The Art of Counting without Counting Quiz

The Art of Counting Without Counting Quiz

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 426 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 6 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 5 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 your strategy: Find out the number of Fe₂O₃ molecules and then it's an easy step to finding the number of iron or oxygen atoms.

Problem 6: Here's a specimen of hematite , which is iron (III) oxide. This is 5 moles of hematite [Fe₂O₃].
6a: How many moles of iron are present?

6b: How many moles of oxygen are present?

Here's the specimen of hematite again. The above problem is not normal. People don't know the moles. They put a sample on a balance and it gives them grams (not moles). So a more realistic question would be "I've got 346.0 grams of hematite here, how many grams of iron can I get out of it?"
Whenever you hear someone say "grams", your first reaction is to think, "I got to change that to moles because counting atoms (counting with moles) is going to be needed." So the first step is to convert 346.0 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:
346.0 grams Fe₂O₃ x     1 mole Fe₂O₃      = 2.167 moles Fe₂O₃
                                   159.7 grams Fe₂O₃
That is moles of hematite, but the question is about iron. We can see there are two iron atoms for every hematite molecule. So the number (moles) of iron atoms is twice the moles of the hematite molecules. So that's 2x2.167=4.334moles. But, he didn't ask for moles, he wants grams. So you need to change moles to grams.
4.334 ~~moles~~ Fe x   55.85 g Fe  = 242.1 grams Fe
                              1 ~~mole~~ Fe
So to answer his question, you would say, "You would get 242.1 grams of iron out of that 346 grams hematite sample."

The whole problem above could (and maybe should) be done as one big dimensional analysis problem. Again, spreadsheets are really good for this. You do another based on the below setup. Problem 7: How many grams of iron are in 245 kilograms of hematite?

Start mass

convert to moles

Fe per molecule

convert to grams

=A2*C2*F2*H2/D3

<-formula for K2

245

kg Fe₂O₃

1000

mole Fe₂O₃

mole Fe

55.85

g Fe

???

grams Fe

kilo

159.7

g Fe₂O₃

mole Fe2O3

mole Fe

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 8: Use your element code name's atomic number for the number of grams of Fe₃O₄ (magnetite) for this problem. For example, if your element code name was Niobium, which is atomic number 41, you would use 41 grams of magnetite. How many grams of iron could be extracted from the number of grams equal to the atomic number of your element code name?

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 nickel (round to 3 sig figs):
5.00 g. x 1 mole = 0.085190 moles > 0.0852 moles
58.692 g.

Problem 9: Do the remaining metals on the chart. (start with copper) Again, the point of this drill and practice is that when you hear someone say grams, you instinctively should start looking up its molar mass using the Periodic Table and get that changed into moles.

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, in the U.S the normal level of calcium in the blood is written as 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. In addition to grams to moles, we need to do deciliters to liters. I'll do one problem, and you do the rest.
Calcium 9.00mg-10.5mg per deciliter 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 x deci = 2.25 millimoles (mmol/L)
deciliter 40.08 g 0.1 liter
10.5 mg x 1 mole x deci = 2.62 millimoles (mmol/L)
deciliter 40.08 g 0.1 liter
So the normal range in the new SI units is 2.25-2.62 mmol/liter.
Normal range for Iron is 60-150 mg per deciliter
Normal range for zinc is 75-120 mg per deciliter
Normal range for lead is less than 40mg per deciliter
Problem 10: Report the normal range of these last 3 metals in millimoles per liter.

Now I want you to see how the problems in 10 are done with a spreadsheet. Note that the values are in a cell to themselves and the units of measurement are in their own cells. At G2, you would type an equal sign "=" and the click on A2 following by typing "*" followed by typing "/" then click on C3 followed by typing "/" following by clicking E3 then press return. Instead of clicking on the cells, you could type the formula as "=A2/C3/E3". The units that cancel are in red.

	A	B	C	D	E	F	G	H
1	U.S. concentration		convert to moles		cancel deci		=A2/C3/E3	<-This is formula that calculates answer. It is placed in cell G2.
2	9.00	mg	1	mole	deci	=	2.25	millimoles (mmol)
3		deciliter	40.08	g	0.1			liter

On a calculator, type 9 / 40.08 / .1 = (You should be able to do it both ways.)
Problem 11: For converting iron's 60mg/deciliter, what would be the values in cells A2 and C3?
(Note: a spreadsheet could be setup to automatically convert the U.S. blood values to International values.

Problem 12: Until everyone adopts this Internation System, this conversion has to go both ways. Let's say you get results from a German hospital but need to send that back to a doctor's office in the United States. Then the conversion is reverse of what is shown above. Vitamin C in the body was reported as 0.0552 millimoles per liter (mmol/L). What is the value in milligrams per deciliter (mg/dL)? (Note: Use dimensional analysis like above to make sure you are setting up your math correctly.)

For students in my CHM151 class, send your answers to chm151@chemistryland.com with subject line of "Art of Counting".

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Since March 26, 2008