Introductory Chemistry

Exploring the chemistry of the Earth's crust.
Answer key.

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This is the answer sheet for a worksheet handed out in class. The questions are based on a graph of the abundance of the elements in the Earth's crust. The two page handout has the questions on page 1 and the graph on page 2. The questions are available as the file crust.doc. The spreadsheet, containing not only the graph that was handed out but also the table on which the graph is based, is available here as the Excel file crust.xls.

Answers

1. The "whole" is 1,000,000 (one million) ppm (parts per million). Divide that into 100 portions, and each would be 10,000 ppm (which is 1%).

Given the scale of the graph, it makes little difference whether you divide by 100 (approximate number of elements), by 85 (the actual number of elements shown on the graph), or by 118 (the total number of known elements). And remember that all the elements not shown have abundance that is essentially zero.

2. There is a general downward trend as you go from left to right on the graph. That is, lighter elements are more abundant than heavier elements.

Other observations? (Remember, the question was open-ended. Different people may reasonably see different things in the graph. The point I made above is one that we will explore further below; I hope you agree that it is a valid point. But other answers may also be quite reasonable, and I am happy to discuss them with you.)

3. Well, it is up to you how many you include as "very abundant". The top two elements alone account for 75% of the mass of the Earth's crust. Perhaps you have heard that silicate minerals -- consisting of Si and O -- are major parts of the crust. If you add together the top eight elements -- the only ones above that 1% line discussed in #1 -- you find that they account for 982,000 ppm -- which is 98.2%. That is, all the remaining elements (77 of them shown here) total less than 2% of the Earth's crust. Note that the eight most abundant elements are all "lighter elements", with Z<30.

4. a. For example, imagine that we had 36 g of H and 12 g of C, corresponding to the given mass ratio of 3:1. That is 36 moles of H (1 g/mol) and 1 mole of C (12 g/mol). So the mole ratio is 36:1 in favor of H.

Should this calculation be in terms of H or of H2? The question is about the element hydrogen, not the specific chemical H2. The H may be in any form. So using H is appropriate in this context. Question #5 may help clarify this. (In the context here, no particular harm was done if you did calculate H2 rather than H. But you should be clear in your labeling... If you calculated moles of H2, you should label your answer in moles of H2.)

b. As part a illustrates, for lighter elements there are more moles per unit mass. Lighter elements are more common on a mass basis; they are even more common on a mole basis. If you re-plotted the data on a mole basis, the trend line would be steeper. Part a illustrates this with one specific example. If you want, try it for a few more elements, chosen over the range of abundances.

5. Although H may not have made your list of "most abundant" elements (#3), it is the 10th most abundant element in the crust (1520 ppm). He is much rarer (0.008 ppm). Why? Well, both are gases in the free elemental state. Gases are not a major part of the Earth's crust. But H can occur in combined forms, such as water, which is not a gas. He is a noble gas, and has no combined or non-gaseous forms.

6. If you scan the bottom of the graph, elements 2, 10, 36, 54, 77 & 88 stand out as being rare compared to elements of similar atomic numbers.

I think you can read the atomic numbers for each point on the graph, with a little care. But this is a case where you may find it helpful to use the table.

The first four of these are noble gases; see #5. Interestingly, Ar is the most abundant of the noble gases; but if you look at the graph, you do see that it is somewhat uncommon compared to elements of similar atomic number. The final noble gas, Rn, is so rare that it is simply listed as "trace".

The final two rare elements shown here are iridium and radium. Ra is radioactive, with a short lifetime; all Ra on Earth is of recent origin, coming from decay of heavier radioactive elements, such as U, in the crust. (There are other radioactive elements of extremely low abundance, not shown on the graph.) Ir stands out as the rarest non-radioactive non-gaseous element.

Other comments?

7. Let us know your comments on this one.


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Last update: August 28, 2012