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## The Mole

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**The Mole**A mole isn’t just a burrowing rodent. “Mole” is a word which represents a number. You already know a bunch of words that represent numbers like few, dozen, gross, ream. Mole is like those. A mole is the number of carbon-12 atoms in 12 grams of carbon-12. There are 6.02 x 1023 atoms of C-12 in a mole of C-12.**The Mole**In other words, a mole is 6.02 x 1023.**The Mole**• 6.02 x 1023 of anything is a mole of that thing. We could have a mole of sand grains on the beach, a mole of water molecules in a glass, or a mole of cheeseburgers, but that last one may not be practical.**The Mole**• 6.02 x 1023 is sometimes referred to as Avogadro’s number. Look up Avogadro’s Number on Wikipedia. • You absolutely need to memorize the number represented by the word, mole.**The Mole**• The mole is an important concept in stoichiometry. It allows you to convert between mass and number of particles, between number of particles and volume of a gas at standard temperature and pressure, and any combination of those quantities. • You can convert from mole to anything, and from anything to mole!!!**For instance, I know if there are two moles of carbon**dioxide gas, there are 12.04 x 1023 molecules of carbon dioxide gas. How did I know that carbon dioxide is molecular? (Review)**The Mole**You try: How many atoms of gold are in 3.0 moles of gold? Start by writing the given information.**The Mole**You try: How many atoms of gold are in 3.0 moles of gold? Put the given information over 1.**The Mole**You try: How many atoms of gold are in 3.0 moles of gold? Write a line for the fraction which will be your unit converter.**The Mole**• You try: • How many atoms of gold are in 3.0 moles of gold? • The unit converter always causes the given units (on the top of your original fraction) to cancel out (because the same unit will be on the bottom of the unit converter fraction). Look at the units!**The Mole**You try: How many atoms of gold are in 3.0 moles of gold? The units you are trying to get to will now go on top of the unit converter. In this case, we are trying to get the number of atoms of gold. Notice that everything is labeled, even before the numbers are filled in.**The Mole**You try: How many atoms of gold are in 3.0 moles of gold? Now the numbers get filled in. You know that a mole has a certain number of particles. I hope you have a calculator.**The Mole**• 18.06 x 1023 atoms of gold are in 3.0 moles of gold, but to translate that into proper scientific notation, I need to move the decimal one space to the left, then adjust the exponent. • 1.806 x 1024 atoms is proper scientific notation. Oops! I forgot about significant figures. My answer cannot have more significant figures than the least precise of my given numbers. 3.0 has only 2 sig figs, so my answer can only have 2 sig figs. • 1.8 x 1024 atoms of Au are in 3.0 moles of Au.**Converting with Moles**Here’s the setup Here’s the question • How many moles of calcium are in 1.5 x 1024 atoms of calcium?**Converting with Moles**You need to figure it out!**The Mole**One more: A certain canister contains .50 moles of propane gas at standard temperature and pressure. How many molecules of propane are in that canister? .50 moles x 6.02 x 1023 molecules/mole = 3.01 x 1023 molecules Adjust the sig figs. Your answer can have only two. 3.0 x 1023 molecules of propane are in that canister.**The Mole**Let’s try converting from particles to moles now: Bob has 3.01 x 1023 atoms of lead in his fishing weight. How many moles of lead are in that weight? 3.01 x 1023 atoms Pb x 1 mole/6.02 x 1023 atoms = .5 moles of lead are in that weight. Is that right? Not quite. Significant figures need to be considered. The given number has three, so the answer needs three. .500 moles of lead are in the weight.**The Mole**As mentioned before, the mole also helps to determine the volume of a gas at standard temperature and pressure (STP). Look up STP online now. Write down the specifications. One mole of any gas at STP has a volume of 22.4 L.That’s a little more than 10 2-liter soda bottles. Think about it – a mole of liquid water has a volume about like a newer I-Pod. Turn that water into gas at STP, and it’s volume becomes comparatively huge! This happens because particles of a gas have much more energy and are not bound to each other, as liquid or solid particles are. Their energy is enough to overcome whatever attraction the molecules feel for each other. Each gas particle goes bouncing around as much space as it has available. Yes, you do need to know the volume of one mole of a gas at STP. Write it down.**The Mole**You try: A certain canister contains .50 moles of propane gas at standard temperature and pressure. What is the volume of that canister? .50 moles x 22.4 L/mole = 11.2 L of propane Sig figs? Oh, yeah – only two. 11 L of propane gas are contained in that canister.**The Mole**It works both ways: How many moles of gas at STP can be held in a 2.0 L bottle? 2.0 L x 1 mole/22.4 L = Calculator? Sig figs?**The Mole**• So far, you have learned two conversions which are possible because of your friend, the mole: • 1 mole = 6.02 x 1023 particles • 1 mole = 22.4 L (for gases at STP) • One more conversion is coming up!**The Mole**• One mole of any element has a mass equal to the average atomic mass of that element, but in grams. • One mole of carbon-12 atoms has a mass of 12 grams. • One mole of a standard mixture of carbon atoms has a mass of 12.011 grams. (Remember the average atomic mass is the average mass of the naturally occurring isotopes) • One mole of oxygen atoms has a mass of 15.999 grams.**The Mole**• Your turn: • What is the mass of one mole of gold atoms? • What is the mass of two moles of gold atoms? • What is the mass of two moles of silver atoms?**The Mole**That mole-mass conversion thing works for molecules/formula units, too. To find the mass of one mole of any substance, just add up the masses of whatever is in the substance. What is the mass of one mole of water? A molecule of water has two hydrogens and one oxygen, so let’s see… 2(1.007) + 1(15.999) = Get out your calculator! I’m not doing this one for you.**The Mole**The mole is your key to stoichiometry. Whatever quantity is given will always be converted to moles first in any stoichiometric conversion – using the conversions you just learned. One the given substance is converted to moles, you can convert from moles to whatever is requested using those same conversions.**The Mole**Last one: Bob has 3.01 x 1023 atoms of lead in his fishing weight. How many grams of lead are in that weight? 3.01 x 1023 atoms Pb x 1 mole/6.02 x 1023 atoms x (how many grams of Pb?)/1 mole of Pb = Copy that problem down, but with numerators over denominators. Fill in the molar mass of lead. Multiply all of the numerators, then divide by the denominator for your answer. Cross-cancel the units that cancel out. You should be left with grams only, as mass of lead was the requested quantity.**The Mole**You are now ready for some serious stoichiometry.