The Mole & Stoichiometry Quantitative study of substances and their relationship to each other in chemical reactions. The “Math” of Chemistry

The Mole Similar to how a dozen = 12 things One mole = 602 billion trillion things 602,000,000,000,000,000,000,000 6.02 X 1023 (in scientific notation)

6.02 X 1023 is called Avogadro’s number. Amedeo Avogadro (1776 – 1856) Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

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.

Mole Concept A mole is equal to 3 things: 1 mole = gram formula mass (molar mass) 1 mole = 6.02 X 1023 particles 1mole = 22.4 liters of a gas at STP

Mole Conversions

The Mole 1 mole Al = 6.02 X 1023 “atoms” 1 mole H2O = 6.02 x 1023 “molecules” Note: the NUMBER of particles is always the same, but the MASS of each mole will be very different! This is because atoms have different atomic masses.

Molar Mass Molar Mass = Mass of 1 mole of particles (in grams) Use average atomic mass rounded to the nearest whole number 1 mole of C atoms = 12 g 1 mole of Mg atoms = 24g 1 mole of Cu atoms = 63.5 g

Learning Check! Find the molar mass = ________ g/mole 1 mole of Br atoms 1 mole of Sn atoms = ________ g/mole

Molar Mass of Molecules and Compounds Called “gram formula mass” or “molecular mass” Add up atomic masses of atoms in the formula 1 mole of CaCl2 1 mole Ca x 40 g/mol + 2 moles Cl x 35.5 g/mol = 111 g/mol

Learning Check! Molar Mass of K2O = ________ B. Molar Mass of Al(OH)3 = ________

Learning Check Prozac, C17H18F3NO, is a widely used antidepressant that inhibits uptake of serotonin by the brain. Find molar mass. C: 12 g/mol x 17 = H: 1 g/mol x 18 = F: 19 g/mol x 3 = N: 14 g/mol x 1 = O: 16 g/mol x 1 = Total = g/mol

Calculations with Molar Mass # moles = given mass (grams) gram-formula mass

Converting Moles and Grams 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

On Ref Tables find molar mass of Al 1 mole Al = 27 g Al 3.00 moles Al = x grams 27 g/mol Answer = 81 g Al

Mole/Gram Conversion Practice If you have 30 grams of CO2 how many moles do you have? If you have 6 moles of MgBr2 how many grams do you have?

Learning Check! The artificial sweetener aspartame (Nutra-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?

Add up the formula mass C: 12 g/mol x 14 = H: 1 g/mol x 18 = N: 14 g/mol x 2 = O: 16 g/mol x 5 = Total = g/mol # moles = ____grams = ______ mol g/mol

Particles and Moles 1 mole = 6.02 x 1023 particles # Moles = # particles 6.02 x 1023 particles

A Mole of Particles Contains 6.02 x 1023 particles = 6.02 x 1023 C atoms = 6.02 x 1023 H2O molecules = 6.02 x 1023 NaCl “formula units” (technically, ionics are compounds not molecules so they are called formula units) 1 mole C 1 mole H2O 1 mole NaCl

A Mole of Gas 1 mole = 22.4 Liters of any gas at STP # Moles = # liters of gas (at STP) 22.4 Liters

Percent Composition and Chemical Quantities Percent Composition and Empirical Formulas Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

Percent Composition Formula on Ref. Tables % Comp. by Mass = Mass of Part x 100 Mass of Whole

Percent Composition Is the percent by mass of each element in a formula. Ex: Calculate the percent composition of CO2. CO2 = 1 (12g) + 2 (16 g) = 44 g/mol) 12. g C x 100 = 27.27 % C 44g CO2 32 g O x 100 = 72.72 % O 44 g CO2

Learning Check What is the percent composition of lactic acid, C3H6O3, a compound that appears in the blood after vigorous activity?

Solution STEP 1 3 (12) + 6 (1) + 3 (16) = 90 g/mol STEP 2 %C = 36 g C x 100 = 40% C 90 g %H = 6 g H x 100 = 6.7% H %O = 48 g O x 100 = 53.3% O

Percent Composition What is the percent carbon in C5H8NO4 (the glutamic acid used to make MSG monosodium glutamate), a compound used to flavor foods and tenderize meats? a) 8.22 %C b) 24.3 %C c) 41.1 %C

Solution 64.58 %C Molar mass C7H14O2 = 7(12) + 14(1) + 2(16) = 130g/mol % C = 84g C x 100 = 64.6 % C 130g

You Try The chemical isoamyl acetate C7H14O2 gives the odor of pears. What is the percent carbon in isoamyl acetate? 1) 7.102 %C 2) 35.51 %C 3) 64.58 %C

Percent of Water in a Hydrate Hydrate: an ionic compound with water molecules loosely attached. Ex: BaCl2 ∙ 2H2O Anhydrous Salt: the hydrate with the water driven off by heating in a crucible

Finding % from Formula Ex: BaCl2 ∙ 2H2O

Finding % from Experimental Data Ex: If 11 grams of an unknown hydrate is heated in a crucible to a constant mass of 9.5 grams calculate the % of water that was in the hydrate.

Chemical Formulas and Moles Formulas can tell us: Relative number of atoms of each element in compound Ex: NO2 2 atoms of O for every 1 atom of N Mole ratio of each element in a formula unit Ex: 1 mole of NO2 contains 2 moles of O atoms to every 1 mole of N atoms Thus if we know or can determine the relative number of moles of each element in a compound, we can determine a formula for the compound.

Types of Formulas Empirical Formula: expresses smallest whole number ratio of the atoms present. Ex: ______________ (Note: Ionic formulas are always empirical) Molecular Formula: states actual number of each kind of atom found in one molecule of the compound.

Writing Empirical Formulas The simplest whole number ratio of the atoms. Some molecular formulas can be reduced to their empirical form Calculated by dividing the subscripts in the actual (molecular) formula by a whole number to give the lowest ratio. C5H10O5  5 = C1H2O1 = CH2O actual (molecular) empirical formula formula

Molecular and Empirical Formulas The molecular formula is the same or a multiple of the empirical.

Learning Check A. What is the empirical formula for C4H8? 1) C2H4 2) CH2 3) CH B. What is the empirical formula for C8H14? 1) C4H7 2) C6H12 3) C8H14 C. Which is a possible molecular formula for CH2O? 1) C4H4O4 2) C2H4O2 3) C3H6O3

Find Empirical Formula Given Grams 1. Determine the mass in grams of each element present, if necessary. 2. Calculate number of moles of each element. Divide each by the smallest number of moles to obtain the simplest whole number ratio. Note: If whole numbers are not obtained* multiply through by the smallest number that will give all whole numbers

Find Empirical Formula Given Grams A compound contains 7.31 g Ni and 20.0 g Br. Calculate its empirical (simplest) formula.

Solution Convert 7.31 g Ni and 20.0 g Br to moles. Moles of Ni = 7.31 g Ni = 0.124 mol Ni 59 g Ni Moles of Br = 20.0 g Br = 0.250 mol Br 80 g Br Divide by smallest # moles to get ratio 0.124 mol Ni = 1 Ni 0.250 mol Br = 2 Br 0.124 0.124 Write ratio as subscripts: NiBr2

Converting Decimals to Whole Numbers When number of moles for an element is a decimal, all the moles are multiplied by a small integer to obtain whole number.

A sample of a brown gas, a major air pollutant, is found to contain 2 A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine empirical formula: You need mole ratios so convert grams to moles moles of N = 2.34g of N = _______moles of N 14 g/mole moles of O = 5.34 g = _________moles of O 16 g/mole Formula: _______________

Empirical Formula from % Composition A substance has the following composition by mass: 60.80 % Na ; 28.60 % B ; 10.60 % H What is the empirical formula of the substance?

Consider a sample size of 100 grams 60.80 grams of Na 28.60 grams of B 10.60 grams H Determine the number of moles of each Determine the simplest whole number ratio

Empirical Formula from % Composition Aspirin is 60.0% C, 4.5 % H and 35.5 % O. Calculate its empirical (simplest) formula.

Solution Calculate moles of each element in 100 g. 100 g aspirin contains 60.0% C or 60.0 g C, 4.5% H or 4.5 g H, and 35.5% O or 35.5 g O. 60.0 g C = 5.00 mol C 12 g C 4.5 g H = 4.5 mol H 1 g H 35.5 g O = 2.22 mol O 16 g O

Solution (continued) Divide by the smallest number of mol. 5.00 mol C = 2.25 mol C (decimal) 2.22 4.5 mol H = 2.0 mol H 2.22 mol O = 1.00 mole O

Solution (continued) Use the lowest whole number ratio as subscripts When the moles are not whole numbers, multiply by a factor to give whole numbers, in this case x 4 . C: 2.25 mol C x 4 = 9 mol C H: 2.0 mol H x 4 = 8 mol H O: 1.00 mol O x 4 = 4 mol O Using these whole numbers as subscripts the simplest formula is C9H8O4

Finding the Molecular Formula Molecular Mass (GFM) of a compound is either equal to or some whole number multiple of the empirical formula’s mass. Molecular Mass = “Magic Number” Empirical Mass Distribute this number through the Empirical formula to determine the Molecular formula

Finding the Molecular Formula A compound has an empirical formula of NO2. The colorless liquid, used in rocket engines has a molar mass of 92.0 g/mole. What is the molecular formula of this substance?

Finding the Molecular Formula A compound has an empirical formula of CH2O. The white crystal, has a molar mass of 180.0 g/mole. What is the molecular formula of this substance?