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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?

• Let's consider the combustion of propane: $\chem{C_3H_8(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)}$

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

• Balanced, the equation is: $\chem{C_3H_8(g) + 5 O_2(g) \rightarrow 3 CO_2(g) + 4 H_2O(g)}$
• The numbers in front of the oxygen, carbon dioxide, and water are stoichiometric coefficients (we’ll just refer to them as coefficients).

### 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

• In mole-mole conversions, we relate the moles of a reactant or product to other reactants or products using a mole ratio.
• Mole ratios:
• are obtained from the coefficients in the balanced chemical equation.
• help us determine the moles of one substance in a reaction when the number of moles of another substance in the same reaction is known.
• are used as conversion factors in dimensional analysis problems.

## Mass-Mass Conversions

### Mass-to-Mass Conversions

• Typically, chemical measuring devices do NOT measure in moles.
• We are often given grams as our beginning unit in problems that use a mole ratio.
• Therefore, we need to convert from grams to moles 1st.
• The conversion factor we need to convert from grams to moles (or vice versa) is the molar mass (MM).

### The Law of Conservation of Mass

• The Law of Conservation of Mass states that the masses of the reactants must equal the masses of the products. $\text{Mass Reactants} = \text{Mass Products}$

## Limiting Reactants

### What are limiting reactants?

• Take the equation: $\chem{2 Na(s) + Cl_2(g) \rightarrow 2 NaCl(s)}$
• When reactants are not mixed in relative amounts as described by the balanced chemical equation, one reactant does not react completely.
• In this case, the two reactants are known as:
• Limiting reactant
• Reacts completely
• Limits the amount of the other reactant that can react
• Limits the amount of product that can be made
• Excess reactant
• DOES NOT react completely

### 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

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

## Energy Changes

### The Law of Conservation of Energy

• Energy can be converted or transferred, but it cannot be created or destroyed.
• Heat is energy that is transferred between two objects because of a difference in their temperatures.

### Exothermic and Endothermic Reactions

• Exothermic reaction
• A reaction that releases energy into the surroundings
• Endothermic reaction
• A reaction that absorbs energy from its surroundings

### Specific Heat

• The amount of heat that must be added to $$\chem{1\, g}$$ of a substance to raise its temperature by $$1^\circ C$$.
• Units are Joules per gram per degree Celsius [$$\bfrac{\text{J}}{\chem{g\,{}^\circ C}}$$]
• Is specific to the substance. See Table 6.2 for some common specific heats. $q = mC \Delta T$ where $$q$$ is heat, $$m$$ is mass, $$C$$ is specific heat, and $$\Delta T$$ is the change in temperature

### Energy of the System and the Surroundings

$\chem{q_{system} + q_{surroundings} =0}$

• A system can be an object such as a piece of pipe, or a process, such as a physical or chemical change.
• The surroundings are everything around the system.

## Heat Changes in Chemical Reactions

### How we measure heat

• A bomb calorimeter is used to measure the heat transfer in a chemical reaction.
• Therefore, $\chem{q_{reaction} + q_{water} = 0}$ $\chem{q_{reaction} + q_{calorimeter} = 0}$

## 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?

### Molar Mass

• The most common evidence of a chemical reaction is:
• Change in color
• Production of light
• Formation of a solid (such as a precipitate in solution, or smoke in air, or a metal coating)
• Formation of a gas (bubbles in solution or fumes in the gaseous state)
• Absorption or release of heat (sometimes appearing as a flame)

## Writing Chemical Equations

### What are chemical equations?

• Chemical equation
• A symbolic representation of a chemical reaction
• Balanced equation
• The number of atoms of each element is the same in the products as in the reactants
• Conservation of mass is always maintained

### 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

• If we depict elements and compounds with letters and spheres: If A and B are elements (monatomic) and C, D, E, and F are possible atoms, monatomic ions, or polyatomic ions arranged to form molecules, then how many different types of chemical reactions can you identify by rearranging these atoms or groups of atoms? (NOTE: Do not react more than two elements or molecules)

### 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: $\chem{2HgO(s) \xrightarrow{heat} 2Hg(l) + O_2(g)}$

### 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

• Two elements, an element and a compound, or two compounds react to produce a single compound.
• Most metals react with most nonmetals to form ionic compounds.
• A nonmetal may react with a more reactive nonmetal to form a molecular compound.
• A compound and an element may combine to form another compound if one exists with a higher atom: atom ratio.
• Two compounds may react to form a new compound.
• Example: $$\chem{2Al(s) + 3Br_2(l) \rightarrow 2AlBr_3(s)}$$

### Single-Displacement Reaction

• A free element displaces another element from a compound to form another compound and a different free element.
• Example: $\chem{2Al(s) + Fe_2O_3(s) \rightarrow Al_2O_3(s) + 2 Fe(s)}$

### 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.

### Double-Displacement Reaction

• Two compounds exchange ions or elements to form new compounds.
• Precipitation reactions
• Gas-forming reactions
• Acid-Base Neutralizations

### Precipitation Reactions

• When one product separates from the reaction solution, it is insoluble.
• An insoluble compound formed in a reaction is a precipitate.
• Example: $\chem{BaCl_2(aq) + Na_2SO_4(aq) \rightarrow 2NaCl(aq) + BaSO_4(s)}$

### 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

• When one product separates from the reaction solution, it is insoluble.
• One product compound separates from the reaction mixture because it forms a gas.
• Example: $\chem{CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l)}$

### Acid-Base Reactions

• A double-displacement reaction involving an acid and a base.
• An acid reacts with a base to form an ionic compound and water.
• Example: $\chem{HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l)}$

### Combustion Reactions Examples

• Any reaction involving oxygen as a reactant and that rapidly produces heat and flame

### Combustion Reactions Molecular Examples

• Example: $\chem{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$

## Representing Reactions in Aqueous Solution

### How can we better represent reactions in a solution?

• When compounds exist in solution, they exist as ions.
• Insoluble compounds do not exist as ions. $\chem{Pb(NO_3)_2(aq) + K_2CrO_4(aq) \rightarrow PbCrO_4(s) + 2 KNO_3(aq)}$
• Ionic Equation
• Separate every compound with an (aq) by it into component ions.
• You cannot separate solids, liquids, or gases. $\chem{Pb^{2+} + 2 NO_3^- + 2 K^+ + CrO_4^{2-} \rightarrow PbCrO_4 + 2 K^+ + 2 NO_3^-}$
• Spectator Ions: ions that exist on both sides of the arrow
• Net Ionic Equation
• The remaining equation without the spectator ions $\chem{Pb^{2+}(aq) + CrO_4^{2-}(aq) \rightarrow PbCrO_4(s)}$

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