Answer :
Sure, I'd be happy to help you with this! Let's break down the process of finding the number of nickel (Ni) atoms in a 99.7 gram sample of elemental nickel.
### Step 1: Identify the Given Information
- Mass of nickel (Ni) sample: [tex]\( 99.7 \)[/tex] grams
- Molar mass of nickel (Ni): [tex]\( 58.69 \)[/tex] grams per mole (g/mol)
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] atoms per mole
### Step 2: Calculate the Number of Moles of Nickel
The number of moles can be calculated using the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Mass of the sample}}{\text{Molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Number of moles of Ni} = \frac{99.7 \, \text{g}}{58.69 \, \text{g/mol}} \approx 1.6988
\][/tex]
### Step 3: Calculate the Number of Atoms
To find the number of atoms, we use Avogadro's number, which is the number of atoms in one mole of a substance. Multiply the number of moles of nickel by Avogadro's number:
[tex]\[
\text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number}
\][/tex]
Substituting the values:
[tex]\[
\text{Number of atoms} \approx 1.6988 \times 6.022 \times 10^{23} \approx 1.02299 \times 10^{24}
\][/tex]
### Final Answer
There are approximately [tex]\( 1.02299 \times 10^{24} \)[/tex] nickel (Ni) atoms in a 99.7 gram sample of elemental nickel.
### Step 1: Identify the Given Information
- Mass of nickel (Ni) sample: [tex]\( 99.7 \)[/tex] grams
- Molar mass of nickel (Ni): [tex]\( 58.69 \)[/tex] grams per mole (g/mol)
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] atoms per mole
### Step 2: Calculate the Number of Moles of Nickel
The number of moles can be calculated using the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Mass of the sample}}{\text{Molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Number of moles of Ni} = \frac{99.7 \, \text{g}}{58.69 \, \text{g/mol}} \approx 1.6988
\][/tex]
### Step 3: Calculate the Number of Atoms
To find the number of atoms, we use Avogadro's number, which is the number of atoms in one mole of a substance. Multiply the number of moles of nickel by Avogadro's number:
[tex]\[
\text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number}
\][/tex]
Substituting the values:
[tex]\[
\text{Number of atoms} \approx 1.6988 \times 6.022 \times 10^{23} \approx 1.02299 \times 10^{24}
\][/tex]
### Final Answer
There are approximately [tex]\( 1.02299 \times 10^{24} \)[/tex] nickel (Ni) atoms in a 99.7 gram sample of elemental nickel.
