Question

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

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

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.

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.

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.

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.

Key concepts

Ocean Mining

Ocean mining refers to the extraction of various minerals and resources from the ocean floor. This includes metals like gold, copper, and silver, as well as resources like oil and gas. The idea of mining gold from seawater sounds intriguing because the ocean contains vast amounts of this precious metal.
However, there are challenges associated with this. The concentration of gold in seawater is incredibly low, roughly 4 parts per trillion. Hence, extracting a significant amount requires processing an enormous volume of water. Due to this dispersion, the cost and complexity of setting up operations vastly outweigh the potential benefits right now. Efficient mining methods are yet to be developed for such diluted resources. Some countries and companies are still researching potential technological advances that might make this feasible in the future.

Environmental Impact

Mining activities have the potential for significant environmental impact. When discussing ocean mining, the risk involves disturbances to marine ecosystems. Ecosystems are delicate, and operations like dredging or drilling can harm the aquatic life and habitat.
The extraction process could destroy the habitat of numerous species living near the sea bed. The introduction of foreign materials and the noise pollution from mining machinery also have detrimental effects. Sediment plumes, when particles are stirred into the water column, can impact the light penetration and hence affect the entire food web.
Due to these factors, environmental concerns present a significant barrier to mining gold from the ocean. Sustainable practices and technologies need development to mitigate these impacts before ocean mining can be pursued responsibly.

Gold Valuation

Gold valuation is crucial when considering whether mining operations are economically viable. Gold is priced per ounce, and it has sufficient value that people consider extracting it from even tiny amounts in seawater.
For example, the calculation showed that the total worth of gold in the oceans amounts to trillions of dollars. However, since the distribution of gold is so sparse, the cost of extraction remains prohibitive. The market price of gold fluctuates based on numerous factors such as demand, inflation, and geopolitical stability.
The valuation of gold is also affected by its demand in industries. It's heavily used in electronics, jewelry, and as financial security. While there is a high potential monetary return, current technological limits on mining make it unfeasible.

Seawater Chemistry

Seawater chemistry plays a pivotal role in the discussion of extracting gold from the oceans. Seawater is a complex mixture of dissolved minerals, salts, and other elements. The presence of gold in seawater is a natural result of these geochemical processes.
Seawater contains a variety of salts, primarily sodium chloride, but also includes other elements like magnesium and calcium. The dilute presence of gold, at about 4 parts per trillion, means it's dissolved at atomic levels across vast expanses. This poses a challenge since standard mining involves extracting concentrated ores, not dispersions.
Understanding the composition and distribution of elements in seawater is crucial for any attempt at resource extraction. Future advancements in chemistry, such as more efficient methods of separating and recovering precious metals, could change the viability of ocean mining.