To become familiar with Avogadro's number and the quantity of material represented by it.
The atomic weight system used by chemists is a relative system which indicates how massive an atom is relative to some arbitrary standard. Throughout history there have been three standards: hydrogen, oxygen, and now C12 . Carbon-12, C12 , the most common isotope of carbon, has arbitrarily been given a value of exactly 12. All other atoms (isotopes) are compared to C12 and assigned a value which reflects how much heavier, or lighter, they are relative to carbon-12 atoms. Therefore, since magnesium atoms are about twice as heavy as C12, they are given a value of about 24; oxygen atoms ,which are about 33% heavier than C12 atoms are given a value of 16. For the elements these relative weights are called atomic weights. Molecular weights are calculated by adding atomic weights so they also are relative weights and represent how many times heavier a molecule is relative to C12.
One of the most important consequences of having a system of relative atomic weights is that it can be proven mathematically that 1 gram-atomic weight (GAW) of element A contains just as many atoms as 1 GAW of element B. One GAW is defined as that mass of an element which is equal to the atomic weight expressed in grams. Therefore, 1 GAW of oxygen is equal to 16 grams of oxygen while 1 GAW of magnesium is equal to 24 grams of magnesium.
In 1811 the first person to realize this was Amedeo Avogadro and so this number has become known as Avogadro's number. It was first measured by the American chemist Robert Millikan at 6.06 X 1023. Today the accepted value of Avogadro's number to six significant digits is 6.02257 X 1023 and is known as the mol. Therefore, 12 grams of carbon equals 1 GAW of carbon which contains 6.02257 X 1023 atoms of carbon and is called one mol of carbon atoms. Likewise, 24 G Mg = 1 GAW Mg = 6.02257 X 1023 atoms Mg =1 mol Mg. Unofficially October 23 has been designated Mol Day by chemists across the country. The Mol is to be remembered between the hours of 6:02 AM and 6:02 PM. (Actually the twelve hour celebration should run from 6:02:25.7 AM and 6:02:25.7 PM.) Today we will join that celebration with a laboratory investigation involving calculations related to the mol.
1. Obtain a cookie of your choice and mass it to the nearest milligram, that is, 0.001 grams. Assuming that this cookie is 70% (7 X 101%) carbohydrates by mass, determine the mass of carbohydrates contained in the cookie. Most carbohydrates are converted to dextrose when they are digested by man. Therefore, we can assume that the formula for dextrose, C6H12O6, will be an accurate representation of the mass of carbohydrates contained in the cookie.
2. Secure about 250 mL of soda pop of your choice and mass it to the nearest milligram. Soda pop is mostly water therefore to a first approximation we will assume that it is 90% (9 X 101%) water by weight. Using this percentage determine the mass of water in your glass of soda pop.
1. Calculate the number of mols of dextrose molecules present in your cookie.
2. Calculate the number of mols of water in your glass of soda pop.
3. From your answers in questions 1 and 2 calculate the number of molecules of dextrose and water present.
4. Determine the number of hydrogen and oxygen atoms present in your glass of soda pop. (Hint: the formula of water indicates how many atoms of hydrogen and oxygen are present in one molecule of water.)
5. Repeat question 4 for the number of carbon, hydrogen, and oxygen atoms present in the carbohydrates contained in your cookie.
6. Get the number of Calories in one cookie from the package that the cookies came in. Assuming that all of the energy comes from carbohydrates, determine how many Calories are supplied by each mole of dextrose calculated in question 1.
7. The number of dietary Calories theoretically contained in one mol of dextrose is 686. Comment on the accuracy of the assumption made in step 1 about the percentage of carbohydrates present in one cookie.
8. Extra Credit: By comparing your answer in step 6 above and the theoretical value of the number Calories per mol of dextrose, calculate a better value for the percentage of carbohydrates present in one of your cookies. (Before doing this question you should probably try to correct the assumption made in question 6, that is, all energy comes from carbohydrates. If the package list the fat content of each cookie subtract the energy due to fat from the total and use this value to recalculate a better answer to question 6.)
(1) What happened to Avogadro when he got bit by 6.0 X 1023 mosquitoes? He got Mol-aria!
(2) Why was Avagadro such a good golfer? He kept getting a mole in one.
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