Unit Conversion Practice Worksheet Init 12/17/2007 by Daniel R. Barnes Hit the “End” key on your keyboard at any time to jump to the table of contents for this presentation. From there you can jump to just about anywhere in the presentation. WARNING: Some images appearing in this presentation may have been swiped without permission from the world wide web. Equally as heinous as this, I completely ignore significant figure conventions when I round numbers. Let’s say you want to buy a sixdollar hamburger, but all you’ve got is pennies. How many pennies would it take to buy that six-dollar burger? How many pennies would it take to buy that six-dollar burger? 6x =?x To figure out how many pennies six dollars is, you need to know how many pennies one dollar is. = ? 100 x Now that we know one dollar is one hundred cents, we can do a unit conversion to find out how many pennies it takes to buy a six dollar burger. $6 1 x 100 ¢ $ 1 = 600 ¢ It takes 600 pennies to equal 6 dollars. We figured this out by converting six dollars into pennies. Dollars and cents are both units for measuring amounts of money. We’ve just done a unit conversion. $6 1 x 100 ¢ $ 1 = 600 ¢ This one was easy. You could have probably done it in your head. Everyone loves money, so they find it pretty easy to do money math. However, in chemistry, we have to do unit conversions that are more bizarre, using funny numbers and weird units, so we have to learn a procedure and stick to it. $6 1 x 100 ¢ $ 1 = 600 ¢ You will use the method shown above to do almost all your unit conversions in chemistry. The numbers are sometimes fancier, and the units are weirder, but the procedure remains the same. Remember that when you perform a unit conversion, the original quantity does not really change. It’s still the same size. It just looks different. “$6” looks quite different than “600¢”, but they mean exactly the same thing. How many nickels would it take to buy a $12.50 taco combo? $12.50 1 20 nickels x $1 = 250 nickels How many hours can you talk if you have 3600 minutes left on your cell plan this month? 3600 min x 1 1h 60 min = 60 h If you’re pressed for time, click the button below. If you have all the time in the world, click anywhere else. Let’s assume that you live to be 100 years old. 100 years 365 days x x 1 1 year 24 hours 60 minutes 60 seconds x x 1 day 1 hour 1 minute 100 yr x 365 days/yr = 36,500 days 36,500 days x 24 hr/day = 876,000 hr 876,000 hr x 60 min/hr = 52,560,000 min 52,560,000 min x 60 s/min = 3,153,600,000 s In scientific notation, 3,153,600,000 s = 3.1536 x 109 s That’s about three billion seconds. Let’s assume that you live to be 100 years old. 100 years 365 days x x 1 1 year 24 hours 60 minutes 60 seconds x x 1 day 1 hour 1 minute 100 yr x 365 days/yr = 36,500 days 36,500 days x 24 hr/day = 876,000 hr 876,000 hr x 60 min/hr = 52,560,000 min 52,560,000 min x 60 s/min = 3,153,600,000 s In scientific notation, 3,153,600,000 s = 3.1536 x 109 s That’s about three billion seconds. A mole of anything is . . . 6.022 x 1023 molecules. Let’s say you can count one molecule per second. 6.022 x 1023 seconds 1 lifetime x 3.1536 x 109 seconds 1 1.9095636 (23-9) lifetimes = 1.91 x 10 3.1536) 6.022 = 1.91 x 1014 lifetimes That’s about 200 trillion lifetimes 3.1536 x 109 s That’s about three billion seconds. = 1.91 x 1014 That’s about 200 trillion lifetimes lifetimes http://www.flinnsci.com/moleconcept Very short video above about the mole. If you’re pressed for time, click the button below. If you have all the time in the world, click anywhere else. Proxima Centauri, a red dwarf, is the second closest star to the earth. The closest star to the earth is . . . . . . the sun. It’s only 93,000,000 miles away from the earth. Proxima Centauri is so far away that the distance between it and the earth is not measured in miles, but in . . . light years. Proxima Centauri is 4.2 light years away from the earth. How many miles is that? A light year is how far light travels in one year. The speed of light is 186,000 miles per second. How fast is that in miles per year? A light year is how far light travels in one year. The speed of light is 186,000 miles per second. How fast is that in miles per year? 186,000 mi 60 s 60 min 24 h 365 days x x x x s 1 min 1 h 1 day 1 yr = 5,865,696,000,000 mi/yr A light year is how far light travels in one year. The speed of light is 186,000 miles per second. How fast is that in miles per year? 186,000 mi 60 s 60 min 24 h 365 days x x x x s 1 min 1 h 1 day 1 yr = 5,865,696,000,000 mi/yr = 5.866 x 1012 mi/yr A light year is about six trillion miles. trillion billion million thousand 5.866 x 4.2 24.6372 Proxima Centauri is 4.2 light-years away, so how far does light travel in 4.2 years? 24.6372 trillion miles = 2.4 x 10 13 miles Proxima Centauri Earth UNIT CONVERSION STEPS original amount x 1 #new new unit . . . #old old unit 1. Original amount over one 2. Times a fraction 3. Old unit on the bottom 4. New unit on the top 5. Put in #’s to make top equal bottom 6. If new unit is not target unit, build another fraction. YOU TRY IT: four weeks? 4 weeks 1 x How many meals does a person eat in (Assume B/L/D) 7 days 1 week x 3 meals 1 day = 84 meals This has all been very interesting, but now we need to focus on the kinds of unit conversions that you’re actually going to have to do on the test. This has all been very interesting, but now we need to focus on the kinds of unit conversions that you’re actually going to have to do on the test. Before actually doing some true mole math problems, you’re going to take a good look at your tool box. Volume of Gas at STP (L) Standard temperature = 0oC = 273 K = 32oF See Prentice Hall’s Chemistry textbook, page 303 MOLE Mass (g) Representative Particles (atoms, molecules) P = 0 atm in outer space “Standard Temperature and Pressure” O oC P = 0.3 atm on top of Mt Everest P = 1 atm at sea level 1 atm These are all different ways of saying standard pressure. One mole of gas at STP occupies 22.4 liters of volume. It doesn’t matter what gas it is. At STP, 6.022 x 1023 gas molecules takes up 22.4 liters of space. 22.4 L = 1 mol That’s just a bit more than the combined volume of 11 two-liter soda bottles. If you don’t memorize it, you better know where to look. A mole of any gas takes up 22.4 L of space at STP. Therefore, you can measure # of molecules, which is hard, by measuring volume, which is easy. The thing is, if you change the temperature or pressure of a gas, it will expand or shrink. Therefore, in order to use the 22.4 L thingie to figure out how many moles of gas you’ve got, you have to get the gas to STP, or your answers will be wrong. Volume of Gas at STP (L) Standard temperature = 0oC = 273 K = 32oF See Prentice Hall’s Chemistry textbook, page 303 MOLE Mass (g) Representative Particles (atoms, molecules) Volume of Gas at STP (L) In what units is each quantity measured? MOLE Mass (g) Representative Particles (atoms, molecules) If the material is a covalently-bonded compound, the “representative particle” unit will be molecules. Representative Particles (atoms, molecules) If the material is a polyatomic non-metal element, the “representative particle” unit will be molecules. Representative Particles (atoms, molecules) If the material is a noble gas, a lattice-forming non-metal, or a metal, the “representative particle” will be atoms. Representative Particles (atoms, molecules) If the material is ionic, technically, the “representative particle” unit would be “formula units”. Na Na Na Cl Na Cl Na Cl Cl Na Cl Na Na Cl Cl Cl Representative Particles (atoms, molecules) Volume of Gas at STP (L) How do you convert from one quantity to another? MOLE Mass (g) Representative Particles (atoms, molecules) Before we answer that question, do remember what piece of information you needed to know in order to turn $6 into 600¢? $1 = 100¢ Or, in another way of saying it . . . 100¢ per $ or 100¢/$ Volume of Gas at STP (L) How do you convert from one quantity to another? MOLE Mass (g) Representative Particles (atoms, molecules) Volume of Gas at STP (L) To go from grams to moles or from moles to grams you need . . . MOLAR MASS In what units is molar mass given? MOLE g/mol Mass (g) Representative Particles (atoms, molecules) Volume of Gas at STP (L) To go from particles to moles or from moles to particles, you need . . . In what units is Avogadro’s number given? MOLE AVOGADRO’S NUMBER molecules/mol Mass (g) Representative Particles (atoms, molecules) Do you remember Avogadro’s Number? What is it? NA = 6.022 x 1023 formula molecules/mol atoms/mol units/mol It’s not on your CST Reference Sheet, so you’d better memorize it. Volume of Gas at STP (L) To go from volume of gas at STP to moles, or from moles to volume of gas at STP, you need . . . 22.4 L/mol MOLE Mass (g) This is a constant, and it Can be found on your CST Reference Sheet. Representative Particles (atoms, molecules) Volume of Gas at STP (L) These three pieces of information are your “mole math tool box”. MOLAR MASS 22.4 L/mol MOLE g/mol Mass (g) AVOGADRO’S NUMBER molecules/mol Representative Particles (atoms, molecules) Volume of Gas at STP (L) 22.4 L/mol MOLAR MASS MOLE g/mol Mass (g) AVOGADRO’S NUMBER molecules/mol Representative Particles (atoms, molecules) Q1: What “tool” allows you to convert grams into moles or convert moles into grams? A: molar mass Q2: Why is molar mass the right tool for converting grams into moles or converting moles into grams? A: Molar mass is given in grams per mol = g/mol Q3: What is Avogadro’s number? A: 6 x 1023 Q4: What is Avogadro’s number useful for? A: converting molecules into moles or moles into molecules Q5: When you see “STP” in a question, what mathematical quantity should immediately pop into your head? A: 22.4 liters per mole of gas = 22.4 L/mol Q6: What does “STP” stand for? A: Standard temperature and pressure Q7: What are the conditions at STP? A: a temperature of zero degrees Celsius (273 Kelvins = 32oF) and a pressure of 1 atm = 101.3 kPa = 14.7 psi = 760 mmHg = . . . Q8: How do you get molar mass? A: calculate it using the chemical’s formula and the atomic masses from the periodic table. Q9: Where can you get Avogadro’s # during a test? A: Sorry. You have to memorize it. Q10: Where can you get that 22.4 L/mol thingie? A: It’s on the back side of the reference sheet. Q11: How many representative particles are in a mole? A: 6 x 1023 representative particles = 1 mole Q12: What does “representative particles” usually mean? A: “molecules” http://what-if.xkcd.com/4/ Unit Conversion Practice Worksheet Try each problem in pencil before you look at the answer. Then, make whatever corrections you need to make to your answer. Don’t just look at the answer first, or you won’t learn as much. 1. How many grams is 72 kilograms? 72 kg 1 x 1000 g = 1 kg 1 kilogram = 1000 grams 72,000 g 2. How many Ag atoms are there in 3.4 moles of silver? 3.4 mol 1 x 6 x 1023 atoms = 20.4 x 1023 atoms 1 mol 2.04 x 1024 atoms 1 mole = 6.022 x 1023 atoms 3.4 x6 20.4 3. How many milliliters is 2 liters? 2L 1 x 1000 mL 1 L 1 liter = 1000 milliliters = 2,000 mL 4. How many grams of carbon are there in 78 moles of carbon? 78 mol 1 x 12.01 g = 937 g 1 mol The periodic table lists carbon’s average atomic mass as 12.01. 1 mole of carbon = 12.01 grams of carbon 12.01 x 78 936.78 5. How many liters does 3200 grams of CH4 occupy at STP? 3200 g 1 molL x g Now, it would be nice if we could convert directly from grams to liters, but I don’t know of any number that tells us how many grams per liter or how many liters per gram. (Well, actually, I do. It’s called density, but we don’t use density in this chapter, so we’ll have to do something else instead.) Your CST Reference Sheet says that one mole of ideal gas at STP takes up 22.4 liters of volume. (It’s the first fact listed under “Constants”.) Now if we could just convert grams into moles, then we could convert moles into liters. This problem is going to take two steps. 5. How many liters does 3200 grams of CH4 occupy at STP? 3200 g 1 1 mol x 22.4 L x 16.05 g CH4: C: 1 x 12.01 = 12.01 H: 4 x 1.01 = 4.04 = 4467 L 1 mol 199.37694 16.05) 3200.0000000 16.05 g/mol 199.4 x 22.4 4466.56 To convert grams into moles, we’re going to need to calculate the molar mass of methane. Now that we’re set up to convert grams into moles, we need to get set up to convert moles into liters. Once again, according to your reference sheet, one mole of ideal gas occupies 22.4 liters of space under STP conditions, so . . . 6. How many moles of zinc are there in 124 grams of zinc? 124 g 1 1 mol x = 1.9 mol 65.39 g The periodic table list’s zinc’s average atomic mass as 65.39. 1 mole of zinc = 65.39 grams of zinc 1.8963144 65.39) 124.0000000000 To convert Celsius to Kelvins . . . add 273. To convert Kelvins to Celsius . . . subtract 273. 7. How many degrees Celsius is 310 Kelvins? oC oC = K – 273 = 310 – 273 = 37 oC 310 -273 37 Your chemistry CST reference sheet says that K = oC +273. Therefore, oC = K – 273. PLEASE NOTE that converting between degrees Celsius and Kelvins is just about the only time that you don’t multiply fractions times fractions to perform a unit conversion. You don’t really need to work with Celsius and Kelvins until chapter 14 (gases) anyway, but I thought I’d throw this in here just so you’d know that unit conversions don’t always follow the same pattern. Time to think-pair-share the rest of the back side of the worksheet. 8. What volume does 2.2 grams of carbon dioxide (CO2) occupy at STP? 2.2 g 1 1 mol x 44.01 g CO2: C: 1 x 12.01 = 12.01 O: 2 x 16.00 = 32.00 22.4 L x 1 mol = 1.12 L 0.0499886 44.01 ) 2.2000000 44.01 g/mol 0.04999 x 22.4 1.119776 9. How many atoms of helium are there in 67.308 moles of helium? 67.308 23 6.02 x 10 atoms 67.308 mol x 6.02 x 1 mol 1 405.19416 = 405.19416 x 1023 atoms 1 mole is 6.02 x 1023 particles (whether it’s helium, carbon dioxide, salt, gold, or whatever) This answer is correct, but it’s not in proper scientific notation. There should be only one digit in front of the decimal, not three. 9. How many atoms of helium are there in 67.308 moles of helium? That move made 405.19416 get 100 times smaller. Therefore, to keep our answer the same size, we need to make the power of 10 get 100 times bigger. 25 atoms 23 405.19416 x 10 . This decimal point needs to move . . . . . . two spaces to the left. 100 is 10 to the 2nd power, so we need to make the exponent get bigger by 2. 23 + 2 = 25 9. How many atoms of helium are there in 67.308 moles of helium? 67.308 23 6.02 x 10 atoms 67.308 mol x 6.02 x 1 mol 1 405.19416 = 405.19416 x 1023 atoms 25 = 4.0519416 x 1025 atoms He 4.0519416 x 10 atoms Now, the answer has been properly converted into scientific notation. Converting it into proper scientific notation didn’t make it get bigger or smaller; it just changed what it looks like. 9. How many atoms of helium are there in 67.308 moles of helium? 67.308 23 6.02 x 10 atoms 67.308 mol x 6.02 x 1 mol 1 405.19416 = 405.19416 x 1023 atoms = 4.0519416 x 1025 atoms 10. How many molecules are there in 126 grams of water (H2O)? 126 g 1 x molecules g It would be nice if there were a number that told us how many molecules per gram of water, but there isn’t. However, there is a number that tells us how many molecules per mole. There are 6.022 x 1023 molecules per mole. (Avogadro’s #) If we can just convert grams into moles, then we can convert moles into molecules using Avogadro’s number. 10. How many molecules are there in 126 grams of water (H2O)? 126 g 1 x mol g It would be nice if there were a number that told us how many molecules per gram of water, but there isn’t. However, there is a number that tells us how many molecules per mole. There are 6.022 x 1023 molecules per mole. (Avogadro’s #) If we can just convert grams into moles, then we can convert moles into molecules using Avogadro’s number. Calculating the molar mass of water will tell us how many grams per mole for water. Let’s do that next. 10. How many molecules are there in 126 grams of water (H2O)? 126 g 1 x 1 mol x 18 g 6 x 1023 molecules 1 H: 2 x 1 = 2 ? molecules mol 7 18 )126.0000 H2O: = 7 x6 42 O: 1 x 16 = 16 18 g/mol 42 x 1023 molecules 4.2 x 1024 molecules 4 x 1024 molecules (If you care about sig figs, you’re only allowed to keep one digit.) 11. How many moles of bismuth are there in 2.56 kg of bismuth? 1000 mol g 1 mol 2.56 kg x x = 12.25 mol 1 1 kg 209 g 2.56 x 1000 2560.00 12.248803 209 ) 2560.000000 The periodic table list’s bismuth’s average atomic mass as 208.98 1 mole of bismuth = 208.98 grams of bismuth Too bad it doesn’t say how many KILOGRAMS one mole is. We’re going to have to convert kg into g first, and THEN turn g into mol. This is going to take two steps. 1 kilogram = 1000 grams. This is always true, not just for bismuth. 11. How many moles of bismuth are there in 2.56 kg of bismuth? 1000 g 1 mol 2.56 kg x x = 12.25 mol 1 1 kg 209 g 2.56 x 1000 2560.00 12.248803 209 ) 2560.000000 12. What is the mass, in kilograms, of 8 x 1028 copper atoms? 8 x 1028 atoms 1 mol 63.55 g 1 kg x x x 23 1 6 x 10 atoms 1 mol 1000 g 63.55 x 8 508.40 84.733 6 ) 508.40 = 84.733 x 10 (28-23-3) kg = 84.733 x 10 2 kg = 8.4733 x 10 3 kg = 8 x 103 kg if you care about sig figs 103 For one guy’s take on the effects of exposure to a vacuum on the human body: http://www.geoffreylandis.com/vacuum.html Slide needed: How many atoms are in a grain of sand? oC K Title Page #1 SWBATS #2 #7 $6 Burger #3 #8 S/Lifetime #4 #9 Lifetimes/mol STP #10 Miles/ly (Prox. Cent.) #5 #11 The Mole Road Map #6 #12