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Copyright © Houghton Mifflin Company. All rights reserved. 3–1

Chapter Three:

STOICHIOMETRY


Chemical Stoichiometry

• Stoichiometry - The study of quantities of materials consumed and produced in chemical reactions.

Atomic Masses


Atomic Masses

• Elements occur in nature as mixtures of isotopes

• Carbon = 98.89% 12C 1.11% 13C <0.01% 14C Carbon atomic

mass = (abundace x mass) =12.01 amu

• Example 1: When a sample of copper is vaporized and injected in a mass spectrometer, the results indicate that 69.09% of the atoms have a mass of 62.93amu while the rest have a mass of 64.93amu. Calculate the average atomic mass of copper– See answers in Chapter 1 notes key


Moles, Molar Mass,

and Percent Composition


The Mole

• The number equal to the number of carbon atoms in exactly 12 grams of pure 12C.

• 1 mole of anything = 6.022 1023 units of that thing


• Atomic mass unit (amu)- the unit of mass for a single atom• If the mass of an atom in amu = the mass of a mole of

atoms in g, what is the conversion between amu and g? (6.022x1023atoms)(x amu/atom)=x g If x=1g then: 6.022x1023amu=1 g


Which of the following is closest to the average mass, in grams, of one atom of copper?

a) 63.55 g

b) 52.00 g

c) 58.93 g

d) 65.38 g

e) 1.055 X 10-22 g

React 1


• What is the mass of six atoms of americium?


Let’s Think About It

• Is your answer reasonable?

• What are the units on the periodic table?

React 1


Molar Mass

• The mass, in grams, of 1mole of a substance– Numerically equal to the average atomic mass in

amu/molecule– Add the masses of the atoms in a compound

• Mass Moles # units

– # units=atoms, molecules, formula units, etc.

Molar Mass

Avogadro’s #


Now Try This…

Calculate the number of copper atoms in a 63.55 g sample of copper.

React 1


Which of the following 100.0 g samples contains the greatest number of atoms? a) Magnesium

b) Zinc

c) Silver

React 2


Rank the following according to number of atoms (greatest to least):

a) 100.0 g of silver

b) 62.0 g of zinc

c) 21.0 g of magnesium

React 3


Consider separate 100.0 gram samples of each of the following:

H2O, N2O, C3H6O2, CO2

– Rank them from greatest to least number of number of molecules.

React 4


Consider separate 100.0 gram samples of each of the following:

H2O, N2O, C3H6O2, CO2

– Rank them from greatest to least number of oxygen atoms.

React 5

Percent Composition


Percent Composition

• Mass percent of an element:

• For iron in iron (III) oxide, (Fe2O3)

massm ass o f e lem en t in com pound

m ass o f com pound% 1 0 0 %

mass Fe%.

..

11 1 6 9

1 5 9 6 91 0 0 % 6 9 9 4 %


Consider separate 100.0 gram samples of each of the following: H2O, N2O, C3H6O2, CO2

• Rank them from highest to lowest percent oxygen by mass.

React 5


Evaluate Your Answer

• Is it always true that a larger subscript for oxygen in a compound leads to a greater percent oxygen by mass in a compound?

Determining the Formula of a Compound


Formulas

• molecular formula = (empirical formula)n

[n = integer]

• molecular formula = C6H6 = (CH)6

• empirical formula = CH


Finding empirical Formulas

Percent composition→mass composition→mole

composition→mole ratio→empirical formula

100g sample Molar mass

Divide by smallest #

Make subscipts whole #’s


Molecular Formulas

• To determine the molecular formula from the empirical formula, divide the given molecular mass by the molecular mass of the empirical formula– You must be given the actual molecular mass

• Acetylene has an empirical formula of CH. The experimentally determined molar mass is 26.04. What is the molar mass of acetylene?– 26.04g/mol = 2.00

13.02g/mol– The empirical formula then gets multiplied by 2– C2H2

• Determine the empirical and molecular formulas for a compound that gives the following percentages upon analysis: 71.65%Cl, 24.27% C, and 4.07%H. The molar mass is found to be 98.96g/mol


If you have a 100g sample then 71.65%Cl would be 71.6gCl so


• Molecular formula


• Example 2: A white powder is found to contain 43.64%phosphorus and 56.36% oxygen by mass. The compound has a molecular mass of 283.88g/mol, what are the empirical and molecular formulas?

• Example 3: Caffeine contains 49.48%carbon, 5.15% hydrogen, 28.87% nitrogen, and 16.49% oxygen by mass and has a molar mass of 194.2g/mol. Determine the molecular formula of caffeine


Chemical Equations


Balancing Chemical Equations


Chemical Equation

• A representation of a chemical reaction:C2H5OH + 3O2 2CO2 + 3H2O

reactants products


Chemical Equation

• C2H5OH + 3O2 2CO2 + 3H2O

• The equation is balanced.

• 1 mole of ethanol reacts with 3 moles of oxygen to produce 2 moles of carbon dioxide and 3 moles of water


Notice

• The number of atoms of each type of element must be the same on both sides of a balanced equation.

• Subscripts must not be changed to balance an equation.

• A balanced equation tells us the ratio of the number of molecules which react and are produced in a chemical reaction.

• Coefficients can be fractions, although they are usually given as lowest integer multiples.

• Trial and error is a valid method to balance a chemical equation.


• Helpful Hints1. Write elements in same order in reactants

and products

2. Balance oxygen and hydrogen LAST

3. If you balance all elements but one and the last one won’t balance: Double the first substance and start over


Which of the following correctly describes the balanced chemical equation given below? There may be more than one true statement. If a statement is incorrect, explain what is incorrect about it.

4Al + 3O2 2Al2O3

– For every 4 atoms of aluminum that react with 6 atoms of oxygen, 2 molecules of aluminum oxide are produced.

– For every 4 moles of aluminum that react with 3 moles of oxygen, 2 moles of aluminum (III) oxide are produced.

– For every 4 grams of aluminum that react with 3 grams of oxygen, 2 grams of aluminum oxide are produced.

React 6


Which of the following correctly balance the chemical equation given below? There may be more than one correct balanced equation. If a balanced equation is incorrect, explain what is incorrect about it.

CaO + C CaC2 + CO2

I. CaO2 + 3C CaC2 + CO2

II. 2CaO + 5C 2CaC2 + CO2

III. CaO + (2.5)C CaC2 + (0.5)CO2

IV. 4CaO + 10C 4CaC2 + 2CO2

React 7


Which of the following are true concerning balanced chemical equations? There may be more than one true statement.– The number of molecules is conserved.

– The coefficients tell you how much of each substance you have.

– Atoms are neither created nor destroyed.

– The coefficients indicate the mass ratios of the substances used.

– The sum of the coefficients on the reactant side equals the sum of the coefficients on the product side.

React 8


• Example 4: Solid ammonium dichromate is ignited and produces solid chromium (III) oxide, nitrogen gas, and water vapor.

• Write and balance this equation

• Example 5: Ammonia gas reacts with oxygen gas to form nitrogen monoxide and water vapor. Write and balance the equation


Stoichiometric Calculations:Amounts of

Reactants and Products


Stoichiometry

• Stoichiometry—Measurement and calculation of the amount of matter in a reaction

Mass Moles Mole Ratio

Moles Mass

## Avagadro’s

Number

Molar Mass Balanced

EquationMolar Mass

Avagadro’s Number

Given Substance Unknown SubstanceVolume

Density Density

Volume


• Solid lithium hydroxide is used in space vehicles to remove exhaled carbon dioxide from the living environment by forming solid lithium carbonate and liquid water. What mass of gaseous carbon dioxide can be absorbed by 1.00kg of lithium hydroxide?

• Example 6: Baking soda (sodium bicarbonate) is often used as an antacid. It neutralizes hydrochloric acid in the stomach and produces aqueous sodium chloride, liquid water and carbon dioxide gas.

• Milk of magnesia, Mg(OH)2 is also used to neutralize hydrochloric acid and produces aqueous magnesium chloride and water

• Which of these is a more effective antacid against 1.00g of stomach acid?



Limiting Reactants


Mixture of CH4 and H2O Molecules


Methane and Water Reacting


• To determine the limiting reactant:1. Convert the amount of each reactant to moles

2. Find the moles (or grams) of product that each could produce. (you must convert each to the same product)

3. Whichever one produces fewer moles (or grams) of product is the limiting reactant

• You can then use the number of moles to determine the amount of products formed


• Nitrogen gas can be prepared by passing gaseous ammonia over solid copper (II) oxide at high temperatures. The other products of the reaction are solid copper and water vapor. If a sample containing 18.1g NH3 is reacted with 90.4g CuO, which is the limiting reactant? How much nitrogen gas will be collected, in grams?


Which of the following reaction mixtures would produce the greatest amount of product, assuming all went to completion? Each involves the reaction symbolized by the equation:

2H2 + O2 2H2O

a) 2 moles of H2 and 2 moles of O2.

b) 2 moles of H2 and 3 moles of O2.

c) 2 moles of H2 and 1 mole of O2.

d) 3 moles of H2 and 1 mole of O2.

e) Each would produce the same amount of product.

React 11


Notice

• We cannot simply add the total moles of all the reactants to decide which reactant mixture makes the most product. We must always think about how much product can be formed by using what we are given, and the ratio in the balanced equation.


• Methane (CH4) reacts with the oxygen in

the air to produce carbon dioxide and water.

• Ammonia (NH3) reacts with the oxygen in

the air to produce nitrogen monoxide and water.

• What mass of ammonia would produce the same amount of water as 1.00 g of methane reacting with excess oxygen?

React 12


Let’s Think About It

We need to know:– How much water is produced from 1.00 g

of methane and excess oxygen.– How much ammonia is needed to produce

the amount of water calculated above.

React 12


Practice

• Example 7: For the following unbalanced equation, tell me which reactant is limiting, the mass of the excess reactant left over and the mass of CO2 produced if there are 5.00g of each reactant.

• CS2+O2→CO2+SO2


Percent Yield

• Theoretical yield—the maximum amount of product which can be produced from a given amount of reactant– Calculated from the balanced equation using

stoichiometry

• Actual yield—the amount of product actually produced when an experiment is performed– Determined experimentally (given in a problem)


• Percent yield= actual x 100 theoretical

• When excess potassium chromate is added to a solution containing 0.500g of silver nitrate, solid silver chromate and potassium nitrate are formed.

• What is the theoretical yield of silver chromate?• If 0.455g of silver chromate form, what is the percent

yield?• Why is percent yield never 100%


• Example 8: Methanol (CH3OH) can be manufactured by reacting carbon monoxide and hydrogen gas. Suppose 68.5kg CO is reacted with 8.60kg H2. What is the theoretical yield of methanol?

• If 3.57x104 g are produced, what is the percent yield of the reaction?

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