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Chapter 2: Problem 111

Gold is present in seawater to the extent of \(0.15 \mathrm{mg} /\) ton. Assume the density of the seawater is \(1.03 \mathrm{g} / \mathrm{mL}\) and determine how many \(\mathrm{Au}\) atoms could conceivably be extracted from 0.250 L of seawater \(\left(1 \text { ton }=2.000 \times 10^{3} \mathrm{lb} ; 1 \mathrm{kg}=2.205 \mathrm{lb}\right)\)

Short Answer

Expert verified
The number of gold atoms that could conceivably be extracted from 0.250 L of seawater is calculated by using unit conversions (from volume to weight), stoichiometric calculations (from weight to moles), and Avogadro's number (from moles to number of atoms).

Step by step solution

01

Convert Liters of Seawater to Tons

seawater of 0.250L, with a density of 1.03g/mL, is first converted to grams, then to kilograms, and finally to tons. Use the relationships \(1L = 1000mL\), \(1kg = 1000g\), \(1ton = 2.000 \times 10^3 lb\), and \(1kg = 2.205lb\) to perform these conversions. Lastly, calculate the number of tons.
02

Calculate the Amount of Gold in Tons of Seawater

Take the number of tons of seawater from Step 1 and multiply it by the given concentration of gold in seawater (\(0.15 \, mg/ton\)). First, convert the result to grams since the atomic weight of gold is often given in grams/mole. Use \(1g = 10^3 mg\) for this conversion.
03

Convert the Amount of Gold to Moles

Based on the Periodic Table, the atomic weight of gold (\(\mathrm{Au}\)) is about 197 g/mole. By dividing the weight of gold (in grams) by the atomic weight of gold, you can find the number of moles present.
04

Calculate the Number of Gold Atoms

Using Avogadro's number (\(6.022 \times 10^{23} atoms/mole\)), multiply the number of moles calculated in Step 3 by Avogadro’s number to find out how many gold atoms are present in 0.250L of seawater.

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