Sure! Let's break down the steps to find out how many atoms of carbon are in a diamond with a mass of 0.568 grams.
1. Determine the molar mass of carbon:
The molar mass of carbon (C) is 12.01 grams per mole.
2. Calculate the number of moles of carbon:
To find the number of moles of carbon in 0.568 grams of diamond, we use the formula:
[tex]\[
\text{moles of carbon} = \frac{\text{mass of diamond}}{\text{molar mass of carbon}}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of carbon} = \frac{0.568 \text{ g}}{12.01 \text{ g/mol}} \approx 0.047293921731890086 \text{ moles}
\][/tex]
3. Use Avogadro's number to find the number of atoms:
Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex], which is the number of atoms in one mole of a substance.
To calculate the number of atoms in the given moles of carbon, we use the formula:
[tex]\[
\text{atoms of carbon} = \text{moles of carbon} \times \text{Avogadro's number}
\][/tex]
Substituting the calculated moles of carbon and Avogadro's number:
[tex]\[
\text{atoms of carbon} = 0.047293921731890086 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \approx 2.8480399666944212 \times 10^{22} \text{ atoms}
\][/tex]
Therefore, in a diamond with a mass of 0.568 grams, there are approximately [tex]\( 2.848 \times 10^{22} \)[/tex] atoms of carbon.
