Question

39.4 kg of gold was recovered from a smuggler. The number of atoms of gold recovered are:

Answer 1

heyA!

here is your answer...

The molar mass of gold = 196.97 g
Number of atoms = given mass / molar mass × 6.022 x 1023 atoms
⇒39.4 g /196.97 g ​× 6.022 x 1023 atoms = 1.2 × 10^23 atoms of gold.

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Answer 2

Answer : The number of atoms of gold recovered are $1.2044\times 10^{26}$.

Solution : Given,

Mass of gold = 39.4 Kg = $39.4\times 10^3$       (1Kg = 1000g)

Molar mass of gold = 197 g/mole

First we have to calculate the moles of gold.

$\text{ Moles of gold}=\frac{\text{ Mass of gold}}{\text{ Molar mass of gold}}=\frac{39.4\times 10^3g}{197g/mole}=0.2\times 10^3moles$

As, 1 mole contains $6.022\times 10^{23}$ atoms

$0.2\times 10^3moles$ contains $(0.2\times 10^3)\times (6.022\times 10^{23})=1.2044\times 10^{26}$ atoms

Therefore, the number of atoms of gold recovered are $1.2044\times 10^{26}$.