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Chapter 6

Quantities in Chemical Reactions

Shaun Williams, PhD

The Meaning of a Balanced Equation

What do the coefficients in a balanced chemical equation mean?

What do the coefficients in a balanced chemical equation mean? Continued

The Meaning of the Coefficients

\( \chem{C_3H_8(g) + 5O_2(g) \rightarrow 3CO_3(g) + 4H_2O(g)} \)
1 molecule 5 molecules 3 molecules 4 molecules
2 molecules 10 molecules 6 molecules 8 molecules
100 molecules 500 molecules 300 molecules 400 molecules
\( 6.022 \times 10^{23}\) molecules \( 5 \times 6.022 \times 10^{23}\) molecules \( 3 \times 6.022 \times 10^{23} \) molecules \( 4 \times 6.022 \times 10^{23} \) molecules
1 mole 5 moles 3 moles 4 moles

Mole-Mole Conversions

Mole-to-Mole Conversions

Mass-Mass Conversions

Mass-to-Mass Conversions

A flowchart of conversion from one mass to another in a chemical reaction.

The Law of Conservation of Mass

A picture of solid sodium reacting with chlorine gas to form sodium chloride solid.

Limiting Reactants

What are limiting reactants?

Steps for Determining the Limiting Reactant

  1. Calculate the amount of one reactant (B) needed to react with the other reactant (A).
  2. Compare the calculated amount of B (amount needed) to the actual amount of B that is given.
    1. If calculated B = actual B, there is no limiting reactant. Both A and B will react completely.
    2. If calculated B > actual B, B is the limiting reactant. Only B will react completely.
    3. If calculated B < actual B, A is the limiting reactant. Only A will react completely.

Percent Yield

What is a percent yield?

  • Percent yield
    • Describes how much of a product is actually formed in comparison to how much should have been formed
  • Theoretical yield
    • The maximum amount of product that can be obtained from given amounts of reactants
  • Actual yield
    • The amount of product we measure in the laboratory
    • Usually less than the theoretical yield

\[ \text{% yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\% \]

A picture of someone pouring a solution containing a precipitate into a filter.

Energy Changes

The Law of Conservation of Energy

A graphic of octane burning to provide energy to move a car.

Exothermic and Endothermic Reactions

A graphic of the energy change for a exothermic reaction and an endothermic reaction.

Specific Heat

Energy of the System and the Surroundings

\[ \chem{q_{system} + q_{surroundings} =0} \]

A graphic showing heat leaving a system for exothermic reactions and heat entering a system for endothermic reactions.

Heat Changes in Chemical Reactions

How we measure heat

  • A bomb calorimeter is used to measure the heat transfer in a chemical reaction.
  • Therefore, \[ \chem{q_{reaction} + q_{water} = 0} \] \[ \chem{q_{reaction} + q_{calorimeter} = 0} \]
A diagram of a bomb calorimeter showing the heat leaving the reaction contained in the bomb and entering the surrounding water.

A Microscopic View of a Chemical Reaction

A graphic showing oxygen and hydrogen molecules forming water molecules.

How Do We Know a Chemical Reaction Occurs?

What makes it a chemical reaction?

Do any of the pictures below show a chemical reaction? How can you tell?

Pictures of various situations used to illustrate chemical reaction vs not chemical reactions.

Molar Mass

Writing Chemical Equations

What are chemical equations?

A General Approach to Balancing Equations

  1. Identify the reactants and products and write their correct formulas.
  2. Write a skeletal equation including physical states.
  3. Change coefficients one at a time until the atoms of each element are balanced. (Start with the elements that occur least often in the equation)
  4. Make a final check by counting the atoms of each element on both sides of the equation.

Writing Chemical Equations - Example 1

\[ \text{Aluminum + iron(III) oxide} \rightarrow \text{aluminum oxide + iron} \] \[ \chem{Al(s) + Fe_2O_3(s) \rightarrow Al_2O_3(s) + Fe(s)} \]

# of atoms (reactants) # of atoms (products)
1 Al 2 Al
2 Fe 1 Fe
3 O 3 O

Therefore, we need to balance the equation with coefficients: \[ \chem{2Al(s) + Fe_2O_3(s) \rightarrow Al_2O_3(s) + 3Fe(s)} \]

Writing Chemical Equations - Example 2

\[ \text{Methane + oxygen} \rightarrow \text{carbon dioxide + water} \] \[ \chem{CH_4(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g))} \]

Currently, the number of atoms of each element is shown below. These numbers were obtained by multiplying the subscript to the right of the element’s symbol by the stoichiometric coefficient.

# of atoms (reactants) # of atoms (products)
1 C 1 C
4 H 2 H
2 O 3 O

Writing Chemical Equations - Example 2 Part 2

\[ \chem{CH_4(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g))} \]

First, we look at the carbon atoms. Since the number of carbon atoms on the reactant side is already equal to the number of carbon atoms on the product side, we don’t need to add coefficients.

Next, we look at the hydrogen atoms. Currently, there are four hydrogen atoms on the reactant side and 2 hydrogen atoms on the product side. Thus, we need to add a coefficient of 2 in front of water to make the hydrogen atoms equal.

\[ \chem{CH_4(g) + O_2(g) \rightarrow CO_2(g) + 2H_2O(g))} \]

Writing Chemical Equations - Example 2 Part 3

\[ \chem{CH_4(g) + O_2(g) \rightarrow CO_2(g) + 2H_2O(g))} \]

Finally, we look at the oxygen atoms. Currently, there are 2 oxygen atoms on the reactant side and 4 oxygen atoms (combined from carbon dioxide and water) on the product side. Thus, we add a coefficient of 2 in front of the oxygen gas.

\[ \chem{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g))} \]

Now the reaction is balanced!

Predicting Classes of Reactions

Background

The Classes of Chemical Reactions

Class Reactants Products Example
Decomposition 1 compound 2 elements (or smaller compounds) \( \chem{CD \rightarrow C+D} \)
Combination 2 elements or compounds 1 compounds \( \chem{A + B \rightarrow AB} \)
Single-Replacement 1 element + 1 compound 1 elements + 1 compound \( \chem{A + CD \rightarrow C+AD} \)
Double-Replacement 2 compounds 2 compounds \( \chem{CD + EF \rightarrow CF+ED} \)

Decomposition Reaction

  • A compound breaks down into its component elements.
  • Example: \[ \chem{2HgO(s) \xrightarrow{heat} 2Hg(l) + O_2(g)} \]
A picture of a glass tube containing mercury(II) oxide being heated and it is being converted into liquid mercury.

Decomposition Reaction - A Molecular View

A graphic showing the molecules being converted to elements.

Decomposition Reactions That Occur When Compounds Are Heated

Oxides and halides of the metals Au, Pt, and Hg decompose to the elements. \( \chem{2HgO(s) \rightarrow 2Hg(l) + O_2(g)} \)
Peroxides decompose to oxides and oxygen gas. \( \chem{2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)} \)
Metal carbonates, except those of group 1A metals, decompose to metal oxides and carbon dioxide gas. \( \chem{NiCO_3(s) \rightarrow NiO(s) + CO_2(g)} \)
Oxoacids decompose in a similar way to form nonmetal oxides and water. \( \chem{H_2CO_3(aq) \rightarrow H_2O(l) + CO_2(g)} \)
Ammonium compounds lose ammonia gas. \( \chem{\left( NH_4 \right)_2SO_4(s) \rightarrow NH_3(g) + H_2SO_4(l)} \)

Combination Reactions

Combination Reaction - Example

A picture of the violent reaction between aluminum metal and liquid bromine.

Combination Reaction - A Molecular View

A diagram of carbon monoxide and oxygen gas forming carbon dioxide gas.

Single-Displacement Reaction

  • A free element displaces another element from a compound to form another compound and a different free element.
  • Example: \[ \chem{2Al(s) + Fe_2O_3(s) \rightarrow Al_2O_3(s) + 2 Fe(s)} \]
A picture of aluminum metal bubbling in a solution of hydrochloric acid.

Activity Series

  • This is a list of metals in order of their reactivity
  • A more active element displaces a less active element from its compounds.
The table of metal elements in increase activity.

Single-Displacement Reactions: Copper and Silver Nitrate

A picture of a strip of copper metal hanging into a solution of clear sliver nitrate. Silver metal is growing on the surface of the copper metal and the solution is turning blue from the formation of copper(II) ions.

Single-Displacement Reactions: Copper and Silver Nitrate - A Molecular View

A molecular diagram of copper metal in a solution of clear sliver nitrate. Silver metal is growing on the surface of the copper metal and the solution is starting to contain copper(II) ions.

Single-Displacement Reactions: Copper and Silver Nitrate - Reversible?

A picture of a strip of copper metal hanging into a solution of clear sliver nitrate reacting while the opposite is not reacting.

Double-Displacement Reaction

  • Two compounds exchange ions or elements to form new compounds.
    • Precipitation reactions
    • Gas-forming reactions
    • Acid-Base Neutralizations
A picture of a clear solution being added to a clear solution forming a white cloudy solution.

Precipitation Reactions

Solubility Rules

Ions Rule
\( \chem{Na^+ ,\, K^+ ,\, NH_4^+} \) (and other alkali metal ions) Most compounds of alkali metal and ammonium ions are soluble.
\( \chem{NO_3^- ,\, C_2H_3O_2^-} \) All nitrates and acetates are soluble.
\( \chem{SO_4^{2-}} \) Most sulfates are soluble. Exceptions are \( \chem{BaSO_4 ,\, SrSO_4 ,\, PbSO_4 ,\, CaSO_4 ,\, Hg_2SO_4 ,\, Ag_2SO_4}\).
\( \chem{Cl^- ,\, Br^- ,\, I^-} \) Most chlorides, bromides, and iodides are soluble. Exceptions are \( \chem{AgX ,\, Hg_2X_2 ,\, PbX_2 ,\, HgI_2} \). (\( \chem{X=Cl ,\, Br ,\, I}\))
\( \chem{Ag^+} \) Silver compounds, except \( \chem{AgNO_3 \, and \, AgClO_4} \) are insoluble. \(\chem{AgC_2H_3O_2}\) is slightly soluble.
\( \chem{O^{2-} ,\, OH^-} \) Oxides and hydroxides are insoluble. Exceptions are alkali metal hydroxides, \(\chem{Ba(OH)_2 ,\, Sr(OH)_2 ,\, Ca(OH)_2}\) (somewhat soluble)
\( \chem{S^{2-}} \) Sulfides are insoluble. Exceptions are compounds of \(\chem{Na^+ ,\, K^+ ,\, NH_4^+}\) and the alkaline earth metal ions.
\( \chem{CrO_4^{2-}} \) Most chromates are insoluble. Exceptions are compounds are \(\chem{Na^+ ,\, K^+ ,\, NH_4^+ ,\, Mg^{2+} ,\, Ca^{2+} ,\, Al^{3+} ,\, Ni^{2+}}\).
\( \chem{CO_3^{2-} ,\, PO_4^{3-} ,\, SO_3^{2-} ,\, SiO_3^{2-}} \) Most carbonates, phosphates, sulfites, and silicates are insoluble. Exceptions are compounds of \(\chem{Na^+ ,\, K^+ ,\, NH_4^+}\).

Gas-Forming Reactions

Acid-Base Reactions

Combustion Reactions Examples

  • Any reaction involving oxygen as a reactant and that rapidly produces heat and flame
A picture of various materials burning.

Combustion Reactions Molecular Examples

A graphic of methane molecules reacting with oxygen molecules forming water molecules and carbon dioxide molecules.

Representing Reactions in Aqueous Solution

Aqueous Reactions

A picture of a yellow solution being poured into a clear solution forming a yellow cloudy solution.

How can we better represent reactions in a solution?

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