To determine the number of molecules of sucrose in the sample, we need to analyze the relationship between the number of carbon atoms and the number of sucrose molecules.
The molecular formula of sucrose is [tex]\(C_{12}H_{22}O_{11}\)[/tex]. This indicates that each molecule of sucrose contains 12 carbon atoms.
Given:
- The sample contains [tex]\( 3.6 \times 10^{24} \)[/tex] carbon atoms.
- Each sucrose molecule contains 12 carbon atoms.
To find out how many molecules of sucrose there are, we perform the following steps:
1. Identify the total number of carbon atoms per molecule of sucrose:
[tex]\[
\text{Number of carbon atoms per molecule} = 12
\][/tex]
2. Calculate the number of sucrose molecules by dividing the total number of carbon atoms in the sample by the number of carbon atoms in one molecule of sucrose:
[tex]\[
\text{Number of sucrose molecules} = \frac{3.6 \times 10^{24} \text{ carbon atoms}}{12 \text{ carbon atoms per molecule}}
\][/tex]
3. Perform the division:
[tex]\[
\text{Number of sucrose molecules} = \frac{3.6 \times 10^{24}}{12} = 3 \times 10^{23}
\][/tex]
Hence, the number of sucrose molecules in the sample is:
[tex]\[
2.9999999999999997 \times 10^{23} \approx 3.0 \times 10^{23}
\][/tex]
Thus, the sample contains [tex]\( 3.0 \times 10^{23} \)[/tex] molecules of sucrose.
