Answer :

Answer:

Let’s calculate the molar quantity of gold first.


(1000×g)/(196.97×g×mol^-1) = 5.077 mole


So we know that 1 mole of anything = 6.02214076×10^23 of individual objects.


So we can multiply this value by our molar quantity of gold.


5.077 × 6.02214076×10^23 = 3.057 × 10^24 atoms of gold.


Therefore, 1 kg of a gold bar has 3.057 × 10^24 atoms

Explanation:

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Rewritten by : Barada

There are approximately 3.057 *10^{25} gold atoms in 1 kg of gold, calculated by converting the mass of gold to moles and then multiplying by Avogadro's number.

To find out how many atoms there are in 1 kg of gold, we first need to know the number of moles in that mass. Gold's atomic mass is 197 u, and since 1 u = 1.66 *10^{-27} kg, we can calculate the molar mass of gold in kilograms as 197 * 1.66 * 10^{-27} kg/mol. For gold, 1 mole corresponds to 197 g (or 0.197 kg).

Now, let's convert 1 kg of gold to moles:

Number of moles = \frac{1 kg}{0.197 kg/mol} = \frac{1000 g}{197 g/mol} = 5.07614213198 moles

Next, we use Avogadro's number, which is 6.022 * 10^{23} atoms/mol, to find the total number of atoms:

Number of atoms = 5.07614213198 moles* 6.022 * 10^{23} atoms/mol = 3.057 *10^{25} atoms

So, there are approximately 3.057 * 10^{25} gold atoms in 1 kg of gold.