The Art of Counting without Counting Assignment

The next step is to use dimensional analysis to convert grams to moles:
454 grams Fe₂O₃ x     1 mole Fe₂O₃      = 2.843 moles Fe₂O₃
                               159.7 grams Fe₂O₃
At this point we have the number of Fe₂O₃ molecules. It's easy to see the number of iron atoms, because it's just double that of the Fe₂O₃ molecules. So the number of iron atoms is 2.843 moles x 2 = 5.686 moles. So to make up a pound of the hematite we need 5.686 moles of iron. We can't count this many iron atoms, but we can change moles to grams, which is just the reverse of what we just did. Again the Periodic Table says a mole of iron weighs 55.85 grams. Since we have 5.686 moles, we can do this multiplication:
5.686 moles x 55.85 grams Fe = 317.6 grams of Fe.
                        1 mole Fe
So to make 454 grams of hematite, we need 317.6 grams of iron. The remaining grams (454-317.6=136.4) must be oxygen.

The Art of Counting Without Counting Assignment
	The chore of counting is simplified by weighing and then calculating the number. This trick does not work with mixtures. For example, you can't weigh all these coins together and be able to count them. You have to separate them first. The same thing is true with chemicals. It must be pure, or at least you need to know what percent the various components are.
	Problem 1: A standard roll of nickels contain 40 nickels with a value of $2. Nickels weigh 5.00 grams. The paper roll weighs 1 gram. What should a roll of nickels weigh? Problem 2: A stack of nickels weigh 326 grams. How many nickels are present?
	Problem 3: For black tattoos, they sometimes use iron (II) oxide with formula of FeO. To make it you need equal numbers of iron and oxygen atoms. 1 mole of iron atoms and 1 mole of oxygen atoms would be one option. How many grams of each would that be? Problem 4: What would be the total weight of the FeO pigment created if we used 1 mole each of Fe and O?
	If this lady were to bleach her hair, she may cause the iron (II) oxide in the tattoo to become iron (III) oxide, which is reddish. The butterfly now looks like flames. Remember the "(III)" means the iron has 3+ charge. If oxygen has 2- charge, the formula has to be Fe₂O₃ in order for the charges to balance 2x(+3)=3x(-2). Problem 5: To make 10 molecules of the iron (III) oxide pigment (Fe₂O₃), how many atoms of iron is needed and how many atoms of oxygen are needed?
The previous question is pretty simple but not very practical. Making 10 molecules of Fe₂O₃ is not enough to work with, but its easy to see how many iron or oxygen atoms are needed if you know how many Fe₂O₃ molecules are needed. This is our strategy: Find out the number of Fe₂O₃ molecules and then it's an easy step to finding the number of iron or oxygen atoms.
	Here's a specimen of hematite, which is iron (III) oxide. If we wanted to make a pound (454g.) of hematite, how many grams of iron is needed? The information here is all in grams, but the strategy we just learned is that by finding the number of Fe₂O₃ molecules, we can easily get the number of iron atoms. So the first step is to convert 454 grams of Fe₂O₃ into moles of Fe₂O₃. To do that means we have to know what one mole of Fe₂O₃ weighs. The Periodic Table is where we look. The table in the textbook shows iron as 55.85 grams per mole and oxygen as 16.00 grams per mole. For Fe₂O₃, we see there will be 2 iron atoms and 3 oxygen atoms Fe₂= 55.85 g. x 2 = 111.7 grams O₃ = 16.00 x 3 = 48.00 grams Added together = 159.7 grams for one mole of Fe₂O₃.
The next step is to use dimensional analysis to convert grams to moles: 454 grams Fe₂O₃ x 1 mole Fe₂O₃ = 2.843 moles Fe₂O₃ 159.7 grams Fe₂O₃ At this point we have the number of Fe₂O₃ molecules. It's easy to see the number of iron atoms, because it's just double that of the Fe₂O₃ molecules. So the number of iron atoms is 2.843 moles x 2 = 5.686 moles. So to make up a pound of the hematite we need 5.686 moles of iron. We can't count this many iron atoms, but we can change moles to grams, which is just the reverse of what we just did. Again the Periodic Table says a mole of iron weighs 55.85 grams. Since we have 5.686 moles, we can do this multiplication: 5.686 moles x 55.85 grams Fe = 317.6 grams of Fe. 1 mole Fe So to make 454 grams of hematite, we need 317.6 grams of iron. The remaining grams (454-317.6=136.4) must be oxygen.
	Problem 6: OK, I just did the above problem asking about the number of grams of iron is need to make a pound of hematite. Now redo the problem, but this time how many grams of iron is needed if we wanted to make just 5 grams of hematite?
	The image is of magnetite. Like the name implies, this rock is magnetic. The formula is Fe₃O₄. If you try to figure out the charge on the iron, something seems wrong. Oxygen is 2- charge, so O₄ would be 8- charge. How can three iron atoms balance an 8- charge? What is happening is two irons are 3+ and one is 2+. That adds up to 8+. The name is iron (II,III) oxide. Now that I've done a similar problem with Fe₂O₃ for you, let's see if you can do this one (Fe₃O₄) on your own. Problem 7: If you wanted to make one pound of magnetite, how many grams of iron would be required?
	Drill and Practice: I'm not that crazy about drill & practice, but it's important to do these kind of calculations almost automatically. Here's a section of the Periodic Table. Let's say we have 5.00 grams of each metal (same weight as a nickel coin), how many moles of each do we have? I'll do copper (round to 3 sig figs): 5.00 g. x 1 mole = 0.078683 = 0.0787 moles 63.546 g. Problem 8: Do the remaining metals on the chart.
	Blood test results: There's a big push to get blood test results reported using an international standard. The organization that has promoted metrics and other standards is called the International System of Units (or SI from the French, Le Système International d'Unités). For example, the blood tests results in the United States are shown differently than what is displayed in other countries. That can lead to confusion and errors. For example, the normal level of calcium in the blood is 9 to 10.5 milligrams per deciliter (tenth of a liter). In the SI units, they want it in millimoles per liter. (millimole is a thousandth of mole) To do these conversions one needs to convert grams to moles, just like the above problems were doing. I'll do one problem, and you do the rest. Right now we won't deal with the volume (deciliter versus liter), we'll save that for a later chapter. For now we are just converting grams to moles. Calcium 9.00mg-10.5mg is normal: Periodic Table shows 40.08 grams per mole. Notice that the "m" in milligrams does not cancel (just grams), so we end up in millimoles, which is what we want. 9.00 mg x 1 mole = 0.225 millimoles (mmol) 40.08 g. 10.5 mg x 1 mole = 0.262 millimoles (mmol) 40.08 g. So the normal range in the new SI units is 0.225-0.262 mmol. Normal range for Iron is 60-150 mg. Normal range for zinc is 75-120 mg. Normal range for lead is less than 40mg. Problem 9: Report the normal range of these metals in millimoles.
	For students in my CHM130 class, send your answers to chm130@chemsitryland.com with subject line of "Art of Counting".