Study Notes on Chemical Reactions and Chemical Quantities

Key Points Overview

• 7.2 Chemical and Physical Changes

• 7.3 Writing and Balancing Equations

• 7.4 Reaction Stoichiometry

• 7.5 Reaction Relationships

• 7.6 Three Examples of Chemical Reactions

7.2 Physical Changes in Matter

• Definition of Physical Change:

  • Changes that only modify the state or appearance of a substance without altering its composition or chemical identity.

  • Examples include melting ice, boiling water, dissolving sugar, or cutting paper. The substance remains chemically the same, just in a different form or state.

  • The identity of the atoms or molecules that constitute a substance remains unchanged; no chemical bonds are broken or formed.

  • Physical changes are often reversible.

7.3 Chemical Changes in Matter

• Definition of Chemical Change:

  • Changes that modify the composition of matter, resulting in the formation of entirely new substances with different properties. These are also known as chemical reactions.

  • During chemical changes, atoms are rearranged; old chemical bonds are broken, and new chemical bonds are formed, leading to the transformation of original substances into different substances.

  • Signs of a chemical change can include a change in color, the production of gas (fizzing or bubbles), the formation of a precipitate (a solid forming in a liquid solution), the absorption or release of heat (temperature change), or the emission of light.

Writing and Balancing Chemical Reactions

• Nature of Reactions:

  • Involves chemical alterations at the molecular level that produce new substances through the rearrangement and exchange of atoms. This process is governed by specific chemical laws.

• Chemical Reaction Definition:

  • A chemical reaction is a concise written representation indicating the chemical identities and relative quantities of substances (reactants and products) and their physical states (solid, liquid, gas, or aqueous).

  • Example of a Chemical Reaction: The combustion of methane gas with oxygen gas to produce carbon dioxide gas and liquid water.

  • $CH<em>4(g) + 2 O</em>2(g) \rightarrow CO<em>2(g) + 2 H</em>2O(l)$

  • Reactants: $CH<em>4(g)$ (Methane), $O</em>2(g)$ (Oxygen)

  • Products: $CO<em>2(g)$ (Carbon Dioxide), $H</em>2O(l)$ (Water)

Chemical Equations: Shorthand for Describing a Chemical Reaction

• Contents of Chemical Equations:

  • Molecular or ionic formulations of both reactants and products, showing their chemical formulas.

  • States of matter are indicated by parenthetical abbreviations: gas (g), liquid (l), solid (s), and aqueous (aq) for substances dissolved in water.

  • Relative quantities of reactant and product molecules (or moles) necessary for the reaction, represented by coefficients. These coefficients represent the simplest whole-number ratios.

  • Chemical equations are highly useful for determining the theoretical weights of reactants consumed and products created.

The Quantities in Chemical Reactions

• Relationship in Chemical Reactions:

  • The quantity of every substance involved in a chemical reaction is interconnected through the coefficients in the balanced chemical equation, following the law of conservation of mass.

• Balancing Equations:

  • Balancing a chemical equation is achieved by ensuring that the number of atoms of each element is equal on both sides of the equation (reactant side and product side). This directly adheres to the Law of Conservation of Mass, stating that atoms are neither created nor destroyed in a chemical reaction.

• Definition of Stoichiometry:

  • The study of the quantitative relationship between chemical quantities (typically in moles, masses, or volumes) in a balanced chemical reaction. It allows chemists to predict the amounts of reactants and products.

Writing Balanced Chemical Equations

• Law of Conservation of Mass:

  • This fundamental law states that in any closed system, the total mass of the reactants before a chemical reaction must equal the total mass of the products after the reaction. This implies that atoms are conserved.

• Example: Consider the reaction where sulfur dioxide gas reacts with oxygen gas to form sulfur trioxide gas. The unbalanced equation is:

  • $SO<em>2(g) + O</em>2(g) \rightarrow SO_3(g)$

  • To balance this, we need to ensure the same number of S and O atoms on both sides. The balanced equation is:

  • $2SO<em>2(g) + O</em>2(g) \rightarrow 2SO_3(g)$

  • Reactants: $SO<em>2(g)$, $O</em>2(g)$

  • Products: $SO_3(g)$

  • This interaction occurs when molecules collide with sufficient energy and correct orientation, leading to the formation of new products.

7.4 Reaction Stoichiometry: What Is It About?

• Coefficients in a Chemical Reaction:

  • The numbers placed in front of chemical formulas (coefficients) in a balanced equation specify the relative amounts in moles (or molecules) of each substance involved. They are crucial for stoichiometric calculations.

• Balanced Chemical Reaction Example: The combustion of octane ($C<em>8H</em>{18}$) in oxygen:

  • $2 C<em>8H</em>{18}(l) + 25 O<em>2(g) \rightarrow 16 CO</em>2(g) + 18 H_2O(g)$

  • This equation states that 2 molecules (or moles) of $C<em>8H</em>{18}$ react with 25 molecules (or moles) of $O<em>2$ to yield 16 molecules (or moles) of $CO</em>2$ and 18 molecules (or moles) of $H_2O$.

• Stoichiometric Ratios Derived: These ratios are used as conversion factors in calculations:

  • $2 \text{ mol } C<em>8H</em>{18} : 25 \text{ mol } O<em>2 : 16 \text{ mol } CO</em>2 : 18 \text{ mol } H_2O$

Practice for Balancing Chemical Reactions

• Exercises: Balance the following equations:

  • $Na (s) + Cl_2 (g) \rightarrow NaCl (s)$

  • $CH<em>4 (g) + O</em>2 (g) \rightarrow CO<em>2 (g) + H</em>2O (l)$

  • $Al (s) + O<em>2 (g) \rightarrow Al</em>2O_3 (s)$

  • $Li (s) + HNO<em>3(aq) \rightarrow LiNO</em>3 (aq) + H_2 (g)$

Additional Practices and Concepts

• Balancing Selected Reaction: Write a balanced equation for the reaction involving solid cobalt(III) oxide and solid carbon to form solid cobalt and carbon dioxide gas.

  • The balanced equation is: $Co<em>2O</em>3(s) + 3C(s) \rightarrow 2Co(s) + 3CO_2(g)$

7.6 Combustion: A Type of Chemical Reaction

• Definition of Combustion Reaction:

  • A combustion reaction describes the rapid chemical process where a substance reacts with an oxidant, usually oxygen ($O_2$), thereby yielding one or more oxygen-containing compounds.

• Typical Products of Combustion:

  • For hydrocarbons (compounds containing only carbon and hydrogen), the typical products of complete combustion are always water ($H<em>2O$) and carbon dioxide ($CO</em>2$), along with the release of significant amounts of heat (energy).

• Example of Combustion Reaction: The combustion of methane gas:

  • $CH<em>4(g) + 2 O</em>2(g) \rightarrow CO<em>2(g) + 2 H</em>2O(g) + \text{Heat}$

• Practice Problem: Formulate a balanced equation for the complete combustion of gaseous butane ($C<em>4H</em>{10}$) in oxygen, producing carbon dioxide and water.

  • The balanced equation is: $2C<em>4H</em>{10}(g) + 13O<em>2(g) \rightarrow 8CO</em>2(g) + 10H_2O(g)$

Cooking Stoichiometry: Making Pizza

• Stoichiometric Relationships in Pizza Making:

  • The number of pizzas that can be made depends on the available quantity of each ingredient, expressed as ratios, similar to moles in chemistry:

  • $1 \text{ crust} : 5 \text{ oz sauce} : 2 \text{ cups cheese} = 1 \text{ pizza}$

  • Evaluating with 6 cups of cheese: If each pizza needs 2 cups of cheese, then 6 cups of cheese can make $6 \text{ cups} / 2 \text{ cups/pizza} = 3$ pizzas, assuming other ingredients are not limiting.

  • Ratio indicates that 2 cups of cheese contributes to making 1 pizza:

  • $1 \text{ crust} + 5 \text{ oz tomato sauce} + 2 \text{ cups cheese} \rightarrow 1 \text{ pizza}$

Mole-to-Mole Conversions

• Conversion Mechanism:

  • Similar to the pizza recipe ratio, the stoichiometric ratio derived from the balanced chemical equation enables direct conversion between moles of any two reactants or products.

• Examples of Stoichiometric Ratios: From the equation for octane combustion: $2 C<em>8H</em>{18}(l) + 25 O<em>2(g) \rightarrow 16 CO</em>2(g) + 18 H_2O(g)$

  • Reactant to product ratio: For example, $2 \text{ mol } C<em>8H</em>{18}$ can be related to $16 \text{ mol } CO<em>2$. This forms a conversion factor like $\frac{16 \text{ mol } CO</em>2}{2 \text{ mol } C<em>8H</em>{18}}$.

  • Reactant to reactant ratio: $2 \text{ mol } C<em>8H</em>{18} : 25 \text{ mol } O<em>2$. This forms factors like $\frac{25 \text{ mol } O</em>2}{2 \text{ mol } C<em>8H</em>{18}}$.

  • Product to product ratio: $16 \text{ mol } CO<em>2 : 18 \text{ mol } H</em>2O$. This forms factors like $\frac{18 \text{ mol } H<em>2O}{16 \text{ mol } CO</em>2}$.

Practice Problems for Mole Conversions

• Determine the moles of $CO<em>2$ produced from the combustion of 10 moles of $C</em>8H_{18}$.

• Calculate $O<em>2$ consumed when combusting 35 moles of $C</em>8H_{18}$.

• Assess how many moles of $C<em>8H</em>{18}$ are used when 27 moles of $CO_2$ are generated.

Mole-to-Mass and Mass-to-Mass Conversions

• Conversion Factors:

  • Stoichiometric ratios (from balanced equations) along with molar masses (grams/mole) serve as crucial conversion factors, allowing translation between grams of a reactant and the mass of a product formed, or vice versa.

• Conversion Strategy:

  • Let A be the reactant and B the product. The general pathway for these conversions is:

  • Mass of A $\rightarrow$ Moles of A (using molar mass of A)

  • Moles of A $\rightarrow$ Moles of B (using stoichiometric ratio from balanced equation)

  • Moles of B $\rightarrow$ Mass of B (using molar mass of B)

Practice Problems for Mass Calculations

• Calculate how many grams of $CO<em>2$ result from 5.0 g of $C</em>8H_{18}$.

• Estimate how many molecules of $CO<em>2$ arise from combusting 5.0 g of $C</em>8H_{18}$.

LA Practice Problem

• Analyze the reaction of plants through photosynthesis for the consumption of $37.8 \text{ g}$ of $CO<em>2$. Calculate the grams of glucose ($C</em>6H<em>{12}O</em>6$) synthesized under sufficient water conditions.

Mole-to-Mass and Mass-to-Mass Conversions Problem Example

• Find mass (grams) of $CO<em>2$ released by burning $3.6 \times 10^{15}$ grams of $C</em>8H_{18}$ in excess oxygen.

• Steps:

  • 1. Identify and write a balanced chemical reaction: $2 C<em>8H</em>{18}(l) + 25 O<em>2(g) \rightarrow 16 CO</em>2(g) + 18 H_2O(g)$

  • 2. Convert the given mass of $C<em>8H</em>{18}$ to moles using its molar mass.

  • 3. Apply the stoichiometric relations (mole ratio) from the balanced equation to find moles of $CO_2$.

  • 4. Convert moles of $CO_2$ to mass (grams) using its molar mass.

Practice on Neutralization Reaction

• Given the reaction: $Mg(OH)<em>2(aq) + 2 HCl(aq) \rightarrow 2 H</em>2O(l) + MgCl<em>2(aq)$, determine grams of $HCl$ neutralized by 3.26 g of $Mg(OH)</em>2$.

LA Practice with Rocket Fuel

• Explore the reaction of ammonium perchlorate ($NH<em>4ClO</em>4$) producing multiple gases and energy.

• Calculate the mass of produced $O<em>2$ when reacting 2.1 g of ammonium perchlorate. The unbalanced reaction is $NH</em>4ClO<em>4(s) \rightarrow N</em>2(g) + Cl<em>2(g) + O</em>2(g) + H_2O(g)$.

7.5 Limiting Reactant and Theoretical Yield

• Limiting Reactant Definition:

  • The reactant that is entirely consumed in a chemical reaction, thereby limiting the maximum amount of product that can be formed (the theoretical yield). Once the limiting reactant is used up, the reaction stops.

  • Example with pizza analogy: If you have 10 crusts, 50 oz sauce, and only 4 cups of cheese, the cheese would be the limiting reactant because it will run out first, dictating that only 2 pizzas can be made (since $4 \text{ cups cheese} / 2 \text{ cups/pizza} = 2 \text{ pizzas}$) even if you have enough of the other ingredients for more.

• Theoretical Yield:

  • The maximum amount of product that can be generated from given amounts of reactants, assuming the reaction goes to completion and is determined by the limiting reactant. This is a calculated value based on stoichiometry.

More on Pizza Making Analogy

• Actual Yield: The actual amount of product obtained from a real reaction, which is almost always less than the theoretical yield due to various factors like incomplete reactions, side reactions, or loss during product isolation.

• Consider scenarios where a pizza was burnt or ingredients were spilled—actual yield accounts for these practical limitations in production.

• The efficiency of the pizza-making process (or any chemical reaction) can be evaluated using percent yield metrics, comparing actual production to theoretical maximum.

Practice for Yield Calculations

• In the reaction: $N<em>2(g) + 3 H</em>2(g) \rightarrow 2 NH<em>3(g)$, analyze the theoretical yield and limiting reagent when starting with 5 g of $N</em>2$ and 5 g of $H_2$.

Additional LA Practice Problem

• Identify the limiting reactant using 10.0 g of $CO$ and 10.0 g of $O<em>2$. The reaction is $2CO(g) + O</em>2(g) \rightarrow 2CO_2(g)$.

• Document the excess reagent as well as the mass of $CO_2$ produced.

Summary on Limiting Reactants and Theoretical Yield

• Key Definitions:

  • Limiting Reactant (Reagent): The reactant that is fully consumed in a chemical reaction and thus determines the maximum amount of product that can be formed.

  • Excess Reactants: Any reactant present in an amount greater than what is needed to react completely with the limiting reactant. A portion of these reactants will remain unreacted after the reaction is complete.

  • Theoretical Yield: The maximum amount of product that can be produced from a given amount of limiting reactant, calculated stoichiometrically. It represents the ideal yield.

  • Actual Yield: The quantity of product empirically obtained from a chemical reaction in the laboratory or industrial setting. It is always less than or equal to the theoretical yield.

  • Percent Yield Calculation: A measure of the efficiency of a reaction.

  • \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100 \text{%}

Practice for Yield and Limitations

• Engage with different configurations of CO and $O_2$ to determine limiting reactants, product masses, and remaining quantities.

• Example Reaction: $2CO(g) + O<em>2(g) \rightarrow 2CO</em>2(g)$. With detailed output predictions based on given masses of reactants, identify which reactant is limiting, the mass of $CO_2$ produced, and the mass of the excess reactant remaining.

Theoretical Yield Calculations Practice Problem

• From the reaction: $2 NO(g) + 5 H<em>2(g) \rightarrow 2 NH</em>3(g) + 2 H_2O(g)$

• Starting materials: 86.3 g of $NO$ and 25.6 g of $H<em>2$. Compute the theoretical yield of ammonia ($NH</em>3$) produced in grams.

LA Practice on Metal Production

• The extraction of titanium from titanium(IV) oxide via: $TiO_2(s) + 2 C(s) \rightarrow Ti(s) + 2 CO(g)$

• Analyze 28.6 kg of $C$ reacting with 88.2 kg of $TiO_2$ yielding 42.8 kg of titanium. Identify the limiting reactant, calculate the theoretical yield in kg, determine the amount of the excess reagent left, and compute the