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Chemistry (including Biochemistry)/Conversions with Two Factors

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Question
Hi,

I am having trouble figuring problems with two factors. I understand how to do individual conversions, but that is all. Here is an example of the type of problems I am trying to do:

The radius of a strontium atom is 215 pm. How many strontium atoms would have to be laid side by side to span a distance of 2.22 mm?

I know how to change pm to mm, but I don't understand what to do in this case because it  is 2.22mm rather than just one. Would I multiply by 2.22? Also, since the radius is 215pm, do I need to multiply it by two to get the diameter.

Thanks for any help you can give.

Answer
Setting up the conversion is similar, you just need to use 215 and 2.22 as scalars:

First lets get the radius into meters

215 pm * 1 m / 10^12 pm = 2.15 * 10^-10 m

then, because radius is half of the diameter, we need to convert to the total width (diameter)

2.15 * 10^-10 m/radius * 2 radius/diameter = 4.30 * 10^-10 m/diameter

Now lets convert the distance 2.22 mm into meters

2.22 mm * 1 m / 10^3 mm = 2.22 * 10^-3 m

Since we are asked how many diameters are in this distance:

distance/diameter -OR-

2.22 * 10^-3 m / 4.30 * 10^-10 m/diameter = 5.16219 * 10^6 diameters

remembering that each diameter is one atom and using sig figs, this puts us at

5.16 * 10^6 atoms

or about 5 million

I hope this walk through helps!

Take care!  

Chemistry (including Biochemistry)

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Dr. Jeffery Raymond

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Materials chemistry. Materials science. Spectroscopy. Polymer science. Physical Chemistry. General Physics. Technical writing. General Applied Mathematics. Nanomaterials. Optoelectronic Behavior. Science Policy.

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Teaching: General Inorganic Chemistry I & II, Organic Chemistry I & II, Physical Chemistry I, Polymeric Materials, General Physics I, Calculus I & II
My prior experience includes the United States Army and three years as a development chemist in industry. Currently I am the Assistant Director of the Laboratory for Synthetic Biological Interactions. All told, 13 years of experience in research, development and science education.

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Texas A&M University, American Chemical Society, POLY-ACS, SPIE

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Journal of the American Chemical Society, Nanoletters, Journal of Physical Chemistry C, Journal of Physical Chemistry Letters, Ultramicroscopy Proceedings of SPIE, Proceedings of MRS, Polymer News, Chemical and Engineering News, Nano Letters, Small, Chemistry.org, Angewandte

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PhD Macromolecular Science and Engineering (Photophysics/Nanomaterials Concentration), MS Materials Science, BS Chemistry and Physics, Graduate Certificate in Science Policy, AAS Chemical Technology, AAS Engineering Technology

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