To determine how many moles of sucrose are present in [tex]\(5.25 \times 10^{29}\)[/tex] sucrose molecules, we follow these steps:
1. Identify the given data and constants:
- Number of sucrose molecules: [tex]\(5.25 \times 10^{29}\)[/tex]
- Avogadro's number ([tex]\(N_A\)[/tex]): [tex]\(6.022 \times 10^{23}\)[/tex] molecules per mole
2. Recall the relationship between molecules and moles:
The number of moles ([tex]\(n\)[/tex]) can be calculated by dividing the number of molecules by Avogadro's number:
[tex]\[
n = \frac{\text{Number of molecules}}{N_A}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
n = \frac{5.25 \times 10^{29}}{6.022 \times 10^{23}}
\][/tex]
4. Perform the division:
Divide the coefficients:
[tex]\[
\frac{5.25}{6.022} \approx 0.8718
\][/tex]
5. Handle the exponents separately:
When dividing exponents, subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
10^{29} / 10^{23} = 10^{29-23} = 10^6
\][/tex]
6. Combine the results:
[tex]\[
n \approx 0.8718 \times 10^6
\][/tex]
7. Adjust for proper scientific notation:
Ensure the prefix is between 1 and 10:
[tex]\[
0.8718 \times 10^6 = 8.718 \times 10^5
\][/tex]
So, the number of moles of sucrose is:
[tex]\[
8.718 \times 10^5
\][/tex]
Prefix (green)
[tex]\[ 8.718 \][/tex]
Exponent (yellow)
[tex]\[ 5 \][/tex]
