Question

a raindrop has a mass of 50. mg and the pacific ocean has a mass of 7.08 × 10²⁰ 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? round your answer to 2 significant digits. how many moles of raindrops are in the pacific ocean? round your answer to 2 significant digits.

Explanation:

Step1: Calculate the mass of 1 mole of raindrops

• We know that 1 mole contains \(6.022\times 10^{23}\) entities.
• The mass of one raindrop \(m = 50\space mg=50\times10^{- 3}\space g\)
• The mass of 1 mole of raindrops \(M=(6.022\times 10^{23})\times(50\times 10^{-3}\space g)\)

$$M = 6.022\times50\times10^{20}\space g=3.011\times 10^{22}\space g\approx3.0\times 10^{22}\space g$$

(rounded to 2 significant digits)

Step2: Calculate the number of moles of raindrops in the Pacific Ocean

• The mass of the Pacific Ocean \(m_{ocean}=7.08\times 10^{20}\space kg = 7.08\times 10^{23}\space g\)
• Let the number of moles of raindrops in the ocean be \(n\)
• Using the formula \(n=\frac{m_{ocean}}{M}\) (where \(M\) is the mass of 1 mole of raindrops)
• Substitute \(M = 3.0\times 10^{22}\space g\) and \(m_{ocean}=7.08\times 10^{23}\space g\)

$$n=\frac{7.08\times 10^{23}\space g}{3.0\times 10^{22}\space g}=23.6\approx24$$

(rounded to 2 significant digits)

Answer:

The mass of 1 mole of raindrops is \(3.0\times 10^{22}\space g\) and the number of moles of raindrops in the Pacific Ocean is \(24\)