 # Mass Relationships in Chemical Reactions

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Mass Relationships in Chemical Reactions
Chapter 3

Atomic mass is the mass of an atom in atomic mass units (amu)
Micro World atoms & molecules Macro World grams Atomic mass is the mass of an atom in atomic mass units (amu) By definition: 1 atom 12C “weighs” 12 amu On this scale 1H = amu 16O = amu 3.1

Average atomic mass of lithium:
Natural lithium is: 7.42% 6Li (6.015 amu) 92.58% 7Li (7.016 amu) Average atomic mass of lithium: (7.42% x 6.015) + (92.58% x 7.016) 100 = amu 3.1

Dozen = 12 Pair = 2 The mole (mol) is the amount of a substance that
contains as many elementary entities as there are atoms in exactly grams of 12C 1 mol = NA = x 1023 Avogadro’s number (NA) 3.2

Molar mass is the mass of 1 mole of in grams marbles atoms
eggs shoes Molar mass is the mass of 1 mole of in grams marbles atoms 1 mole 12C atoms = x 1023 atoms = g 1 12C atom = amu 1 mole 12C atoms = g 12C 1 mole lithium atoms = g of Li For any element atomic mass (amu) = molar mass (grams) 3.2

One Mole of: S C Hg Cu Fe 3.2

1 g = 6.022 x 1023 amu = molar mass in g/mol M NA = Avogadro’s number
1 amu = 1.66 x g M = molar mass in g/mol NA = Avogadro’s number 3.2

Do You Understand Molar Mass?
How many atoms are in g of potassium (K) ? 1 mol K = g K 1 mol K = x 1023 atoms K 1 mol K 39.10 g K x x 6.022 x 1023 atoms K 1 mol K = 0.551 g K 8.49 x 1021 atoms K 3.2

molecular mass (amu) = molar mass (grams)
Molecular mass (or molecular weight) is the sum of the atomic masses (in amu) in a molecule. SO2 1S 32.07 amu 2O + 2 x amu SO2 64.07 amu For any molecule molecular mass (amu) = molar mass (grams) 1 molecule SO2 = amu 1 mole SO2 = g SO2 3.3

Do You Understand Molecular Mass?
How many H atoms are in 72.5 g of C3H8O ? 1 mol C3H8O = (3 x 12) + (8 x 1) + 16 = 60 g C3H8O 1 mol C3H8O molecules = 8 mol H atoms 1 mol H = x 1023 atoms H 1 mol C3H8O 60 g C3H8O x 8 mol H atoms 1 mol C3H8O x 6.022 x 1023 H atoms 1 mol H atoms x = 72.5 g C3H8O 5.82 x 1024 atoms H 3.3

Heavy Light KE = 1/2 x m x v2 v = (2 x KE/m)1/2 F = q x v x B 3.4

Percent composition of an element in a compound =
n x molar mass of element molar mass of compound x 100% n is the number of moles of the element in 1 mole of the compound %C = 2 x (12.01 g) 46.07 g x 100% = 52.14% C2H6O %H = 6 x (1.008 g) 46.07 g x 100% = 13.13% %O = 1 x (16.00 g) 46.07 g x 100% = 34.73% 52.14% % % = 100.0% 3.5

Types of Formulas Empirical Formula
The formula of a compound that expresses the smallest whole number ratio of the atoms present. Ionic formula are always empirical formula Molecular Formula The formula that states the actual number of each kind of atom found in one molecule of the compound.

To obtain an Empirical Formula
1. Determine the mass in grams of each element present, if necessary. 2. Calculate the number of moles of each element. 3. Divide each by the smallest number of moles to obtain the simplest whole number ratio. If whole numbers are not obtained* in step 3), multiply through by the smallest number that will give all whole numbers * Be careful! Do not round off numbers prematurely

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 a formula for this substance. require mole ratios so convert grams to moles moles of N = 2.34g of N = moles of N 14.01 g/mole moles of O = g = moles of O 16.00 g/mole Formula:

Calculation of the Molecular Formula
A compound has an empirical formula of NO2. The colourless liquid, used in rocket engines has a molar mass of 92.0 g/mole. What is the molecular formula of this substance? empirical formula mass: (16.00) = g/mol n = molar mass = g/mol emp. f. mass g/mol n = 2 N2O4

Empirical Formula from % Composition
A substance has the following composition by mass: % Na ; % B ; % H What is the empirical formula of the substance? Consider a sample size of 100 grams This will contain: grams of Na, grams of B, and grams H Determine the number of moles of each Determine the simplest whole number ratio

g of O = g of sample – (g of C + g of H) 4.0 g O = 0.25 mol O
Combust 11.5 g ethanol Collect 22.0 g CO2 and 13.5 g H2O g CO2 mol CO2 mol C g C 6.0 g C = 0.5 mol C g H2O mol H2O mol H g H 1.5 g H = 1.5 mol H g of O = g of sample – (g of C + g of H) 4.0 g O = 0.25 mol O Empirical formula C0.5H1.5O0.25 Divide by smallest subscript (0.25) Empirical formula C2H6O 3.6

Mass Changes in Chemical Reactions
Write balanced chemical equation Convert quantities of known substances into moles Use coefficients in balanced equation to calculate the number of moles of the sought quantity Convert moles of sought quantity into desired units 3.8

Other units Molarity Gases Moles solute / L solution
22.4 L = 1 mole of ANY GAS at STP

Methanol burns in air according to the equation
2CH3OH + 3O CO2 + 4H2O If 209 g of methanol are used up in the combustion, what mass of water is produced? grams CH3OH moles CH3OH moles H2O grams H2O molar mass CH3OH coefficients chemical equation molar mass H2O 1 mol CH3OH 32.0 g CH3OH x 4 mol H2O 2 mol CH3OH x 18.0 g H2O 1 mol H2O x = 209 g CH3OH 235 g H2O 3.8

Limiting Reagents 6 red left over 6 green used up 3.9

Method 1 Pick A Product Try ALL the reactants
The lowest answer will be the correct answer The reactant that gives the lowest answer will be the limiting reactant

Limiting Reactant: Method 1
10.0g of aluminum reacts with 35.0 grams of chlorine gas to produce aluminum chloride. Which reactant is limiting, which is in excess, and how much product is produced? 2 Al + 3 Cl2  2 AlCl3 Start with Al: Now Cl2: 10.0 g Al 1 mol Al mol AlCl g AlCl3 27.0 g Al mol Al mol AlCl3 = 49.4g AlCl3 35.0g Cl mol Cl mol AlCl g AlCl3 71.0 g Cl mol Cl mol AlCl3 = 43.9g AlCl3

Solving for Multiple Products
Once you determine the LR, you should only start with it! A + B  X + Y + Z A  X B  X To find Y and Z B  Y B  Z Let’s say B is the LR! There is no need to use A to find Y and Z It will give you the wrong answer – a lot of extra work for nothing

Method 2 Convert one of the reactants to the other REACTANT
See if there is enough reactant “A” to use up the other reactants If there is less than the GIVEN amount, it is the limiting reactant Then, you can find the desired species

Do You Understand Limiting Reagents?
In one process, 124 g of Al are reacted with 601 g of Fe2O3 2Al + Fe2O Al2O3 + 2Fe Calculate the mass of Al2O3 formed. g Al mol Al mol Fe2O3 needed g Fe2O3 needed OR g Fe2O3 mol Fe2O3 mol Al needed g Al needed 1 mol Al 27.0 g Al x 1 mol Fe2O3 2 mol Al x 160. g Fe2O3 1 mol Fe2O3 x = 124 g Al 367 g Fe2O3 Start with 124 g Al need 367 g Fe2O3 Have more Fe2O3 (601 g) so Al is limiting reagent 3.9

Use limiting reagent (Al) to calculate amount of product that
can be formed. g Al mol Al mol Al2O3 g Al2O3 2Al + Fe2O Al2O3 + 2Fe 1 mol Al 27.0 g Al x 1 mol Al2O3 2 mol Al x 102. g Al2O3 1 mol Al2O3 x = 124 g Al 234 g Al2O3 3.9

Finding Excess Practice
10.0g of aluminum reacts with 35.0 grams of chlorine gas 2 Al + 3 Cl2  2 AlCl3 We found that chlorine is the limiting reactant, and 43.8 g of aluminum chloride are produced. 35.0 g Cl2 1 mol Cl2 2 mol Al g Al 71 g Cl mol Cl mol Al = 8.8 g Al USED! 10.0 g Al – 8.8 g Al = 1.2 g Al EXCESS Given amount of excess reactant Amount of excess reactant actually used Note that we started with the limiting reactant! Once you determine the LR, you should only start with it!

Theoretical Yield is the amount of product that would
result if all the limiting reagent reacted. Actual Yield is the amount of product actually obtained from a reaction. % Yield = Actual Yield Theoretical Yield x 100 3.10

Chemistry In Action: Chemical Fertilizers
Plants need: N, P, K, Ca, S, & Mg 3H2 (g) + N2 (g) NH3 (g) NH3 (aq) + HNO3 (aq) NH4NO3 (aq) 2Ca5(PO4)3F (s) + 7H2SO4 (aq) 3Ca(H2PO4)2 (aq) + 7CaSO4 (aq) + 2HF (g) fluorapatite