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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 $1.5 \times 10^{21}$ L. Calculate the total amount of gold (in grams) that is present in seawater, and the worth of the gold in dollars (see Problem 1.82 ). With so much gold out there, why hasn't someone become rich by mining gold from the ocean?

$$2.0 \times 10^{14}$$

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

Carleton College

University of Central Florida

University of Kentucky

University of Toronto

Lectures

02:29

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications.

04:42

In chemistry and physics, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles and objects that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (known as phases) that are defined by various physical properties, such as state of matter, phase, shape, and density. The Standard Model of particle physics and the general theory of relativity describe fundamental particles and the fundamental forces acting between them that control the structure and dynamics of matter.

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A 1.0 -mL volume of seawat…

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Gold is found in seawater …

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Gold occurs in seawater at…

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Gold in the Ocean About $6…

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Gold is present in seawate…

Hi. So this question here is a unit conversion question. They tell you how much gold is in a one millimetre volume of seawater, which is 4.0 times 10 to the negative, 12 grams of gold. And then they tell you the volume of the ocean, which is 1.5 times 10 to 21 leaders. And they want you to tell calculate the total amount of gold in the ocean in grams that is present. And it's worth in dollars. And for the value of the gold per weight, we look at problem 1.82 which says that assume gold costs $948 per outs. So we're gonna also have to convert our grams two ounces to get that value. Okay, so the first part of this is we want to find how much gold there is in the ocean. Okay, so we have four 0.0 times 10 to the nega, 12 grams per familiar, just one millimetre. So we can just use one there. And then, um, we want to convert this to the bottom part. Two leaders won't know how much it is per leader. So when I put no leaders on the top, right? So we can cancel the unit. So 1000 milliliters per leader. And this way, we'll get grams per leader, right? And then we can just multiply this by the volume of the ocean, which they give us and leaders. It's 1.5 times 10 to the 21 leaders. Okay? And this will equal our total amount of, um, gold in the ocean in grams. So 4.0 times 10 to the negative, 12 times, 1000 times 1.5 times 10 to the 21 she should get 6.0 times 10 to the 12 grams of gold. Okay, so that's the first part of the answer. Um, and then now you want to convert this into ounces so that we can find the total value. Right? So it's convert this ounces. The conversion factor from grams two outs is one gram equals 0.3 53 ounces. You could just look that up on Google. So let me do that real quick to this unit conversion Ground of Gold times zero point 0353 houses over one ground. It's of course, cancel out, and then we multiply this by number the top here, get to 0.1 times 10 to the 11th. Oh, announces. Okay. And then we just take our value from problem one way to which is 9 $48 per ounce. And then we could just multiply those together and you should get the amount of amount of, um, how much all the gold in the ocean is worth. As you can see, it's gonna be a huge number dollars per ounce. It will be very large number. You couldn't one times 10 to the 11th time 9 48 and you should get 2.0 times 10 to the 14th. We're rounding to 266 year Just why it's 2.0 dollars. Okay, so very, very large number. Um, and last part, this question is asking, Why hasn't some become rich by mining all the gold from the ocean? Well, that's very, very, very difficult. You can have to go through all the water and have machinery to kind of cycle through and purify all the water in the ocean to get all of it. So it is, of course, a very time consuming and probably not very cost efficient. Um, adventure, our endeavor. I mean, so that's probably reason why I hope this was helpful and allowed you to understand you two conversions a little better And kisum, maybe some, uh, real life applications, So thanks for listening.

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