9.1 Chemical Reactions & Stoichiometric Balancing

9.1 Chemical Reactions & Stoichiometric Balancing

Chemical reactions represent the fundamental processes by which substances undergo chemical transformations to form new materials with distinct chemical and physical properties. For the TEAS 7 Science exam, mastering chemical equations requires understanding how matter is conserved, recognizing reaction classifications, balancing equations quantitatively, and analyzing the kinetic parameters that govern reaction velocity.

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Fundamentals of Chemical Equations & Conservation of Mass

A chemical equation is a symbolic representation of a chemical reaction. It aligns the starting materials, known as reactants, on the left side of a reaction arrow with the newly produced substances, known as products, on the right side.

$$\text{Reactants} \longrightarrow \text{Products}$$

State designators written in parentheses indicate the physical state of each component: solid $(s)$, liquid $(l)$, gas $(g)$, or dissolved in water as an aqueous solution $(aq)$.

The Law of Conservation of Mass

Formulated by Antoine Lavoisier, the Law of Conservation of Mass states that matter can neither be created nor destroyed in an isolated system during an ordinary chemical reaction. Consequently, the total mass of the reactants must equal the total mass of the products. At the atomic level, every single atom present in the reactant mixture must be accounted for among the product molecules. Atoms are simply broken apart from initial molecular arrangements and recombined into new chemical bonds.

Coefficients vs. Subscripts

When balancing chemical equations, two types of numbers are encountered:

1. Subscripts: Part of the chemical formula (e.g., the '2' in $H_2O$). Subscripts define the fixed chemical identity of a compound. Subscripts must never be changed when balancing an equation. Altering a subscript changes the substance itself (e.g., changing $H_2O$ to $H_2O_2$ converts harmless water into corrosive hydrogen peroxide).
2. Stoichiometric Coefficients: Whole numbers placed in front of chemical formulas (e.g., $2H_2O$). Coefficients multiply every atom in the entire molecular formula that follows. Coefficients represent the relative molar quantities of reactants and products involved in the reaction and are the only numbers modified during equation balancing.

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Step-by-Step Chemical Equation Balancing

To balance a chemical equation, systematically adjust coefficients until the total number of atoms of each element is identical on both sides of the arrow.

General Rules for Balancing

1. Write the unbalanced skeletal equation with correct chemical formulas for all reactants and products.
2. Count the atoms of each element present on the reactant side and the product side.
3. Balance polyatomic ions as single units if they appear unchanged on both sides of the equation.
4. Balance elements that appear in only one reactant and one product first, starting with metals, followed by nonmetals (excluding hydrogen and oxygen).
5. Balance hydrogen and oxygen atoms last, as they frequently appear in multiple compounds.
6. Verify the final atom counts to ensure all elements are perfectly balanced with the lowest whole-number coefficient ratio.

Worked Example: Combustion of Propane

Consider the unbalanced combustion reaction of propane ($C_3H_8$):

$$\text{Unbalanced: } C_3H_8(g) + O_2(g) \longrightarrow CO_2(g) + H_2O(g)$$

• Step 1: Balance Carbon ($C$): There are 3 carbons on the left ($C_3H_8$) and 1 on the right ($CO_2$). Place a coefficient of 3 before $CO_2$: $$C_3H_8 + O_2 \longrightarrow 3CO_2 + H_2O$$
• Step 2: Balance Hydrogen ($H$): There are 8 hydrogens on the left ($C_3H_8$) and 2 on the right ($H_2O$). Place a coefficient of 4 before $H_2O$: $$C_3H_8 + O_2 \longrightarrow 3CO_2 + 4H_2O$$
• Step 3: Balance Oxygen ($O$): Count oxygen atoms on the right side: $(3 \times 2) + (4 \times 1) = 10$ oxygen atoms. The left side has $O_2$ (2 atoms per molecule). Place a coefficient of 5 before $O_2$ ($5 \times 2 = 10$): $$C_3H_8 + 5O_2 \longrightarrow 3CO_2 + 4H_2O$$
• Verification: Left ($3\text{ C}, 8\text{ H}, 10\text{ O}$) = Right ($3\text{ C}, 8\text{ H}, 10\text{ O}$). The equation is balanced.

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Main Types of Chemical Reactions

Chemical reactions are grouped into distinct categories based on structural patterns of reactant reorganization.

Oxidation-Reduction (Redox) Reactions

Redox reactions involve the transfer of electrons between chemical species, altering their oxidation states. Redox consists of two paired half-reactions that occur simultaneously:

• Oxidation: The loss of electrons (or an increase in oxidation state). The species that loses electrons is oxidized and acts as the reducing agent.
• Reduction: The gain of electrons (or a decrease in oxidation state). The species that gains electrons is reduced and acts as the oxidizing agent.

Memory Mnemonic — OIL RIG:

• Oxidation Is Loss (of electrons)
• Reduction Is Gain (of electrons)

In the single replacement reaction $Fe(s) + Cu^{2+}(aq) \rightarrow Fe^{2+}(aq) + Cu(s)$, elemental iron ($Fe^0$) loses 2 electrons to become $Fe^{2+}$ (oxidation), while copper ions ($Cu^{2+}$) gain 2 electrons to become elemental copper ($Cu^0$) (reduction).

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Reaction Kinetics & Factors Affecting Reaction Rates

Reaction kinetics studies the rates of chemical processes. According to collision theory, for a reaction to occur, reactant particles must physically collide with sufficient energy (equal to or greater than the activation energy, $E_a$) and with the proper molecular orientation.

Four primary factors influence reaction rate by altering collision frequency or energy requirement:

1. Temperature: Raising the temperature increases the average kinetic energy of molecules. Particles move faster, colliding more frequently and with greater thermal energy to exceed the activation energy barrier ($E_a$).
2. Concentration & Pressure: Increasing reactant concentration in solution (or increasing pressure for gaseous reactants) packs more particles into a given volume. This raises the overall frequency of intermolecular collisions.
3. Surface Area: For heterogeneous reactions involving solids, crushing a solid into smaller particles or fine powder exposes significantly more surface area to surrounding reactants, dramatically increasing collision opportunities.
4. Catalysts: A catalyst is a substance that increases the reaction rate without being permanently consumed in the process. Catalysts operate by providing an alternative reaction pathway with a lower activation energy ($E_a$). Biological catalysts are known as enzymes.