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Chapter 18: Problem 42

Platinum is found in seawater at very low levels, about 0.23 ppt (parts per trillion) by mass. How much platinum can be found in the entire ocean \(\left(1.3 \times 10^{21} \mathrm{~L}\right)\) ? Assume the density of seawater is \(1.03 \mathrm{~g} / \mathrm{mL}\). Estimate the price of the following amount of platinum: \(\$ 1,600\) per troy ounce.

Short Answer

Expert verified
The estimated price of the platinum in the entire ocean is approximately \( \$ 15.843\) trillion.

Step by step solution

01

Calculate the mass of the seawater

To find the mass of the seawater, we need to use the formula mass = volume * density. We are given the volume of the ocean as \(1.3\times10^{21}\mathrm{~L}\) and the density of seawater as \(1.03\mathrm{~g/mL}\). First, convert the volume of the ocean to milliliters (1 L = 1000 mL): \(1.3\times10^{21}\mathrm{~L} \times 1000 \mathrm{~mL/L} = 1.3\times10^{24}\mathrm{~mL}\) Now we can find the mass of the seawater by multiplying the volume by the density: \(1.3\times10^{24}\mathrm{~mL} \times 1.03 \mathrm{~g/mL} = 1.339\times10^{24} \mathrm{~g}\)
02

Calculate the mass of platinum in the entire ocean

We are given the concentration of platinum in seawater as 0.23 ppt (parts per trillion). To find the mass of platinum, we need to multiply the mass of the seawater by the ratio of platinum to seawater: \((1.339\times10^{24}\,\mathrm{g})\times(0.23 \,\mathrm{ppt}) = (1.339\times10^{24}\,\mathrm{g})\times(0.23\times 10^{-12})\) \(= 3.0797\times10^{11}\,\mathrm{g\, of\, platinum}\)
03

Convert the mass of platinum to troy ounces

Now, we need to convert the mass of platinum from grams to troy ounces. There are approximately 31.1035 grams in a troy ounce, so: \((3.0797\times10^{11}\,\mathrm{g})\times\dfrac{1\,\mathrm{troy\, ounce}}{31.1035\,\mathrm{g}} = 9.902\times10^{9}\,\mathrm{troy\,ounces\,of\,platinum}\)
04

Estimate the price of the platinum

To estimate the price of the platinum, we need to multiply the amount of platinum in troy ounces by the price per troy ounce. We are given the price per troy ounce as \( \$ 1,600\), so: \((9.902\times10^{9}\,\mathrm{troy\, ounces})\times(\$1,600/\mathrm{troy\,ounce}) = \$15.843\times10^{12}\) So, the estimated price of the platinum in the entire ocean is approximately \( \$ 15.843\) trillion.

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