mass of any element which is also known as the mass of a mole of a substance can also be determined from the atomic mass of the element on the periodic table.