Question

The number of gold atoms in 300mg of a gold ring of 20 -carat gold ( \[Au = 197\] : pure gold is 24 carat) are:

Answer 1

Hint: 1 Carat gold is equal to 0.2 gram gold. Therefore 20 carat gold equals 4 grams. And 24 carats is said to be pure gold.
Formula used: 1mole = atomic weight \[ = 6.023 \times {10^{23}}\] no. of atoms

Complete step by step answer:
If 24 carats is pure gold then if the number of atoms in 24 carats is calculated then calculation of no. of atoms of 20 carat will be easy.
Now at first, according to the mole concept we know 1 mole of any substance is equal to its molecular weight. And 1 mole is also equal to the Avogadro’s number of atoms i.e. \[6.023 \times {10^{23}}\] .
Therefore, 1mole = atomic weight \[ = 6.023 \times {10^{23}}\] no. of atoms
According to this it can be said that 197 gm pure gold contains \[ = 6.023 \times {10^{23}}\] number of atoms.
Now according to the question 24 carat is pure gold. Therefore, it can be said that,
197 gm 24-carat gold contains \[ = 6.023 \times {10^{23}}\] number of atoms.
 300mg is equal to \[\dfrac{{300}}{{1000}} = 0.3grm\] .
Now,0.3 grams 24-carat gold contains \[\dfrac{{6.023 \times {{10}^{23}} \times 0.3}}{{197}}\] number of atoms
 So, 0.3 grams of 24-carat gold contains \[9.172 \times {10^{20}}\] number of atoms.
Therefore, 0.3 grams 20-carat gold contains \[\dfrac{{9.172 \times {{10}^{20}} \times 20}}{{24}}\] number of atoms.
Which is equal to \[7.643 \times {10^{20}}\] number of atoms .
So , 0.3 grams of 20-carat gold contains \[7.643 \times {10^{20}}\] number of atoms.

Note:
1mole = atomic weight \[ = 6.023 \times {10^{23}}\] no. of atoms. The formula of equivalent weight is,
 \[Equivalent\,weight = \dfrac{{Molecular\,weight}}{{number\,of\,equivalent\,moles}}\] .
 For acids the number of equivalents is equal to the number of \[{H^ + }\] present in one molecule. And for bases the number of \[H{O^ - }\] groups present in one molecule. The equivalent weight of any substance cannot be greater than its molecular weight. Either the value of equivalent weight is equal or less than the molecular weight of that substance.