Chapter 3: Stoichiometry - Mass, Formulas, and Reactions

Course Readings, Problems, and Homework

• Reading Assignments:

  • 7th Edition: Sections 3.1 through 3.3 and 3.5 through 3.8
  • 6th Edition: Sections 3.1 through 3.3 and 3.5 through 3.8 (identical to the 7th edition)
  • 5th Edition: Sections 3.1 through 3.3, 3.5 through 3.7, and 3.9

• Suggested Textbook Problems:

  • 7th Edition / Current: 3.19, 3.31, 3.33, 3.35, 3.55, 3.57, 3.61, 3.63, 3.79, 3.85, 3.99, 3.117
  • 6th Edition: 3.19, 3.31, 3.33, 3.55, 3.57, 3.63, 3.79, 3.85, 3.95, 3.103, 3.105, 3.117
  • 5th Edition: 3.19, 3.33, 3.35, 3.55, 3.57, 3.61, 3.77, 3.85, 3.87, 3.99, 3.111, 3.117

• Smartworks Online Homework:

  • Chapter 3 Assignment (Estimated Duration: 88 minutes): Problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14

Chemical Reactions and Chemical Equations

• Chemical Reactions Notation:

  • Chemical reactions are written using chemical shorthand notation for convenience and clarity.
  • Reactants: Any substance consumed during a chemical reaction.
  • Products: Any substance formed during a chemical reaction.

• Combination Reaction:

  • A chemical reaction in which two or more substances combine to form a single product.
  • Example: One mole of sulfur trioxide gas and one mole of liquid water react to form one mole of liquid sulfuric acid:

$\text{SO}_3(g) + \text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{SO}_4(l)$

• Key Structural Aspects of Chemical Equations:
  • Reaction Arrow ($\rightarrow$): Signifies "reacts to form", "yields", "produces", or "makes".
  • Coefficients: Numbers placed in front of chemical formulas indicating the relative number of molecules or formula units involved. If no coefficient is shown, it is understood to be $1$.
  • States of Matter (Phases): Denoted in parentheses following the chemical formula:
  • Solid: $(s)$
  • Liquid: $(l)$
  • Gas: $(g)$
  • Aqueous solution: $(aq)$
  • Reaction Conditions: Environmental or experimental factors required for a reaction are indicated above or below the reaction arrow:
  • Delta symbol ($\Delta$): Indicates that heat is supplied to the reaction mixture.
  • Catalyst: Listed to indicate a chemical species that accelerates the reaction without being consumed.
  • Solvent Conditions: Indicated when specific media are necessary (e.g., acidic or basic conditions).

The Mole Concept and Avogadro's Constant

• The Mole Concept:

  • A mole is a fundamental grouping or "packaging" unit used in chemistry to count macroscopic quantities of microscopic entities (such as atoms, molecules, ions, particles, or formula units).
  • Mole ($\text{mol}$): The SI base unit for expressing the quantity of a substance.
  • Exact Value: One mole contains exactly $6.02214076 \times 10^{23}$ particles (atoms, molecules, ions, etc.).

• Avogadro's Number ($N_A$):

  • The fundamental physical constant representing the number of characteristic particles in exactly $1\,\text{mole}$ of a substance.
  • Standard numerical representation used in calculations:

$N_A = 6.022 \times 10^{23}\,\text{particles/mol}$

Molar Mass, Molecular Mass, and Formula Mass

• Molar Mass ($\mathcal{M}$):

  • The mass of $1\,\text{mole}$ ($6.022 \times 10^{23}$ particles) of a given substance.
  • The molar mass of an element in grams per mole ($\text{g}\,\text{mol}^{-1}$) is numerically equivalent to that element's average atomic mass expressed in unified atomic mass units ($\text{u}$).
  • Equivalent terms and related units include: atomic mass, atomic mass units ($\text{amu}$), Daltons ($\text{Da}$), molecular weight ($\text{MW}$), and formula weight ($\text{FW}$).

• Physical Examples of 1 Mole Quantities:

  • Sulfur ($\text{S}$): $32.07\,\text{g}$
  • Iron ($\text{Fe}$): $55.85\,\text{g}$
  • Sodium chloride ($\text{NaCl}$): $58.44\,\text{g}$
  • Potassium dichromate ($\text{K}_2\text{Cr}_2\text{O}_7$): $294.18\,\text{g}$
  • Sucrose ($\text{C}<em>{12}\text{H}</em>{22}\text{O}_{11}$): $342.30\,\text{g}$

• Molecular Mass vs. Formula Mass:
  • Molecular Mass (a.k.a. Molecular Weight): The mass of a single molecule of a molecular/covalent compound.
  • Practice Examples: Water ($\text{H}_2\text{O}$), ammonia ($\text{NH}_3$), ethanol ($\text{CH}_3\text{CH}_2\text{OH}$).
  • Formula Mass (FM) (a.k.a. Formula Weight, FW): The mass of a single formula unit of an ionic compound.
  • Practice Examples: Sodium chloride ($\text{NaCl}$), magnesium hydroxide ($\text{Mg(OH)}_2$), sodium carbonate ($\text{Na}_2\text{CO}_3$).

Mole Calculations and Dimensional Analysis

• Dimensional Analysis Methodology:
  • Molar mass serves as a conversion factor between mass in grams and amount in moles.
  • Using $1\,\text{mol}$ of ethanol ($\text{CH}_3\text{CH}_2\text{OH}$), two complementary conversion factors can be established:

$\frac{1\,\text{mol ethanol}}{\text{molar mass in g ethanol}} \quad \text{and} \quad \frac{\text{molar mass in g ethanol}}{1\,\text{mol ethanol}}$

• Practice Calculations:
  • Practice 3.1: How many moles of $\text{Mg}$ atoms are present in $73.40\,\text{g}$ of $\text{Mg}$?
  • Practice 3.3: Calculate the number of atoms in one-millionth of a gram ($1.00 \times 10^{-6}\,\text{g}$) of $\text{Mg}$ to 3 significant figures.
  • Practice 3.4: How many atoms are contained in $1.67\,\text{moles}$ of $\text{Mg}$?
  • Practice Example (Ethanol):
  • How many moles of ethanol are in $10.0\,\text{g}$ of ethanol?
  • How many molecules of ethanol are in $10.0\,\text{g}$ of ethanol?
  • Practice 3.2: Calculate the number of propane ($\text{C}_3\text{H}_8$) molecules in $74.600\,\text{g}$ of propane.

Stoichiometry and Conservation of Mass

• Stoichiometry Definition:

  • The quantitative relationship between the quantities of reactants consumed and products formed in a chemical reaction.

• Law of Conservation of Mass:

  • The fundamental principle that the sum of the masses of reactants in a chemical reaction equals the sum of the masses of the products.
  • Mass is strictly conserved during a chemical reaction.

• Molar Proportionality:

  • The number of moles (or molecules, atoms, formula units, or ions) participating in a chemical reaction is directly proportional to the coefficients in the balanced chemical equation.
  • Example (The Haber Process): Nitrogen gas reacting with hydrogen gas to form ammonia gas:

$\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)$

• In this reaction, $1\,\text{mole}$ of $\text{N}_2(g)$ reacts with $3\,\text{moles}$ of $\text{H}_2(g)$ to yield $2\,\text{moles}$ of $\text{NH}_3(g)$.

Writing and Balancing Chemical Equations

• Reaction Writing Examples:
  • Combustion of natural gas (methane) forming carbon dioxide and water vapor:

$\text{CH}_4(g) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(g)$

• Combustion of hydrogen gas to form water vapor:

$\text{H}_2(g) + \text{O}_2(g) \rightarrow \text{H}_2\text{O}(g)$

• Combustion of propane forming carbon dioxide and water vapor:

$\text{C}_3\text{H}_8(g) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(g)$

• Additional Equations for Practice:
  • Reaction of solid magnesium with oxygen gas:

$\text{Mg}(s) + \text{O}_2(g) \rightarrow \text{MgO}(s)$

• Reaction of solid aluminum with liquid bromine:

$\text{Al}(s) + \text{Br}_2(l) \rightarrow \text{AlBr}_3(s)$

• Oxidation of sulfur dioxide gas:

$\text{SO}_2(g) + \text{O}_2(g) \rightarrow \text{SO}_3(g)$

• Reaction of tetraphosphorus hexoxide with oxygen gas:

$\text{P}_4\text{O}_6(g) + \text{O}_2(g) \rightarrow \text{P}_4\text{O}_{10}(g)$

• Decomposition of aqueous hydrogen peroxide:

$\text{H}_2\text{O}_2(aq) \rightarrow \text{O}_2(g) + \text{H}_2\text{O}(l)$

• Decomposition of solid ammonium hydrogen carbonate:

$\text{NH}_4\text{HCO}_3(s) \rightarrow \text{NH}_3(g) + \text{H}_2\text{O}(g) + \text{CO}_2(g)$

Stoichiometry Calculations in Chemical Reactions

• Mole Ratio Calculations:
  • Practice Example 1: How many moles of ammonia ($\text{NH}_3$) can be produced from $4.8\,\text{moles}$ of hydrogen ($\text{H}_2$)?

$\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)$

• Practice Example 2: How many moles of sodium chloride ($\text{NaCl}$) are produced from $3.34\,\text{g}$ of chlorine gas ($\text{Cl}_2$) reacting with excess sodium?

$2\text{Na}(s) + \text{Cl}_2(g) \rightarrow 2\text{NaCl}(s)$

• Calculations for Iron(III) Oxide Reduction:

$\text{Fe}_2\text{O}_3(s) + 3\text{CO}(g) \xrightarrow{\Delta} 2\text{Fe}(s) + 3\text{CO}_2(g)$

• Practice 3.5: What mass of $\text{CO}$ is required to react completely with $146.0\,\text{g}$ of iron(III) oxide ($\text{Fe}_2\text{O}_3$)?
• Practice 3.6: What mass of carbon dioxide ($\text{CO}_2$) can be produced by the reaction of $0.54\,\text{mole}$ of iron(III) oxide with excess carbon monoxide?
• Practice 3.7: How many iron ($\text{Fe}$) atoms can be produced by the reaction of $2.50 \times 10^5$ molecules of carbon monoxide with excess iron(III) oxide?
• Practice 3.8: What mass of iron(III) oxide reacted with carbon monoxide if the carbon dioxide produced by the reaction had a mass of $8.650\,\text{g}$?

Limiting Reactants and Percent Yield

• Limiting and Excess Reactants:

  • Reactants are frequently added in laboratory reactions in quantities that differ from the exact stoichiometric ratios indicated in the balanced equation.
  • Limiting Reactant (Limiting Reagent): The reactant that is completely consumed first in a chemical reaction.
  • The maximum quantity of product formed is strictly governed by the initial amount of the limiting reactant.
  • When the limiting reactant is exhausted, the reaction stops.
  • Excess Reactant: Any reactant that remains unreacted after the limiting reactant has been completely consumed.
  • Analogy: Making cheese sandwiches ($2\text{ slices of bread} + 1\text{ slice of cheese} \rightarrow 1\text{ sandwich}$). The ingredient that runs out first determines the total number of sandwiches produced.

• Practice Problems on Limiting Reactants:

  • Practice Example 1: $2.5\,\text{moles}$ of carbon disulfide react with $2.5\,\text{moles}$ of oxygen. What is the limiting reactant?

$\text{CS}_2(g) + 3\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{SO}_2(g)$

• Practice Example 2: Reaction of $95.6\,\text{g}$ of carbon disulfide with $1.10 \times 10^2\,\text{g}$ of oxygen:

  • Identify the limiting reactant.

  • How many grams of carbon dioxide will be produced from this reaction?

  • How many grams of carbon disulfide remain in excess (leftover)?

  • Summary Procedure for Limiting Reactant Problems:

• Identify the limiting reactant.

• Calculate the theoretical mass or amount of product formed from the limiting reactant.

  • Theoretical, Actual, and Percent Yield:

• Theoretical Yield (Stoichiometric Yield): The maximum calculated quantity of product possible in a chemical reaction based on given initial amounts of reactants.

• Actual Yield: The mass or amount of product actually obtained from performing the reaction in the laboratory (often lower than theoretical yield due to side reactions or experimental loss).

• Percentage Yield: The ratio, expressed as a percentage, of the actual yield to the theoretical yield:

$\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%$

• Yield Calculation Problems:
  • Practice 3.9: $15.0\,\text{g}$ of methanol and $10.0\,\text{g}$ of carbon monoxide are reacted to produce acetic acid:

$\text{CH}_3\text{OH}(g) + \text{CO}(g) \rightarrow \text{CH}_3\text{COOH}(g)$

* What is the theoretical yield of acetic acid?
* If the actual yield obtained in this experiment is $19.1\,\text{g}$, what is the percentage yield?

• Practice 3.10: A $10.0\,\text{g}$ sample of ethanol ($\text{C}_2\text{H}_5\text{OH}$) was boiled with excess acetic acid ($\text{CH}_3\text{COOH}$). The actual experiment produced $14.8\,\text{g}$ of actual ethyl acetate ($\text{CH}_3\text{COOC}_2\text{H}_5$). What is the percent yield?

$\text{CH}_3\text{COOH}(aq) + \text{CH}_3\text{CH}_2\text{OH}(aq) \rightarrow \text{CH}_3\text{COOC}_2\text{H}_5(aq) + \text{H}_2\text{O}(l)$

Empirical Formulas and Percent Composition

• Percent Composition:
  • The mass percentage of each element present in a compound:

$\text{Percent Composition} = \left( \frac{\text{Mass of Element in Compound}}{\text{Total Mass of Compound}} \right) \times 100\%$

• Practice Example (Formaldehyde, $\text{CH}_2\text{O}$): A $30.0\,\text{g}$ sample of formaldehyde contains $12.0\,\text{g}\,\text{C}$, $2.02\,\text{g}\,\text{H}$, and $16.0\,\text{g}\,\text{O}$. What is the mass percentage of each element?
• Percent composition experiments and calculations provide the information necessary to determine the empirical formula of a compound.

Determining Molecular Formulas from Empirical Formulas

• Empirical Formula:

  • Provides the simplest whole-number ratio of the elements contained in a compound.
  • Merely indicates the mole ratio of atoms in the compound.
  • Different compounds can share the exact same empirical formula and thus possess identical mass percent compositions (e.g., acetylene, $\text{C}_2\text{H}_2$, and benzene, $\text{C}_6\text{H}_6$, both have the empirical formula $\text{CH}$; hydrogen peroxide, $\text{H}_2\text{O}_2$, has the empirical formula $\text{HO}$).

• Requirements for Determining Molecular Formula:

  • To establish the true molecular formula, two distinct pieces of information are required:
  1. Percent composition (or empirical formula mass)
  2. Actual molecular mass

• Practice Problems for Empirical and Molecular Formulas:

  • Practice Example 1: A sample weighing $1.587\,\text{g}$ is found to contain $0.483\,\text{g}$ nitrogen ($\text{N}$) and $1.104\,\text{g}$ oxygen ($\text{O}$). What is the empirical formula?
  • Practice Example 2: The actual molecular mass obtained by mass spectrometry for the compound in Example 1 was determined to be $92.0\,\text{g}\,\text{mol}^{-1}$. What is the molecular formula of this compound?
  • Practice 3.8: Acetic acid is composed of $39.9\%\,\text{C}$, $6.72\%\,\text{H}$, and $53.4\%\,\text{O}$. Determine the empirical formula. The actual molecular mass was determined to be $60.0\,\text{g}\,\text{mol}^{-1}$. What is the molecular formula?