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Chapter 1: Problem 62

A 1.0 -mL volume of seawater contains about \(4.0 \times\) \(10^{-12} \mathrm{~g}\) of gold. The total volume of ocean water is \(1.5 \times 10^{21} \mathrm{~L} .\) Calculate the total amount of gold in grams that is present in seawater and its worth in dollars, assuming that the price of gold is \(\$ 350\) an ounce. With so much gold out there, why hasn't someone become rich by mining gold from the ocean?

Short Answer

Expert verified
The total amount of gold in the ocean's seawater is around \(6.0 \times 10^{12}\) grams, which is approximately \(2.11 \times 10^{11}\) ounces. If sold at a rate of $350 per ounce, that would correspond to approximately \(7.39 \times 10^{13}\) dollars. However, this gold is not mined due to its extremely low concentration and the high cost and environmental impact of such an operation.

Step by step solution

01

Calculate total gold in the ocean

Find the total amount of gold in the ocean by multiplying the volume of water in the ocean by the amount of gold in each liter of seawater. Now, given that each 1.0 mL of seawater contains \(4.0 \times 10^{-12}\) g of gold, each liter (which is 1000 mL), therefore, contains \(4.0 \times 10^{-12}\) g/mL x 1000 mL/L = \(4.0 \times 10^{-9}\) g of gold. The total amount of gold in the ocean is therefore: \(1.5 \times 10^{21}\) L x \(4.0 \times 10^{-9}\) g/L = \(6.0 \times 10^{12}\) g.
02

Convert gold amount from grams to ounces

We now need to convert the amount of gold from grams to ounces since the price of gold is given per ounce. The conversion factor to remember is that there are approximately 28.35 grams in one ounce. To convert our value of gold in grams to ounces, we divide by 28.35. Therefore, \(6.0 \times 10^{12}\) g / 28.35 g/oz = \(2.11 \times 10^{11}\) ounces.
03

Calculate worth of gold in dollars

To find the worth of the gold in dollars, simply multiply the total number of ounces by the price per ounce. Therefore, \(2.11 \times 10^{11}\) ounces x 350 dollars/ounce = \(7.39 \times 10^{13}\) dollars.
04

Reason why gold isn't typically mined from the ocean

Even though the computation has shown that there is a vast amount of gold in the ocean, the concentration of gold in seawater is extremely low (about 4 parts per trillion). Mining gold from the ocean would be very difficult and costly because it is dispersed throughout the ocean and not found in large quantities in one place. Also, the environmental impact of such a process could be damaging. Therefore, current technology and economics make it impractical.

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Most popular questions from this chapter

Write the numbers for these prefixes: (a) mega-,(b) kilo-, (c) deci-, (d) centi-, (e) milli-, (f) micro-, (g) nano-, (h) pico-.

Carry out these conversions: (a) 242 lb to milligrams, (b) \(68.3 \mathrm{~cm}^{3}\) to cubic meters.

Convert these to nonscientific notation: (a) \(1.52 \times\) \(10^{4},\) (b) \(7.78 \times 10^{-8}\)

A 250 -mL glass bottle was filled with 242 mL of water at \(20^{\circ} \mathrm{C}\) and tightly capped. It was then left outdoors overnight, where the average temperature was \(-5^{\circ} \mathrm{C}\). Predict what would happen. The density of water at \(20^{\circ} \mathrm{C}\) is \(0.998 \mathrm{~g} / \mathrm{cm}^{3}\) and that of ice at \(-5^{\circ} \mathrm{C}\) is \(0.916 \mathrm{~g} / \mathrm{cm}^{3}\)

Give an example of a homogeneous mixture and an example of a heterogeneous mixture.
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