Math & Measurement
Assignment |
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11th Edition |
12th Edition |
Instructions are given for the 11th, 12th, and 13th Editions. |
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Temperature: Read what the book says about temperature and the three scales used for temperature. Learn how to convert between the three scales. Notice that the book gives you names of the three scales, (Fahrenheit, Celsius, & Kelvin) but does not explain how these names came about or the how the temperature scales were created. I feel that if you don't know this background information, there will always be a hole in your learning. I will cover temperature in a separate tutorial, but if I didn't, you should do your own background check. |
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Density: 11th Edition, page 35: Density can be calculated with simple measurements-volume and mass. Read Section on Density |
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The book shows both the algebraic approach and the Dimensional Analysis approach. Trust me, the Dimensional Analysis will be easier in the long run, so focus on that approach. They use parentheses to indicate multiplication, but as I've shown before, a faster way to write it is with vertical lines. |
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Book Example 2.23: Here is my suggested style. Write the 25mL as the starting amount and the grams as the end dimensions. The density is given as 19.3 g/mL. These dimensions are good because the grams stays and the mL cancels out the mL in 25.0 mL. |
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If this problem said, "You have 483 grams of gold. What is the volume?", then the 483 grams would be written first and the density would be written upside down (1 mL/19.3grams) so that the grams cancels out and the mL stays. The answer would be 25.0 mL. |
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Gold Density Problem 1: |
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In the above calculations the cubic centimeters (cm3) will cancel leaving just grams. The formula in cell J2 if written in a spreadsheet is "=A2*C2*E2*G2". |
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Gold Density Problem 2: They give a conversion of 14.58 troy oz = 1 pound.
You will also need to know that 2.2 lbs = 1 kg = 1,000 g. See spreadsheet below for help with layout. |
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Problem #3: In the textbook they show this graphic to explain density.
What's nice they drew the boxes to scale. In other words, the sulfur box
measured about 1.7 centimeters (cm) on each side. That gives the volume
of 1.7cm x 1.7cm x 1.7cm = 4.9cm3, which is close to the volume
they show for sulfur. |
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Oil Slick Problem example: This is a bit tricky problem. The slick is considered
a very flat box with a volume equal to L x W x H. Volume is 200cm3(about a cup full).
Height is 0.5nm (about 1/200 of human hair) and the width times the length is the area |
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With dimensional analysis we put our starting amount on the left (volume divided by height) and what we want to find on the right (area in square meters). Realize that cm3 is cm x cm x cm. cm3 has "m" three times (cubic meter); however, our answer is square meters (m2). The meter in "nm" will cancel one of the meters in the cubic centimeters. Then we end up with the meters squared (m2) that we want. The starting amount also has "centi" (c) three times, so we cancel them by multiplying by 0.01 over "c" three times. Remember "centi=0.01". Then "n" in 0.5nm needs to be canceled so we put "n" on top and its equivalent on the bottom (10-9), which is one billionth). If dimensions are in the right place, everything that needs to cancel will cancel and you are left with the correct final units (m2). Now we just multiply all of the numerators together and divide by each of the denominators. So the 200cm3, which is less than a cup of oil, can form an oil slick that covers 400,000 m2, which is the area of about 100 football fields! |
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Problem #4. Here is a picture of the Exxon Valdez. It spilled 11 million gallons of oil. How many square miles of ocean could it cover if the oil also coated the surface also with 0.5nm thickness of oil? Setup the problem the same as before. We know dividing the volume by the height is the area. However, a volume of gallons divided by a height of nanometers does not give us square miles. We will have to do some conversions. Since our height is in nanometers, it would help to convert gallons to cubic meters. Then both height and volume will be measured in meters. Searching the Web for "metric conversions" we find sites that give us conversions. We find that 1 cubic meter = 264 gallons. Instead of writing "cubic meters", it is better to show "m x m x m" to recognize meters times itself 3 times. At that point we have gotten rid of gallons and have square meters (mxm). Next we need to convert square meters into square miles. We look it up and see that 2,589,988 square meters equals 1 square mile. We use that as the conversion. Finally we need to get rid of the "nano" in "nm". We do that by putting "n" on top and its equivalent "10-9" on the bottom. Problem #4: Do the arithmetic to solve for the square miles. In other words multiply all numerators and divide by each denominator. Hint: The answer will be in millions of square miles. Below I will recreate the last part of the dimensional analysis shown on the left, but use a spreadsheet style layout which gives me some extra ways to organize it. |
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Problem #5: Density is a very useful property because it connects weight to volume. 5a) Use wikipedia to search for your element code name. http://en.wikipedia.org/wiki/Main_Page Once you find the article for your element, look on the right side for table that gives a lot of data. One section of that table is the Physical Properties. In there should be the density of the element. If a gas, it will be given as grams per liter. If solid or liquid, it will be grams per cubic centimeter (abbreviated as g·cm-3or g/cm3). Sometimes they give a range and sometimes they give the melted density. You can just report the density of the solid at room temperature (r.t.). (Don't use the density in the image on the left. That is for cadmium) 5b) Using that density what would a liter (1000 cubic centimeters) weigh? Give answer in grams and in pounds (454 grams = 1 pound) 5c) Water's density is 1 gram per cubic centimeter. Will your element sink or float in water? |
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email your answers to me at chm130@chemistryland.com | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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