A raindrop has a mass of [tex]50 \, \text{mg}[/tex] and the Pacific Ocean has a mass of [tex]7.08 \times 10^{20} \, \text{kg}[/tex].

Use this information to answer the questions below. Be sure your answers have the correct number of significant digits.

\begin{tabular}{|l|l|}
\hline
What is the mass of 1 mole of raindrops? & [tex]$\square \, \text{g}$[/tex] \\
\hline
How many moles of raindrops are in the Pacific Ocean? & [tex]$\square$[/tex] \\
\hline
\end{tabular}



Answer :

To solve these questions, let's break down the problem step by step.

1. Convert the mass of a raindrop to grams:
- Given: [tex]\( 50 \text{ mg} \)[/tex]
- There are [tex]\( 1000 \text{ mg} \)[/tex] in a gram.
- Conversion: [tex]\( \text{mass of raindrop in grams} = \frac{50 \text{ mg}}{1000} = 0.05 \text{ g} \)[/tex]

2. Convert the mass of the Pacific Ocean to grams:
- Given: [tex]\( 7.08 \times 10^{20} \text{ kg} \)[/tex]
- There are [tex]\( 1000 \text{ g} \)[/tex] in a kilogram.
- Conversion: [tex]\( \text{mass of Pacific Ocean in grams} = 7.08 \times 10^{20} \text{ kg} \times 1000 \text{ g/kg} = 7.08 \times 10^{23} \text{ g} \)[/tex]

3. Calculate the mass of 1 mole of raindrops:
- Avogadro's number (the number of entities in a mole) is [tex]\( 6.022 \times 10^{23} \)[/tex].
- Using this, the mass of 1 mole of raindrops is calculated as:
[tex]\[ \text{mass of 1 mole of raindrops} = 0.05 \text{ g} \times 6.022 \times 10^{23} = 3.011 \times 10^{22} \text{ g} \][/tex]

4. Calculate the number of moles of raindrops in the Pacific Ocean:
- We now use the mass of the Pacific Ocean (in grams) and the mass of 1 mole of raindrops to find the number of moles:
[tex]\[ \text{number of moles} = \frac{\text{mass of Pacific Ocean in grams}}{\text{mass of 1 mole of raindrops}} \][/tex]
[tex]\[ = \frac{7.08 \times 10^{23} \text{ g}}{3.011 \times 10^{22} \text{ g}} \approx 23.514 \][/tex]

Given these calculations, we have:

[tex]\[ \begin{array}{|l|l|} \hline \text{What is the mass of 1 mole of raindrops?} & 3.011 \times 10^{22} \text{ g} \\ \hline \text{How many moles of raindrops are in the Pacific Ocean?} & 23.514 \\ \hline \end{array} \][/tex]

Remember that significant digits are important:
- The mass of a raindrop (50 mg) has 2 significant digits.
- The mass of the Pacific Ocean (7.08 × 10²⁰ kg) has 3 significant digits.
- Therefore, the final answers should be rounded to match the number of significant digits in the given data.

Thus, if strictly following significant digits:
- Mass of 1 mole of raindrops: [tex]\( 3.01 \times 10^{22} \text{ g} \)[/tex]
- Moles of raindrops in the Pacific: [tex]\( 23.5 \)[/tex]

So, the refined answers would be:

[tex]\[ \begin{array}{|l|l|} \hline \text{What is the mass of 1 mole of raindrops?} & 3.01 \times 10^{22} \text{ g} \\ \hline \text{How many moles of raindrops are in the Pacific Ocean?} & 23.5 \\ \hline \end{array} \][/tex]