To find out how many carbon (C) atoms are present in 0.400 moles of sucrose ([tex]$C_{12}H_{22}O_{11}$[/tex]), follow these steps:
1. Determine the number of carbon atoms in one molecule of sucrose:
Sucrose has a chemical formula of [tex]$C_{12}H_{22}O_{11}$[/tex], which means each molecule of sucrose contains 12 carbon atoms.
2. Use Avogadro's number to find out how many molecules are in 0.400 moles:
Avogadro's number is [tex]\(6.02 \times 10^{23}\)[/tex], which represents the number of molecules in one mole of any substance.
3. Calculate the total number of molecules in 0.400 moles of sucrose:
[tex]\[
\text{Number of molecules} = 0.400 \text{ moles} \times 6.02 \times 10^{23} \text{ molecules/mole}
\][/tex]
4. Now, calculate the total number of carbon atoms:
Since each molecule of sucrose has 12 carbon atoms, multiply the number of molecules by 12.
[tex]\[
\text{Number of carbon atoms} = \text{Number of molecules} \times 12
\][/tex]
Plugging in the number of molecules we calculated:
[tex]\[
\text{Number of carbon atoms} = 0.400 \, \text{moles} \times 6.02 \times 10^{23} \, \text{molecules/mole} \times 12
\][/tex]
5. Simplify the expression:
[tex]\[
\text{Number of carbon atoms} = 0.400 \times 6.02 \times 10^{23} \times 12
\][/tex]
[tex]\[
\text{Number of carbon atoms} = 2.89 \times 10^{24}
\][/tex]
Hence, there are [tex]\(2.89 \times 10^{24}\)[/tex] carbon atoms in 0.400 moles of sucrose.
Therefore, the correct answer is:
[tex]\[ 2.89 \times 10^{24} C \text{ atoms} \][/tex]
