Moles GPS 13 -write 6.022 x 10^23 on the board -ask: ever baked a cake? What if the recipe called for 6.02 x 10^23 individual crystals of sugar? Of course, that would be ridiculous. What do we use instead (cup)? So we have a unit of measurement when baking…we use cups, tablespoons, and teaspoons. Same thing in chemistry. I would never ask you to count out atoms of an element or ions/molecules in a compound. Not only is it ridiculous, it’s impossible to do with just your eyes alone. When we are talking about a huge amount of something, we use moles (which is 6.02 x 10^23 of something) to make our counting process much faster and easier. So, instead of saying I have 6.02 x 10^23 crystals of sugar, you can say I have exactly one mole of sugar. - If you were to try to count out 6.022 x 10^23 of something, how long to you think it would take? 4 generations.

The Mole: A unit of measurement Moles are a unit of measurement much like other units of measurement you are familiar with. Examples of familiar units of measurement: 12 eggs = 1 dozen or 12 eggs/dozen 4 quarts = 1 gallon or 4 quarts/gallon 100 pennies = 1 dollar or 100 pennies/dollar 12 inches = 1 foot or 12 inches/foot

Moles: A unit of measurement Moles can be used to express or to calculate the following: The number of particles in a sample The mass of a sample The volume of a gas (at 1 atm pressure, 0˚C)

Mole Map Moles Mass: grams Particles: Molar Mass grams/mole Particles: atoms, ions, formula units, molecules Moles 6.02 x 1023 particles/mole 22.4 liters/mole Gas Volume: liters

Avogadro’s Number 602,000,000,000,000,000,000,000 particles = 1 mole 6.02 x 1023 particles / mole 1 mole of Cl atoms 6.02 x 1023 atoms of Cl

“Particles” include the following: Water (H2O) Copper (Cu) Sodium Chloride (NaCl) molecules atoms formula unit (boxed in) ions: Na+ and Cl-

Dimensional Analysis: Converting Units Dimensional analysis: Using equivalencies to convert units for a substance Example: Convert 24 inches to feet (12 inches = 1 foot)

Dimensional Analysis: Converting Units Examples: Convert 275 eggs to dozens (12 eggs = 1 dozen) Convert 2.75 dozen to eggs

Conversions: Particles and Moles Example: How many molecules of water are there in 3.0 moles of water? - Work problem on board 1.8 x 1024 molecules of water

Conversions: Particles and Moles Example: How many moles of barium chloride are there in 9.28 x 1033 formula units of BaCl2? 1.54 x 1010 moles of BaCl2

Conversions: Particles and Moles Example: How many moles of magnesium are in 4.21 x 1023 atoms of magnesium? 0.699 moles of magnesium

Mole Map Moles Mass: grams Particles: Molar Mass grams/mole Particles: atoms, ions, formula units, molecules Moles 6.02 x 1023 particles/mole 22.4 liters/mole Gas Volume: liters

Molar Mass 1 mole He = 4.0 g He 1 mole Cu = 63.5 g Cu 1 mole Hg = 200.6 g Hg 1 mole S = 32.1 g S

Molar Mass = grams/mole Molar Mass (a.k.a. Formula Mass, Formula Weight, Molecular Weight) the mass of one mole of a given compound or element Molar Mass = grams/mole The molar mass of an element is simply its average atomic mass with grams/mole as units Example: Find the molar mass of Nitrogen - Notice that in all of the previous problems, you were given the amount of substance in moles. However, most of our measurements in chemistry are in grams. Therefore, you must be able to convert from grams to moles using molar mass. 14.0 g/mol

Conversions: Grams and Moles Example: How many moles of sodium are in 56.32 grams of sodium? - work problem on board 2.45 mol Na

Molar Mass of a Compound 17.04 g/mol

Molar Mass of a Compound 1 mole of water, H2O, on the balance 18.0 g of water = 1 mole of water

Molar Mass of a Compound Molar mass of a compound: use “SSMT” chart Example: Find the molar mass of K2S S S M T *multiply across, add down total column Symbol Subscript Molar mass Total K 2 x 39.1 = 78.2 S 1 x 32.1 = 32.1 + 110.3 g/mol

Molar Mass of a Compound Determine the molar mass for the following: Na2CO3 Pb(NO3)2 106.0 g/mol - Molar mass is a bit more complex for compounds….must add up the atomic mass for each atom of each element present in the compound. - do SSMT charts for each on the board 331.2 g/mol

Conversions: Grams and Moles Example: What is the mass (in grams) of 1.50 mole of potassium sulfate? 261 grams of K2SO4

Conversions: Grams and Moles Example: How many moles of copper (II) nitrate are in 544 grams of Cu(NO3)2? 2.90 moles of copper (II) nitrate

Mole Map Moles Mass: grams Particles: Molar Mass grams/mole Particles: atoms, ions, formula units, molecules Moles 6.02 x 1023 particles/mole 22.4 liters/mole Gas Volume: liters

Conversions: Particles and Grams There is no single conversion factor between particles and grams. You must always convert to moles first.

Conversions: Particles and Grams Example: How many atoms of Cu are in 121.5 grams of Cu? 121.5 g Cu 1 mol Cu 6.02 x 1023 atoms Cu = 63.5 g Cu 1 mol Cu 1.15 x 1024 atoms Cu

Conversions: Particles and Grams Example: How many molecules of water are present in 39 grams of water? 1.3 x 1024 molecules of water

Conversions: Particles and Grams Example: How many grams of gold are there in 4.21 x 1023 atoms of gold? 138 grams of gold

Mole Map Moles Mass: grams Particles: Molar Mass grams/mole Particles: atoms, ions, formula units, molecules Moles 6.02 x 1023 particles/mole 22.4 liters/mole Gas Volume: liters

Molar Volume of a Gas Molar Volume = 22.4 L/mol Molar volume of a gas: The volume of one mole of a gas at standard temperature and pressure STP: temperature = 0ºC pressure = 1 atmosphere - Think about a balloon filled with 22.4 liters of helium. If the temperature is zero celcius and the pressure is one atmosphere, then that would be exactly one mole of helium.

Molar Volume of a Gas

Conversions: Liters and Moles Example How many moles of any gas are present in 12.5 liters of any gas at STP? 0.558 moles of gas

Conversions: Liters and Grams Example How many grams of He gas are present in 82 liters of He gas at STP?

Conversions: Liters and Particles Example How many liters of CO2 gas are present in 2.1 x 1025 molecules of CO2 gas at STP?

Percent Composition The percentage of mass that each element contributes to the total mass of the compound % Comp. = Molar mass of element x 100 Molar mass of entire compound Example: Percent composition of Water 11%H - fruit salad analogy 89% O

Percent Composition Symbol Subscript Molar mass Total K 2 x 39.1 = 39.1 = 78.2 S 1 x 32.1 = 32.1 + 110.3 g/mol % K = 78.2 / 110.3 x 100 = 70.9% K % S = 32.1 / 110.3 x 100 = 29.1 % S

Percent Composition % Al = 15.8 % % S = 28.1 % % O = 56.14 % Example: Find the percent composition for each element in Al2(SO4)3 - work problem on board % Al = 15.8 % % S = 28.1 % % O = 56.14 %

Empirical Formula The empirical formula for a compound represents the smallest whole number molar ratio of elements in that compound two moles hydrogen one mole oxygen Empirical Formula from Mass (grams) of Elements: 1. Convert each element’s mass to moles 2. Divide by the smallest number of moles 3. Round to the nearest whole number and use as subscripts H2O

Empirical Formula Na2SO3 Example: Determine the empirical formula for a compound containing 36.5 grams of sodium, 25.4 grams of sulfur, and 38.1 grams of oxygen. Na2SO3 16

Empirical Formula Example: What is the empirical formula for a compound that has 38.67 g of carbon, 16.22 g hydrogen, and 45.11 g of nitrogen? - work example on board CH5N

Empirical Formula from Lab Data An iron chloride sample was reacted with excess lead in order to determine the formula of the iron chloride. Determine the formula for the iron chloride compound. Mass (grams) Initial mass of iron chloride 4.89 g Mass of solid iron produced 1.30 g

Empirical Formula from % Composition Same procedure, however start by assuming 100 g sample. Why assume 100g sample? It makes for easier math! Sucrose C12H22O11 - the percentage composition for each element will remain the same no matter the sample size, so 100 g is picked for easier calculations

Empirical Formula from % Composition Example: What is the empirical formula for a compound that has a percent composition of 40.0% carbon, 6.71% hydrogen, and 53.3% oxygen? CH2O

Molecular Formula from Empirical Example: If the empirical formula for a compound is CH2Cl and the molar mass for the molecular formula is 98.96 g/mol, what is the molecular formula? empirical molecular CH2Cl ? 49.5 g/mol 98.96 g/mol 98.96 / 49.5 = 2 Molecular twice as massive as empirical Find using “SSMT” Molecular C2H4Cl2

Molecular Formula from Empirical Example: If empirical formula for a compound is CH2O and the molar mass of the molecular formula is 90.09 g/mol, what is the molecular formula? molecular = C3H6O3

Empirical Formula: Hydrates Hydrate: a compound that contains water molecules within its crystalline structure Example: Copper(II) sulfate pentahydrate 5 water molecules within crystal SO42- CuSO4 • 5H2O H2O Cu2+

Empirical Formula: Hydrates Heating a hydrate produces water vapor and anhydrous salt Lab simulation: http://group.chem.iastate.edu/Greenbowe/sections/projectfolder/flashfiles/stoichiometry/empirical.html

Empirical Formula: Hydrates In a hydrate, the coefficients represent the mole ratio between the anhydrous salt and the water: one mole CuSO4 five moles H2O Empirical Formula for a Hydrate: 1. Determine the mass of water and mass of anhydrous salt 2. Convert each mass to moles 3. Divide by the smallest number of moles 4. Round to the nearest whole number and use as subscripts CuSO4 • 5H2O

Empirical Formula: Hydrates Example: A 9.87 gram sample of BaCl2 • __H2O is heated. After it is heated completely, the sample now has a mass of 7.84 grams. Find the empirical formula for the hydrate. / 0.03766 = 2.99 / 0.03766 = 1 BaCl2 • 3H2O

Empirical Formula: Hydrates Example: A 100.0 gram sample of FeCl3 • __H2O is heated. After it is heated completely, the sample now has a mass of 56.28 grams. Find the empirical formula for the hydrate.

Hydrate Formula from Lab Data A student is assigned the task of determining the number of moles of water in one mole of MgCl2• n H2O. The student collects the data shown below: Determine the formula for the hydrate.

SOL covered during lesson CH 4 a, b CH 3 c

Extra Slides

Empirical/Molecular Formula Example: Caffeine has a percent composition of 49.48% carbon, 5.15% hydrogen, 28.87% nitrogen, and 16.49% oxygen. If the molar mass of the compound is 194.2 g/mol, what is the molecular formula of caffeine? C8H10N4O2

Empirical Formula empirical = CH2Cl molecular = C2H4Cl2 Example: What is the empirical formula for a compound that has a percent composition of 71.65% chlorine, 24.27% carbon, and 4.07% hydrogen? If the molar mass for the molecule is 98.96 g/mol, what is the molecular formula? empirical = CH2Cl molecular = C2H4Cl2

Empirical/Molecular Formula Example: What is the empirical formula for a compound that has a percent composition of 40.0% carbon, 6.71% hydrogen, and 53.3% oxygen? If the molar mass of the compound is 60.06 g/mol, what is the molecular formula? empirical = CH2O molecular = C2H4O2

The Mole Two-step problems: Example: How many atoms of oxygen are in 3.9 moles of carbon dioxide? - recall: smallest units of elements are atoms, of covalent compounds are molecules, of ionic compounds are ions or formula units (draw chart) 4.7 x 1024 atoms of O

The Mole Example How many hydroxide ions are there in 13.2 moles of Mn(OH)3? 2.38 x 1025 hydroxide ions