To determine the number of sucrose molecules in 3.0 moles of sucrose, we need to use Avogadro's number. Avogadro's number, which is [tex]\(6.02214076 \times 10^{23}\)[/tex] molecules per mole, tells us how many molecules are present in one mole of any substance.
Here is the step-by-step process to find the number of molecules:
1. Identify the given quantity of moles:
[tex]\[
\text{Moles of sucrose} = 3.0 \, \text{moles}
\][/tex]
2. Use Avogadro's number:
[tex]\[
\text{Avogadro's number} = 6.02214076 \times 10^{23} \, \text{molecules/mole}
\][/tex]
3. Multiply the number of moles by Avogadro's number to find the number of molecules:
[tex]\[
\text{Number of molecules} = 3.0 \, \text{moles} \times 6.02214076 \times 10^{23} \, \text{molecules/mole}
\][/tex]
Substituting the values gives:
[tex]\[
\text{Number of molecules} = 3.0 \times 6.02214076 \times 10^{23}
\][/tex]
4. Perform the multiplication:
[tex]\[
3.0 \times 6.02214076 = 18.06642228 \times 10^{23}
\][/tex]
5. Express the result in scientific notation:
[tex]\[
18.06642228 \times 10^{23} = 1.806642228 \times 10^{24}
\][/tex]
Since the given data (3.0 moles) has two significant figures, we should limit our answer to two significant figures:
[tex]\[
1.8 \times 10^{24}
\][/tex]
Thus, the number of sucrose molecules in 3.0 moles of sucrose is:
[tex]\[
1.8 \times 10^{24}
\][/tex]
