How many moles of sucrose are in [tex]$5.25 \times 10^{29}$[/tex] sucrose molecules?

Enter your answer with the correct number of significant figures. The prefix should be a number between 1 and 10.

Prefix (green): [tex]$\square$[/tex]
Exponent (yellow): [tex]$\square$[/tex]



Answer :

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]
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