Answer :
To determine how many gold atoms are in a 1.00 kg bar of gold, let's break down the problem step by step:
1. Convert the Mass of Gold to Grams:
The mass of the gold bar is given as 1.00 kg. Since 1 kg equals 1000 grams, the mass of the gold bar in grams is:
[tex]\[
1.00 \, \text{kg} = 1.00 \times 1000 \, \text{g} = 1000 \, \text{g}
\][/tex]
2. Find the Moles of Gold:
The molar mass of gold is approximately 197 g/mol. To find the number of moles of gold, you divide the mass of the gold by its molar mass:
[tex]\[
\text{Moles of gold} = \frac{1000 \, \text{g}}{197 \, \text{g/mol}} \approx 5.08 \, \text{mol}
\][/tex]
3. Calculate the Number of Atoms:
Avogadro's number tells us there are [tex]\(6.022 \times 10^{23}\)[/tex] atoms in one mole. To find the total number of atoms in the gold bar, multiply the number of moles by Avogadro's number:
[tex]\[
\text{Atoms of gold} = 5.08 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 3.06 \times 10^{24} \, \text{atoms}
\][/tex]
Therefore, the number of gold atoms in a 1.00 kg bar of gold is approximately [tex]\(3.06 \times 10^{24}\)[/tex] atoms. The correct choice is:
e. [tex]\(3.06 \times 10^{24}\)[/tex] atoms.
1. Convert the Mass of Gold to Grams:
The mass of the gold bar is given as 1.00 kg. Since 1 kg equals 1000 grams, the mass of the gold bar in grams is:
[tex]\[
1.00 \, \text{kg} = 1.00 \times 1000 \, \text{g} = 1000 \, \text{g}
\][/tex]
2. Find the Moles of Gold:
The molar mass of gold is approximately 197 g/mol. To find the number of moles of gold, you divide the mass of the gold by its molar mass:
[tex]\[
\text{Moles of gold} = \frac{1000 \, \text{g}}{197 \, \text{g/mol}} \approx 5.08 \, \text{mol}
\][/tex]
3. Calculate the Number of Atoms:
Avogadro's number tells us there are [tex]\(6.022 \times 10^{23}\)[/tex] atoms in one mole. To find the total number of atoms in the gold bar, multiply the number of moles by Avogadro's number:
[tex]\[
\text{Atoms of gold} = 5.08 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 3.06 \times 10^{24} \, \text{atoms}
\][/tex]
Therefore, the number of gold atoms in a 1.00 kg bar of gold is approximately [tex]\(3.06 \times 10^{24}\)[/tex] atoms. The correct choice is:
e. [tex]\(3.06 \times 10^{24}\)[/tex] atoms.
