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Sagot :
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]
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]
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