To determine the number of moles of raindrops in the Pacific Ocean, we need to perform a few conversions and calculations. Here’s how we can approach the problem step-by-step:
1. Convert the mass of a raindrop from milligrams (mg) to kilograms (kg):
- Given: The mass of a single raindrop is 50 mg.
- Conversion: [tex]\(1 \text{ mg} = 1 \times 10^{-6} \text{ kg}\)[/tex].
So, the mass of one raindrop in kilograms is:
[tex]\[
50 \, \text{mg} \times 1 \times 10^{-6} \, \text{kg/mg} = 5 \times 10^{-5} \, \text{kg}
\][/tex]
2. Given mass of the Pacific Ocean:
- The mass of the Pacific Ocean is [tex]\(7.08 \times 10^{20} \, \text{kg}\)[/tex].
3. Calculate the number of raindrops in the Pacific Ocean:
- The number of raindrops can be found by dividing the total mass of the ocean by the mass of one raindrop.
[tex]\[
\text{Number of raindrops} = \frac{\text{Mass of the Pacific Ocean}}{\text{Mass of one raindrop}} = \frac{7.08 \times 10^{20} \, \text{kg}}{5 \times 10^{-5} \, \text{kg}} = 1.416 \times 10^{25}
\][/tex]
4. Round the answer to 2 significant digits:
- The number already presented is [tex]\(1.416 \times 10^{25}\)[/tex]. For 2 significant digits, it rounds to:
[tex]\[
1.42 \times 10^{25}
\][/tex]
Therefore, the number of moles of raindrops in the Pacific Ocean is [tex]\(1.42 \times 10^{25}\)[/tex].
