Questions: A raindrop has a mass of 50 mg and the Pacific Ocean has a mass of (7.08 times 10^20) kg. Use this information to answer the questions below. Be sure your answers have the correct number of significant digits. What is the mass of 1 mole of raindrops? (3.0 times 10^23) g How many moles of raindrops are in the Pacific Ocean? 23.5

Solution Steps

The mass of a raindrop is given as \(50 \, \text{mg}\). To convert this to kilograms, we use the conversion factor \(1 \, \text{mg} = 10^{-6} \, \text{kg}\).

\[ 50 \, \text{mg} = 50 \times 10^{-6} \, \text{kg} = 5.0 \times 10^{-5} \, \text{kg} \]

The mass of 1 mole of raindrops is given as \(3.0 \times 10^{23} \, \text{g}\). To convert this to kilograms, we use the conversion factor \(1 \, \text{g} = 10^{-3} \, \text{kg}\).

\[ 3.0 \times 10^{23} \, \text{g} = 3.0 \times 10^{23} \times 10^{-3} \, \text{kg} = 3.0 \times 10^{20} \, \text{kg} \]

The mass of the Pacific Ocean is given as \(7.08 \times 10^{20} \, \text{kg}\). We are given that there are 23.5 moles of raindrops in the Pacific Ocean.

To find the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{Mass of the Pacific Ocean}}{\text{Mass of 1 mole of raindrops}} \]

Substituting the given values:

\[ \text{Number of moles} = \frac{7.08 \times 10^{20} \, \text{kg}}{3.0 \times 10^{20} \, \text{kg}} = 23.6 \]

Final Answer