ANSWERS: 1
  • 4.4*10^46 Here's how I got it: The total volume of the earth's oceans is estimated at 1.3 x 10^9 cubic kilometers of liquid water. My source (http://hypertextbook.com/facts/2001/SyedQadri.shtml) gives four different scientific estimates which all agree to two significant figures. So don't expect an answer better than within one percent of actual. Let's start by assuming the oceans are pure water. The gram molecular weight of H2O is 1+1+16 = 18 grams per mole. How many grams are there? Let us calculate: Grams of ocean water = (1.3*10^9 cubic km)(10^9 cubic m / 1 cubic km)(10^6 cubic cm/1 cubic m)(1 gram of water/1 cubic cm of water) = 1.3*10^24 grams. Divide by 18 to get 7.2*10^22 moles of water. Using good ol' Avogadro's number: (6.02*10^23 molecules/mole) (7.2*10^22 moles) = 4.3*10^46 molecules of water in the oceans. Seawater, of course, has dissolved sodium chloride and other solutes including heavy metals. Let's just say for now that it's pure NaCl. At.Wt of sodium=23, chlorine=35; so 23+35 = 58 grams/mole Now it gets a little tricky. Since each molecule of sodium chloride dissolved in water is actually ionized into Na+ and Cl-, I would count each NaCl as TWO molecules, because the sodium and chlorine atoms are swimming around independently, not bound to each other. So 58 grams represents not one but two moles, making the effective gram molecular weight of salt (remember, the question is 'how many molecules?') would be 29 grams/mole. On average, seawater in the world's oceans has a salinity of ~3.5% (http://en.wikipedia.org/wiki/Seawater). So each cubic centimeter of ocean water (containing exactly one gram of water) also contains an additional .035 grams of salt, representing (.035 grams)(1 mole/29 grams) = .0012 moles of salt per cc seawater, whereas for pure water, one cubic centimeter contains 1/18 = .055 moles per cc. So the salt adds a correction factor .0012/.055 = .021 = 2.1 percent more molecules of ocean saltwater compared to pure water. So adding 2% to 4.3*10^46 bumps it up to to 4.4*10^46. There would be additional molecules of other solute species, as noted earlier. You can see, however, that the molecule count is dominated by H2Os and I doubt would change the overall figure by an appreciable amount.

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