One carat is .20g, how many gold atoms are in one carat of gold?

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Answer 1 · 2018-04-12T14:11:36

$6.11 \times 10^{20} atoms of gold$ $6.11 xx 10^20" atoms of gold"$

$number of moles = \frac{mass}{relative formula mass}$ $"number of moles" = "mass" / "relative formula mass"$
$n = \frac{m}{M_{r}}$ $n = m/M_r$

Mass = $0.20$ $0.20$

$M_{r}$ $M_r$ of gold = $197$ $197$

$n = \frac{0.20}{197} = \frac{1}{985}$ $n = 0.20/197 = 1/985$ moles

$1$ $1$ mole = $6.02 \times 10^{23}$ $6.02 xx 10^23$ atoms

$\frac{1}{985}$ $1/985$ moles = $\frac{1}{985} \times 6.02 \times 10^{23}$ $1/985 xx 6.02 xx 10^23$ atoms

$= 6.1116... xx 10^20$ atoms

$color(red)(~~ 6.11 xx 10^20" atoms of gold")$

(3 significant figures)