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So I just started chem 101 and I'm not sure how to solve this problem. This is a problem from the dimensional analysis section of our book. It seems like the question wants me to get mass purely from density? The book never talked about that. It feels like I need more information to solve this problem.

Anyway here's the problem:

A substance known as aerogel has one of the lowest known densities of any solid. Around 2004, NASA used aerogel to obtain interstellar dust from the tail of a comet. How many pounds of aerogel are in a cubic foot? The density of aerogel is 3.0 mg/cc. Do not enter “pounds” as part of your answer. Do not use scientific notation. Report your answer to two significant figures.

I'm not looking to be given the answer. I want to know how to solve this.

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  • $\begingroup$ Hmm, I thought NASA already used metric system at that time. $\endgroup$ – andselisk Jan 10 '18 at 21:54
  • $\begingroup$ NASA did, but the book doesn't. $\endgroup$ – Ivan Neretin Jan 10 '18 at 22:00
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The question is poorly-worded: if you are asked to report your answer as "There are X pounds of aerogel in a cubic foot of aerogel," you necessarily have to use the word "pounds."

In any event, density is mass per unit volume; thus, you need to convert milligrams to pounds and cubic centimeters to cubic feet, and that's your answer (spoiler alert):

$$3.0\,{\mathrm{mg}\over\mathrm{cm}^3}\times\left({2.20462\times10^{-6}\,\mathrm{lb}\over\mathrm{mg}}\right)\times\left({1\,\mathrm{cm}^3\over 3.53147\times 10^{-5}\,\mathrm{ft}^3}\right) = 0.19\,{\mathrm{lb}\over\mathrm{ft}^3}$$

or

"There are 0.19 pounds of aerogel in one cubic foot of aerogel."

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    $\begingroup$ Thank you! And this is a question on the web that will only accept numbers, so the answer I have to give is just "0.19". $\endgroup$ – Haruku Jan 10 '18 at 22:27

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