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Let's start by setting up an equation of what is going on chemically. Sucrose

is a sugar dimer of 1 fructose and 1 glucose molecule, so:

1 Sucrose --> 1 Glucose + 1 Fructose

So, what we need to do from here is calculate how many moles of glucose would

be needed to make 1 microgram (ug). The Atomic Mass of glucose is 180.16 g/mol,

so 1ug = .000001 g. 0.000001g divided by 180.16 g/mol = 5.55 X 10^9 moles.

Avogadro's number is 6.02214 X 10^23 and represents how many molecules are in 1

mole of a substance. Multiply this number by the moles of glucose and we should

get 3.34 X 10^15 molecules in 1 microgram of glucose.

Since the decomposition of 1 molecule of sucrose liberates 1 molecule of glucose,

we do not have to take into account stoichiometric ratios.

So, we need 3.34X 10^15 molecules of sucrose to decompose to get the same

number of molecules of glucose. If we divide this by 1 million, we get

3.34 x 10^9. This is the number of seconds that would be needed for the

decomposition to take place. Divide that by 60 we get 5.57 X 10^7 minutes,

divide by 60 again and we get 9.28 X 10^5 hours, divide by 24 and we get 38,684

days and finally divide by 365 to get just under 106 years!

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