Atomic Masses & the MOLE…

Neon is a gas that can be found in the atmosphere. Dry air contains about 0.002% Ne That’s 500,000,000,000,000,000 atoms of neon every breath Scientists can deal with atoms quant-itatively because they know some fundamental properties of the atoms of each element

An atom of Oxygen -16 literally weighs 0.0000000000000000000000266 g Masses of atoms expressed in grams are extremely small. An atom of Oxygen -16 literally weighs 0.0000000000000000000000266 g

-For most calcs in chemistry it is easier to use a relative atomic mass. - For relative masses, an atom was arbitrarily chosen as the standard, by which all other masses are compared

Atomic Mass A. Relative Mass is when you measure the mass of all atoms based on the measurement of one particular atom.

6 CARBON C 12 C-12 atom acts as the standard to compare all other atoms A single C-12 atom was assigned a mass of 12 atomic mass units (amu) 1 amu is exactly 1/12 of the mass of a C-12 atom Carbon has 12 nucleons therefore, the mass of a proton = 1 amu

3. The masses of all other atoms are based on the mass of 1 amu H has 1 proton= 1 amu He has 2 protons and nuetrons= 4 amus

A proton weighs 1.007276 amu A neutron weighs 1.008665 amu

A. Most elements exist in nature as isotopes II. Average Atomic Mass A. Most elements exist in nature as isotopes 75% of all of the Cl atoms found in nature are the isotope Cl-35 25% of the all of the Cl atoms found in nature are the isotope Cl-37

1.Average atomic mass is the mass on the PT and is the average of all of the naturally occurring isotopes of an element

Example: We have 25 marbles that each weigh 2 g and 75 marbles that weigh one gram. What is the average atomic mass for these marbles?

2. Calculating average atomic masses: a. Cu 69.17% Cu-63 has a mass of 63 amu, 30.83% Cu-65 has a mass of 65 amu. It’s calculated by multiplying the atomic mass of each isotope by its abundance and adding the results.

63.6 amu Cu-63 (0.6917)(63 amu) Cu-65 + (0.3083)(65 amu) The reported average atomic mass of naturally occurring Cu is 63.55 amu.

Your Turn: b. Practice #1. Gallium consists of two isotopes of masses 68.95 amu and 70.95 amu with abundances of 60.16% and 39.84%, respectively. What is the average atomic mass of gallium?

c. Practice #2. Naturally occurring element X exists in three isotopic forms: X-28 (27.977 amu, 92.21% abundance), X-29 (28.976 amu, 4.70% abundance), X-30 (29.974 amu, 3.09% abundance) . Calculate the atomic weight of X.

B. Relating Mass to the number of Atoms

It is impractical to get caught up into working with 1 atom’s mass because usually you working with a large number of atoms. Scientists were challenged to figure out a way to define a collection of particles And which could still be described in terms of a relative mass

1. The average C atom with an atomic mass of 12 1. The average C atom with an atomic mass of 12.0 amus is 12 times heavier than the average H atom So 100 C atoms are 12 times heavier than 100 H atoms b. any # of C atoms would be 12 times heavier than the same # of H atom

If we assume we can relate the relative masses from the PT in the terms of grams With the literal masses of an atom (g) for each atom we use we seem to get the same number of atoms Oxygen:

Counting Atoms Hydrogen: Carbon:

Counting Atoms The number of atoms that are in the relative masses of elements identical in grams to the atomic masses on the PT is called Avogadro’s Number And is defined as a mole The mole becomes a counting unit much like the dozen. 1 dozen eggs = 12 eggs 1 mole of eggs = 602,000,000,000,000,000,000,000 eggs

Counting Atoms The word “mole” was introduced by Wilhelm Oswald, who derived the term from the word moles meaning a “heap” or “pile.” We are just defining the pile as con-taining 6.02x1023 items Because it is such a huge number of items we usually reserve the mole for atoms or molecules 1 mole is always = 6.02 x 1023 items

Counting Atoms The mole, whose abbreviation is “mol”, is the SI base unit for meas-uring amount of a pure substance. The mole is the chemist’s six-pack or dozen. Many objects in our everyday lives come in similar counting units. 1 ream = 500 sheets of paper 1 pair of socks = 2 socks 1 cube = 24 cans

REPRESENTATIVE PARTICLES & MOLES Atomic Nitrogen Atom N 6.02x1023 Nitrogen gas Molec. N2 Water H2O Calcium ion Ion Ca2+ Calcium Fluoride Formula unit CaF2 CHEMICAL REP. PARTICLE SUBTANCE REPRESENTATIVE FORMULA PARTICLE IN 1 MOL

Counting Atoms We will learn in the near future that when a chemist reasons through a chemical reaction (recipe) they think in terms of X number of mols of this compound reacts with Y number of mols of this compound. So we need to know how to calculate the number of molecules or atoms are involved in that X number of mols

How many moles of Magnesium Counting Atoms Using the mole in calculations #1 How many moles of Magnesium is 1.25 x 1023 atoms of Magnesium? unit equality: 1 mol Mg = 6.02 x 1023 atoms Mg

Counting Atoms = .208 mol Mg The desired conversion is: atoms moles 1 mole Mg 1.25x1023 atoms Mg 6.02x1023atoms Mg = .208 mol Mg

Your Turn: To make sure adequate amounts of product AB is being made during a rxn you might need 3.33 mols of A reacting with 2.68 mols of B. How many atoms of A are reacting with how many atoms of B? If you burn sugar (C12H22O11) in pure oxygen you produce carbon dioxide and water as products. To burn 6.02x1023 molecules of sugar you also need 7.22x1024 molecules of oxygen and you produce 6.62x1024 molecules of water and 7.22x1024 molecules of carbon dioxide. How many mols are reacted or produced for each component of the rxn?

Counting Atoms Now suppose you want to determine how many atoms are in a mol of a compound or molecule To do this you must know how many atoms are involved in the molecule. To determine the number of atoms represented in a molecule requires knowing the chemical formula Eg, each molecule of Carbon Dioxide (CO2) is composed of 3 atoms

Counting Atoms 1 mole of Carbon Dioxide contains Avogadro’s number of Carbon Dioxide molecules. Thus a mole of CO2 contains three times Avogadro’s # of atoms

How many atoms of Carbon are in 2.12 mols of Propane (C3H8)? Counting Atoms Using the mole in calculations #2 How many atoms of Carbon are in 2.12 mols of Propane (C3H8)? unit equalities: 1 mol C3H8 = 6.02x1023 molecules C3H8 1 molecule C3H8 = 3 atoms C

The desired conversions are: Counting Atoms The desired conversions are: moles  molecules  atoms 6.02x1023 molecules C3H8 2.12 mols C3H8 3 atoms C 1 molecule C3H8 1 mole C3H8 =3.83x1024 atoms C

Your Turn: Back to burning sugar, 1 mol of sugar (C12H22O11) was burned with 12 mols of oxygen (O2) to produce 11 mols of water (H2O) and 12 mols of Carbon dioxide (CO2). How many total atoms of oxygen are burned in the reaction (reactants), and how many total atoms of oxygen are produced in the reaction (products)?

Counting Atoms We can also relate mass to the number of atoms and the mole. Relative atomic masses and the mol can be used to develop a method of measuring the amount of a sample. If we had a pile of C atoms that weighed 12 g and a pile of H atoms that weighed 1g each pile would contain the same number of atoms or 6.02x1023 atoms

Counting Atoms The gram atomic masses of any 2 elements (since they are relative to C) must contain the same # of atoms A pile of any atom that corresponds to its average atomic mass from the PT contains exactly 6.02x1023 atoms of that element. And is equal to how much 1 mole of that sample would weigh in grams

18.99g F atoms=1 mol F atoms=6.02x10 F atoms Counting Atoms What this allows us to do is to use the mass off of the periodic table to represent the mass of 1 mole (or 6.02x1023 atoms) of that element 1 mol of C atoms weighs 12.01 g 1 mol of H atoms weighs 1.008 g 1 mol of W atoms weigh 183.8 g 18.99g F atoms=1 mol F atoms=6.02x10 F atoms 23

Counting Atoms This new version of mass from the periodic table is called the gram molar mass, or molar mass. Molar Mass = mass of 1 mole of atoms/molecules/or formula units in grams abbreviated = MM units = grams/mol

Counting Atoms We get the mass of 1 mole of any element off of the Periodic Table So how do we figure out the mass of a mole of a compound rather than just an element? To answer that question you must have the formula of the compound.

Counting Atoms What is the mass of 1 mole of Sulfur Trioxide (SO3) A.K.A. Molar Mass? The formula of a compound tells you how many atoms of each element combine to make the representative particle of that compound. Model Formula SO 3 H O 2 2 Hydrogen atoms per molecule 3 oxygen atoms per molecule

Counting Atoms You can calculate the mass of a mol-ecule of SO3 by adding the MM of each of the atoms in the molecule The mass of 1 mole of S is 32.1g. The mass of 3 atoms of O is 3 times the MM of a single O atom, or (3)(15.99g) = 47.97g So MM of 1 molecule of SO3 is 32.1g + 47.97g = 80.1 g/mol

6.02x1023 molecules of the compound – it would weigh 180 grams Counting Atoms What is the MM of glucose (C6H12O6)? (6C’S)(12.011g/mol) = 72.066g/mol (12H’S)(1.008 g/mol) = 12.096g/mol (6O’S)(15.99 g/mol) = 95.94g/mol 180.1g/mol 1 mole of C6H12O6 or 6.02x1023 molecules of the compound – it would weigh 180 grams

Practice Time: Determine the mass of 1 mole (Molar mass) of each of the following: Zn Gd Zn(C2H3O2)2 (NH4)3PO4 C12H22O11

How many grams are in 9.45 mol of Dinitrogen Trioxide (N2O3) Counting Atoms Using the mole in calculations: How many grams are in 9.45 mol of Dinitrogen Trioxide (N2O3) The only connection to N2O3 and its mass is how much 1 mol of the compound weighs. But, using it as a comparison we can calculate the mass of 9.45 mol.

Counting Atoms Step 1: Determine the mass of 1 mol of N2O3 (2N’s)(14.01g) = 28.02g (3O’s)(15.99g) = 47.97g 75.99g If 1 mole of N2O3 weighs 75.99g than how much will 9.45 mols of N2O3 weigh?

Counting Atoms 75.99 g N2O3 9.45 mol N2O3 1 mol N2O3 =718 g N2O3 Step 2: Convert the given moles to grams using the Molar mass equality. 75.99 g N2O3 9.45 mol N2O3 1 mol N2O3 =718 g N2O3

Counting Atoms Find the number of moles of 92.2g of Iron (III) Oxide (Fe2O3) The only connection to the mass of Fe2O3 and how that corresponds to mols is how that 1 mol of the compound weighs a certain # of grams. Using that we can figure out how many moles weigh 92.2 g

Counting Atoms (2Fe’s)(55.85g) = 111.7g (3O’s)(15.99g) = 47.97g Step 1: Determine the mass of 1 mol of Fe2O3 (2Fe’s)(55.85g) = 111.7g (3O’s)(15.99g) = 47.97g 159.67g If 1 mole of Fe2O3 weighs 157.67g than how many mols will weigh 92.2 g of Fe2O3?

Counting Atoms 1 mol Fe2O3 92.2 g Fe2O3 159.67 g Fe2O3 =.577mol Fe2O3 Step 2: Convert the given mass to mols using the Molar mass equality 1 mol Fe2O3 92.2 g Fe2O3 159.67 g Fe2O3 =.577mol Fe2O3

Practice Time: Vitamin C (C6H8O6), cannot be stored by the body and therefore, must be present in the diet. If an orange contains 70 mg of Vit C how many oranges are necessary to consume 2.5 mols of Vit C?

Counting Atoms Another generality about the mole is that with matter in the gas phase we can develop another equality. Under the same conditions, equal volumes of gases contain equal numbers of particles. 1 mol of a gas will occupy the same volume as 1 mol of any other gas under the same conditions.

Molar Volume of a Gas 22.4 L 22.4 L 1 mole of any gas under the specific conditions of 0°C and 1 atm (STP) will occupy a volume of 22.4 L. 6.02x1023 molecules of O2 6.02x1023 molecules of CO2

What volume, in Liters, does 0.60 mol of SO2 gas occupy at STP? Counting Atoms What volume, in Liters, does 0.60 mol of SO2 gas occupy at STP? The only connection to the volume of any gas and how that corresponds to mols is that 1 mol of a gas occupies 22.4 Liters of space. Using that we can figure out the volume of 0.60 mols of a gas at STP.

Counting Atoms 22.4 L SO2 0.60 moles SO2 1 mole SO2 = 13 L SO2 Step 1: Use the equality 1 mol = 22.4 L to do the conversion 22.4 L SO2 0.60 moles SO2 1 mole SO2 = 13 L SO2

Practice Time: The Snoopy balloon featured at the Macy’s Thanksgiving Day Parade has a volume of 15650 ft3. How many moles of Helium are required to fill it up @ STP?

Counting Atoms If you have a 35.67g piece of Chro-mium metal on your car, how many atoms of Chromium do you have? You are given mass and asked for number of particles Let’s get some strategy

Counting Atoms = 4.130x1023 atoms of Cr 1 mole Cr 6.02x1023 atoms 1st convert given mass into moles To do this we use the molar mass (MM) of Cr which on the PT is 51.996g/mol Then we need to convert from mols to atoms using Avogadro’s number. 1 mole Cr 6.02x1023 atoms 35.67g Cr 51.996g Cr 1 mole Cr = 4.130x1023 atoms of Cr

Calculate the Missing Info… Formula Molar Mass Moles Mass Particles Gas Vol. @ STP CH4 1.5 mol H2SO4 79.0 g CO 9.03x1023 molecules Cu(NO3)2 93.8 g