|MadSci Network: Chemistry|
This is similar to some other questions I've answered previously about salt and water, so I'll start with the same basic calculations. Common table sugar is sucrose, which has a molecular mass of 342.3 grams per mole. Assuming you're using granulated sugar, one grain of sugar has a mass around 0.625 mg (5/8 of a milligram), as measured by the analytical balance in our lab. So, one grain is 1.82588 x 10-6 moles or around 1.8 µM (micromoles). As you said, Avogadro's Number is 6.022 x 1023 molecules per mole, so a single grain of sugar contains 1.09954 x 1018 molecules of sucrose, or 1.1 quintillion molecules per grain of sugar (in American terms).
Also, one cubic centimeter of sucrose (again using the analytical balance) has a mass around 950 mg, which is a little over 1,500 grains. I don't know how big your sugar jar is, but if it holds about half of a liter (just over a pound of sugar), that would be around 750,000 grains - for demonstration purposes, you could use a little more sugar and call it a million grains. So, the number of molecules of sucrose in a single grain of sugar is the same as the number of sugar grains in a million million jars of sugar. (That's one trillion US or one billion UK.) I like the concept of explaining molecules this way, and for younger students, I think this would be completely acceptable, since you would be conveying the basic idea of many tiny things making up one unit; however, for older students with better grasps of large numbers, I think the idea of millions of millions of jars of sugargrains in a single tiny crystal is more staggering and provocative.
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