Chapter 3 & 9 Chemical Reactions and Quantities The Mole Calculations Using Molar Mass

MOLE CONCEPT So far we were in the microscopic world of atoms and molecules. But it is very important that chemists be able to measure and observe, in order to gather data. To do this we must take sufficient quantities of atoms and molecules. How many atoms or molecules must the chemists take? Let us not bother about the numbers but instead call this amount a mole.

Oxygen was the best candidate to define a mole. The most universal atom at the time was oxygen. About 50% of the earth crust is oxygen. Oxygen can react with all the other atoms.

2 Fe + O2 2 FeO ; 144 grams FeO 2 H2 + O2 2 H2O ; 36 grams H2O Let us weigh 32 grams of oxygen gas (O2) and define this amount of molecules as one mole of oxygen gas molecules. If we react this amount with the following atoms and the weight of the products obtained were as given, how much will one mole of the atoms of Fe, H, and S weigh? 2 Fe + O2     2 FeO ; 144 grams FeO 2 H2 + O2     2 H2O ; 36 grams H2O S + O2     SO2 ; 64 grams SO2

2Fe + O2     2 FeO ; 144 grams. Fe = 56g 2 H2 + O2     2 H2O ; 36 grams H = 1g S + O2     SO2 ; 64 grams S = 32g

So chemists agreed that the number of molecules in 32 grams of gaseous oxygen should be known as a mole of molecules. By reacting other atoms with oxygen chemists were able to determine how much a mole of all other atoms weigh. The purpose of the mole concept was to scale up the quantity of atoms and molecules so that we can conduct experiments.

The Mole A counting unit Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000 6.02 X 1023 (in scientific notation) This number is named in honor of Amedeo _________ (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present

Just How Big is a Mole? Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles. If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

Avogadro’s Number (N) = 6.02 x 1023 How big is this? • If 6.02 x 1023 hydrogen atoms were laid side by side, the total length would encircle the earth about a million times. • The mass of 6.02 x 1023 Olympic shotput balls is about equal to the mass of the Earth. • The volume of 6.02 x 1023 softballs is about equal to the volume of the Earth.

Everybody Has Avogadro’s Number! But Where Did it Come From? It was NOT just picked! It was MEASURED. One of the better methods of measuring this number was the Millikan Oil Drop Experiment Since then we have found even better ways of measuring using x-ray technology

Q: How would you describe a stinky chemist? A: Mole-odorous

Collection Terms 1 trio 1 six-pack Cola 1 dozen donuts 1 gross of pencils = 3 singers = 6 cans Cola drink = 12 donuts = 144 pencils

A Mole of Particles Contains 6.02 x 1023 particles 1 mole C 1 mole H2O 1 mole NaCl = 6.02 x 1023 C atoms = 6.02 x 1023 H2O molecules = 6.02 x 1023 Na+ ions and 6.02 x 1023 Cl– ions

Q: How does Avogadro write to his friends? A: By e-mole!

More Examples of Moles Moles of elements 1 mole Mg = 6.02 x 1023 Mg atoms 1 mole Au = 6.02 x 1023 Au atoms Moles of compounds 1 mole NH3 = 6.02 x 1023 NH3 molecules 1 mole C9H8O4 = 6.02 x 1023 aspirin molecules

Learning Check M1 Suppose we invented a new collection unit called a mep. One mep contains 8 objects. A. How many paper clips in 1 mep? 1) 1 2) 4 3) 8 B. How many oranges in 2.0 meps? 1) 4 2) 8 3) 16 C. How many meps contain 40 gummy bears? 1) 5 2) 10 3) 20

Solution M1 Suppose we invented a new collection unit called a mep. One mep contains 8 objects. A. How many paper clips in 1 mep? 3) 8 B. How many oranges in 2.0 meps? 3) 16 C. How many meps contain 40 gummy bears? 1) 5

Q: On which American mountain was Avogadro's face carved in stone? A: Mount Rushmole

Using Avogadro’s Number in Calculations How many particles are in 3.0 moles of Al?

Review Conversion Factors Make a T-chart Put whatever information the problem gave you in the top left Put the units of whatever you were given in the bottom right of the T Put the units of what you want to find in the top right. particles 3 moles = mole

6.02 x 1023 particles 1 mole or 1 mole Avogadro's Number 6.02 x 1023 particles 1 mole or 1 mole Each of these can be used as a conversion factor

3 moles 6.02 x 1023 particles 1 mole = Ans: 1.81 x 1024 particles = 2 x 1024 particles

Learning Check M2 1. Number of atoms in 0.500 mole of Al 1) 500 Al atoms 2) 6.02 x 1023 Al atoms 3) 3.01 x 1023 Al atoms 2.Number of moles of S in 1.8 x 1024 S atoms 1) 1.0 mole S atoms 2) 3.0 mole S atoms 3) 1.1 x 1048 mole S atoms

Solution M2 1. Number of atoms in 0.500 mol of Al 3) 3.01 x 1023 Al atoms 2. Number of moles of S if a sample of S contains 1.8 x 1024 S atoms 2) 3.0 mole S atoms

Q: Why did Avogadro stop going to a chiropractor on October 24th? A: He was only tense to the 23rd.

Weighing can be used as a way to count! A Rice Analogy Rufus’ favorite food is rice. But he rarely eats it even though it is economical and easily prepared. He knows it is healthy for him and he was told once that one serving is 12,000 grains. So every time Rufus wants to eat rice he has to prepare 2 hr. ahead of time and count out 12,000 grains. How can we help my friend Rufus? Weighing can be used as a way to count!

A rice analogy Rufus’ favorite food is rice. But he rarely eats it even though it is economical and easily prepared. He knows it is healthy for him and he was told once that one serving is 12,000 grains. So every time Rufus wants to eat rice he has to prepare 2 hr. ahead of time and count out 12,000 grains. How can we help my friend Rufus? 1 grain of rice weighs an average of 19 mg. 12000 grains 19 mg 1 g 1 grain 1000mg = 228 grams

Start on this: How many molecules of C2H6 are in 0.115 moles?

How do we measure the mass of an object that is too small to be seen? Atomic Mass Unit The atomic mass unit (amu) has been used as a standard for a mass of an atom. 1 amu = 1.66 x 10-24 g = 1/12 mass of a 12C atom 1 proton = approx. 1 amu

Atomic mass gives us the mass of one atom. one atom of potassium 39K weighs 39 amu. one atom of zinc 65Zn weighs 65 amu. Molecular mass gives us the mass of one molecule (mC) one water (H2O) molecule = 18 amu (2-H, 1-O = 2amu + 16amu) one glucose (C6H12O6) molecule = 144 amu (6C, 12H, 6O = [6 C x12amu] + [12 H x 1 amu] + [6 O x 16amu]

Question: Why is the mass of carbon 12.011 amu according the periodic table instead of just 12? Why is the mass of chlorine 35.453 amu ? Answer: Atomic mass, as shown in the periodic table, is the average mass of all isotopes found in nature.

Molar Mass Number of grams in 1 mole of particles Equal to the numerical value of the atomic mass (from Periodic Table)

Review: Atomic Mass The mass of the atom in atomic mass units (amu) What value for the atomic mass is given for carbon on the periodic table? 12.0 amu What value for the atomic mass is given for magnesium on the periodic table? 24.3 amu

How much do 6. 02 x 1023 carbon atoms weigh if one atom weighs 12 How much do 6.02 x 1023 carbon atoms weigh if one atom weighs 12.0 amu and 1 amu equals 1.66 x 10-24 g 6.02 x 1023 molecules 12.0 amu 1.66 x 10-24g = 12.0 grams 1 molecule 1 amu

The MOLAR MASS is equal to the numerical value of the atomic mass (from Periodic Table) 1 mole of C atoms = 12.0 g 1 mole of Mg atoms = 24.3 g 1 mole of Cu atoms = 63.5 g 1 mole of C atoms = 6.02 x 1023 atoms 1 mole of Mg atoms = 6.02 x 1023 atoms 1 mole of Cu atoms = 6.02 x 1023 atoms

Q: How did Avogadro get through the desert? A: He rode on a camole

Learning Check M3 Give the molar mass to 0.1 g A. 1 mole of Br atoms = ________ B. 1 mole of Sn atoms = ________

Solution M3 Give the molar mass to 0.1 g A. 1 mole of Br atoms = 79.9 g/mole B. 1 mole of Sn atoms = 118.7 g/mole

Molar Mass of Compounds Mass in grams of 1 mole of a compound is equal numerically to the sum of the atomic masses of the atoms in the compound. 1 mole of CaCl2 = ? grams 1 mole Ca x 40.1 g/mole = 40.1 g/mole + 2 moles Cl x 35.5 g/mole = 71.0 g/mole 111.1 g/mole

1 mole of N2O4 = ? grams 2 moles N x 14.0 g/mole = 28.0 g/mole + 4 moles O x 16.0 g/mole = 64.0 g/mole 92.0 g/mole

Learning Check M4 A. 1 mole of K2O = ______g B. 1 mole of antacid Al(OH)3 = ______g

Solution M4 A. 1 mole of K2O 2 K x 39.1 g/mole = 78.2 g/mole + 1 O x 16.0 g/mole = 16.0 g/mole 94.2 g/mole B. 1 mole of antacid Al(OH)3 1 Al x 27.0 g/mole = 27.0 g/mole + 3 O x 16.0 g/mole = 48.0 g/mole + 3 H x 1.0 g/mole = 3.0 g/mole 78.0g/mole

Learning Check M5 Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. It has a molar mass of 1) 40.0 g/mole 2) 262.0 g/mole 3) 309.0 g/mole

Solution M5 Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. It has a molar mass of 3) 309.0 g/mole 17C (12.0) + 18H (1.0) + 3F (19.0) + 1N (14.0) + 1 O (16.0)

Molar Mass Factors for CH4 Methane CH4 known as natural gas is used in gas cook tops and gas heaters. Express the molar mass of methane in the form of conversion factors. Molar mass of CH4 = 16.0 g 16.0 g CH4 and 1 mole CH4 1 mole CH4 16.0 g CH4

Learning Check M7 Acetic acid CH3COOH is the acid in vinegar . It has a molar mass of 60.0 g/mole. 1 mole of acetic acid = ____________ 1 mole acetic acid or g acetic acid g acetic acid 1 mole acetic acid

Solution M7 Acetic acid CH3COOH is the acid in vinegar . It has a molar mass of 60.0 g/mole. 1 mole of acetic acid = 60.0 g 1 mole acetic acid or 60.0 g acetic acid 60.0 g acetic acid 1 mole acetic acid

Calculations with Molar Mass Moles Number of grams molar mass Both Avogadro’s number and the molar mass can be used as conversion factors.

Let us look at both of these unit factors: 12.00 g Carbon-12 1 mole of Carbon-12 atoms = 1 1 mole carbon-12 6.022 x 1023 atoms of carbon-12 = 1 These two give us the ability to….

Q: What does Avogadro put in his hot chocolate? A: Marsh-mole-ows!

All About Mole Calculations How many moles are in 22 grams of copper metal?

The Four Steps to Solving Mole Problems: Looking at the diagram above (your roadmap), we can see that we are going between grams and moles, which is a one-step conversion. Furthermore, we can see that we need to use the atomic mass of copper as our conversion factor.

Step 2: Make a T-chart, and put whatever information the problem gave you in the top left. Put the units of whatever you were given in the bottom right of the T Put the units of what you want to find in the top right.

Step 3: Put the conversion factors into the T-chart in front of the units on the right. As we saw from the "map", the conversion factor between grams and moles is the atomic mass of copper. Because we measure atomic mass in grams, you need to put the atomic mass in front of the unit "grams of copper". What do you put in front of moles? Whenever you do a calculation of this kind, you need to put "1" in front of moles, like you see here:

And that's how you do a one-step problem of this kind! Step 4: Cancel out the units from the top left and bottom right, then find the answer by multiplying all the stuff on the top together and dividing it by the stuff on the bottom. In this case, you'd multiply 22 by one and divide the result by 63.5. Your answer, 0.35 moles of copper:                                                                                                                        And that's how you do a one-step problem of this kind!

Moles and Grams 3.00 moles Al ? g Al Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al? 3.00 moles Al ? g Al

Setup 3.00 moles Al 27.0 g Al 1 mole Al Molar mass of Al 1 mole Al = 27.0 g Al Setup 3.00 moles Al 27.0 g Al 1 mole Al = Answer = 81.0 g Al

Learning Check M9 The artificial sweetener aspartame (Nutri-Sweet) formula C14H18N2O5 is used to sweeten diet foods, coffee and soft drinks. How many moles of aspartame are present in 225 g of aspartame?

Solution M9 1. Molar mass of Aspartame C14H18N2O5 (14 x 12.0) + (18 x 1.0) + (2 x 14.0) + (5 x 16.0) = 294.0 g/mole 2. Setup 225 g aspartame 1 mole aspartame 294.0 g aspartame = 0.765 mole aspartame

Q: How would you describe Avogadro's room while he was a teenager? A: A Molar mess