Introduction to General Chemistry Final Exam, Key Concepts

Dissociation Constant of Acids and Bases

The dissociation constant is a measure of how much an acid or base breaks down into ions in water. For acids, it is called Ka, and for bases, it is called Kb. A higher value means a stronger acid or base because more molecules ionize. Ka is calculated by dividing the product of the conjugate base and hydrogen ion concentrations by the concentration of the undissociated acid at equilibrium, while Kb is calculated similarly for bases using the hydroxide ion concentration.

Acid-Dissociation Constant

The acid-dissociation constant is a measure of the strength of an acid in aqueous solution. It quantifies the equilibrium constant for the dissociation of the acid into its ions, usually represented as Ka. It is calculated by dividing the product of the conjugate base and hydrogen ion concentrations by the concentration of the undissociated acid at equilibrium, and higher Ka values indicate a stronger acid because it means the acid has a greater degree of dissociation.

Equilibrium Constant

The equilibrium constant (K) is a number that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced chemical equation. This ratio is constant for a specific reaction at a given temperature, regardless of initial concentrations. It shows the extent to which a chemical reaction proceeds before reaching a state where the forward and reverse reaction rates are equal.

Properties and Function of Buffers

Buffers are aqueous solutions that resist changes in pH when small amounts of acid or base are added. They usually consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. Buffers help maintain a stable environment in chemical and biological systems.

Buffer Solution

A buffer solution is an aqueous mixture that resists changes in pH when small amounts of acid or base are added. It usually contains a weak acid and its conjugate base or a weak base and its conjugate acid. A buffer is most effective when the pH is near the pKa of the weak acid, within a range of approximately pKa ± 1.

Strength of Acids and Bases

The strength of acids and bases indicates how completely they dissociate into ions in water. Strong acids and bases fully separate into ions, while weak acids and bases only partially dissociate, affecting their ability to react in aqueous solutions. This is quantified by the acid dissociation constant (Ka) for acids and the base dissociation constant (Kb) for bases.

Theories of Acids and Bases

Theories of acids and bases explain how acids and bases behave in water. Common theories include Arrhenius, which defines acids as substances that increase hydrogen ion concentration and bases as those that increase hydroxide ions. Bronsted-Lowry theory describes acids as proton donors and bases as proton acceptors. Lewis theory defines acids as electron pair acceptors and bases as electron pair donors.

Brønsted-Lowry Theory

The Brønsted–Lowry theory defines acids as proton (H⁺) donors and bases as proton acceptors. A key feature is the concept of conjugate acid-base pairs, where the base forms a conjugate acid after accepting a proton, and the acid forms a conjugate base after donating one. This theory expands the definition of acids and bases beyond just aqueous solutions.

Electrochemical Cells

Electrochemical cells are devices that convert chemical energy into electrical energy or vice versa. They consist of two electrodes placed in electrolyte solutions where oxidation happens at the anode and reduction takes place at the cathode. Examples include galvanic cells and electrolytic cells.

Electrochemical Cell

An electrochemical cell is a device that converts chemical energy into electrical energy or electrical energy into chemical energy through redox reactions occurring in two separate half-cells connected by an external circuit.

Galvanic (Voltaic) Cell

A galvanic or voltaic cell is an electrochemical cell that generates electrical energy from spontaneous chemical reactions, typically by separating oxidation and reduction, which are submerged in an electrolyte solution, into two half-cells. An external wire connects the electrodes to conduct electrons, while a salt bridge or porous membrane connects the solutions to allow ion flow and maintain neutrality.

Redox Reactions in Electrochemistry

Redox reactions involve the transfer of electrons between two species. In electrochemistry, these reactions occur at electrodes where one substance is oxidized (loses electrons) at the anode and another is reduced (gains electrons) at the cathode. This electron transfer drives electrical current in electrochemical systems.

Balancing Redox Reactions

Balancing redox reactions involves adjusting the number of atoms and electrons in oxidation and reduction half-reactions to follow the law of conservation of mass and charge in the overall reaction.

Chemical Measurements

Chemical measurements involve determining the amount, concentration, or properties of chemicals in a sample. These measurements are essential for analyzing substances and include techniques such as titration, weighing, volume measurement, and spectroscopic analysis to obtain accurate and quantitative data. Every measurement has an associated uncertainty, which is conveyed by using the correct number of significant figures.

Chemical Concentrations

Chemical concentration refers to the amount of a substance present in a given volume or mass of a mixture or solution. It expresses how much of a chemical component is contained in the sample, commonly measured in units like molarity (moles per liter), molality (moles per kilogram), mass percent, or parts per million. Understanding concentration helps assess how substances interact in an analytical experiment.

Molarity

Molarity is the number of moles of a solute dissolved in one liter of solution. It is expressed in moles per liter (mol/L) and indicates the concentration of a chemical species in a solution.

Statistics in Analytical Chemistry

Statistics in Analytical Chemistry involve using mathematical tools and methods to analyze data, ensure accuracy and precision, and interpret results from chemical measurements.

Errors in Chemical Analysis

Errors in chemical analysis are deviations between the measured value and the true value of an analyte. They can be classified as systematic errors, which are consistent and predictable, or random errors, which vary unpredictably and affect precision.

Titrimetric Analysis

Titrimetric Analysis is a method where a solution of known concentration (titrant) is added to react with the analyte until a reaction endpoint is reached, which is detected by a visible change, such as a color change from an indicator. The volume of titrant used helps determine the concentration of the unknown solution.

Fundamentals of Titrations

Titrations are analytical methods to determine the concentration of a substance by reacting it with a standard solution of known concentration. The process involves the gradual addition of the titrant until the reaction reaches an equivalence point, which is signaled by an endpoint change detected by an indicator or instrumentation. Common types of titration include acid-base, redox, and precipitation titrations.

Equivalence and End Point

The equivalence point in a titration is the stoichiometric moment when the amount of titrant added is chemically equal to the amount of substance in the sample being analyzed. The end point is the experimentally observed point in the titration when the indicator changes color, signaling that the titration is complete. The end point is used to estimate the equivalence point, although they may not be exactly the same.

Titration

Titration is a laboratory method used to determine the concentration of an unknown solution by adding a solution of known concentration until the reaction reaches completion. The process involves the gradual addition of the titrant until the reaction reaches an equivalence point, which is signaled by an endpoint change detected by an indicator or instrumentation. Common types of titration include acid-base, redox, and precipitation titrations.

Volume vs. pH

Volume vs. pH refers to the way the pH is plotted as a function of the volume of titrant added during titration. The shape of the volume vs. pH curve provides important information for identifying key points like the equivalence point. Key features include the initial pH, a steep rise or drop near the equivalence point where moles of acid and base are equal, and a buffer region in weak acid/strong base titrations.

Neutralization Titrations

Neutralization titrations involve the reaction between an acid and a base to determine the concentration of one of them. The titrant and analyte react to form water and a salt, and the endpoint is commonly detected using pH indicators.

Titration Curves for Weak Acids and Bases

These are graphs plotting pH versus volume of titrant added during titration. For weak acids or bases, the curves show gradual changes in pH and a buffering region before the equivalence point, reflecting partial dissociation. A key feature is the "buffer region" where pH changes slowly, occurring around the half-equivalence point, where pH equals the acid's or base's pKa. At the equivalence point, the pH will be greater than 7 for a weak acid-strong base titration and less than 7 for a weak base-strong acid titration.

Titration of Weak Acid with Strong Base

This is a type of neutralization titration where a weak acid is gradually reacted with a strong base. During the process, the acid is neutralized by the base, causing changes in the pH of the solution. The titration curve shows a gradual increase in pH at the beginning, followed by a sharp rise near the equivalence point, which is above pH 7 because the conjugate base of the weak acid affects the pH.

Acid-Dissociation Constant and Acid Strength

The acid-dissociation constant (Ka) is a numerical value that measures how strongly an acid donates protons (H+) in a solution. A larger Ka means the acid releases more H+ and is therefore stronger. Acid strength refers to how well an acid ionizes in water, producing hydrogen ions.

Acid Dissociation Equilibrium

Acid dissociation equilibrium is the state where the forward reaction of an acid releasing H+ ions and the reverse reaction of ions recombining to form the acid happen at the same rate. At this point, the concentrations of all species stay constant.

pH

pH is a measure of how acidic or basic a solution is. It is calculated as the negative logarithm of the concentration of hydronium ions (H3O+) in the solution.

pH Scale

The pH scale is a numeric scale that ranges from 0 to 14 and is used to express the acidity or basicity of a solution. Lower values indicate acidic solutions, higher values indicate basic solutions, and 7 is neutral.

Calculating pH and Ion Concentrations

pH is calculated by taking the negative base-10 logarithm of the hydronium ion concentration. Ion concentrations of acids and bases in solutions can be found using equilibrium expressions and acid or base dissociation constants.

Relationship Between pH and pOH

The relationship between pH and pOH states that the sum of pH and pOH in any aqueous solution equals pK_w, which is 14 at 25°C. This can be written as pH + pOH = 14, revealing the balance between acidity and basicity.

pK_a

pK_a is a value that represents the acidity of an acid. It is the negative logarithm of the acid dissociation constant (K_a), showing how easily an acid releases protons in water. Lower pK_a means a stronger acid.

Brønsted-Lowry Theory

The Brønsted–Lowry Theory defines acids as substances that can donate a proton (H+ ion) and bases as substances that can accept a proton. This theory focuses on the transfer of protons between substances during acid-base reactions.

Proton Donor

A proton donor is any molecule or ion that can give a proton (H+) to another species during an acid-base reaction.

Aqueous Ionic Equilibria

Aqueous Ionic Equilibria examine the balance between ions in water solutions. It includes how ions dissociate, the formation of solids, and how salts affect the pH and conductivity of solutions.

Acid-Base Titration Curves

Acid–Base Titration Curves show the pH of a solution as a function of the amount of added titrant during a titration. The curve helps identify important points like the equivalence point and the buffer region, which reveal information about the acid and base strengths.

Strong Acid-Strong Base Titration

A strong acid–strong base titration is a process where a strong acid is gradually neutralized by a strong base, or vice versa. The pH changes sharply at the equivalence point, usually around pH 7, and the titration curve shows a steep rise or drop near this point.

Neutral Solution at Equivalence

A neutral solution at equivalence means that at the equivalence point of a strong acid-strong base titration, the solution has a pH of about 7. This occurs because the acid and base neutralize each other completely, producing water and a neutral salt.

Buffer Components and pH Calculations

Buffer components are a weak acid and its conjugate base, or a weak base and its conjugate acid, present in solution to resist changes in pH. pH calculations for buffer solutions often use the Henderson-Hasselbalch equation, which relates the pH to the pKa and the ratio of conjugate base to acid concentrations.

Conjugate Acid-Base Pair

A conjugate acid-base pair consists of two species that differ by one proton (H+), where the acid donates a proton to become its conjugate base, and the base accepts a proton to form its conjugate acid.

Logarithmic Relationship of pH

The pH scale is logarithmic, meaning a change of one pH unit corresponds to a tenfold change in hydrogen ion concentration.

pH Calculation

pH calculation is the process of determining the hydrogen ion concentration in a solution to measure how acidic or basic the solution is. pH is the negative logarithm of the hydrogen ion concentration.

Solubility Equilibria

Solubility equilibria describe the balance between a solid substance and its ions in a saturated solution. When a salt dissolves in water, it reaches a state where the rate of dissolution equals the rate of precipitation. The solubility product constant (Ksp) quantifies this equilibrium and helps predict whether a solid will dissolve or precipitate.

Common Ion Effect on Solubility

The Common Ion Effect refers to the decrease in the solubility of an ionic compound when a solution already contains one of the ions in the compound. Added common ions shift the dissolution equilibrium, reducing solubility according to Le Chatelier's principle.

Decreased Solubility by Added Ion

Decreased solubility by added ion describes how the solubility of a salt lowers due to the addition of an ion already present in the equilibrium, called the common ion.

Relative Solubility and Precipitation

Relative Solubility refers to how much different ionic compounds dissolve in the same solvent under similar conditions. Precipitation occurs if the ionic product exceeds the solubility product (Ksp), meaning the solution becomes supersaturated and the excess compound forms a solid precipitate.

Solubility Product Constant (Ksp)

The Solubility Product Constant, or Ksp, is the equilibrium constant for the dissolution of a sparingly soluble ionic compound in water. It represents the maximum product of the concentrations of the ions each raised to the power of their stoichiometric coefficients at equilibrium.

Ionic Concentrations in Equilibrium

Ionic concentrations in equilibrium refer to the fixed molar amounts of ions present in a saturated solution when the solute dissolution and precipitation rates are equal, resulting in a stable ion concentration.

Ksp Expression

The Ksp expression is the mathematical representation of the solubility product constant for a sparingly soluble salt, showing the product of the molar concentrations of its ions each raised to the power of their stoichiometric coefficients at equilibrium.

Product of Ion Concentrations

The multiplication of the concentrations of the dissolved ions, each raised to the power of their stoichiometric coefficients, used to compare with the Ksp to predict precipitation.

Elements and Isotopes

Elements are pure substances made of only one type of atom defined by the number of protons they have. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, causing slight differences in their masses.

Proton Count

Proton count is the number of protons present in the nucleus of an atom. It determines the identity of an element because each element has a unique number of protons.

Isotopes and Atomic Masses of the Elements

Isotopes are different forms of the same element that have the same number of protons but a different number of neutrons. This results in atoms of the element having different mass numbers. Atomic mass is the weighted average mass of the atoms in a naturally occurring sample of the element, considering the relative abundance of each isotope.

Foundations of Atomic Theory

Foundations of atomic theory refer to the basic principles describing atoms as the smallest units of matter that combine to form all substances. Originating from Democritus’s idea of indivisible particles and developed scientifically by John Dalton, the theory states that atoms of the same element are identical, cannot be created or destroyed in chemical reactions, and form compounds in fixed ratios. Later discoveries by Thomson, Rutherford, and Bohr refined these ideas, shaping the modern understanding of atomic structure.

Laws Leading to Atomic Theory

These are fundamental laws discovered from chemical experiments that helped develop the atomic theory. Important laws include the Law of Conservation of Mass (mass is neither created nor destroyed in a chemical reaction), the Law of Definite Proportions (a chemical compound always contains the same elements in the same ratio), and the Law of Multiple Proportions (different compounds formed by the same elements in different ratios). These laws supported the idea that matter is made of atoms.

The Law of Conservation of Mass

This law states that mass is neither created nor destroyed in a chemical reaction. The total mass of the reactants is equal to the total mass of the products.

Conversion between Mass and Moles

To convert between the mass of a substance and the number of moles, use the substance's molar mass. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole. To find moles from mass, divide the mass by the molar mass. To find mass from moles, multiply the moles by the molar mass.

Mass and Moles Conversion Factor

The mass and moles conversion factor is the ratio used to convert between the mass of a substance and the amount in moles. It is usually based on the molar mass, allowing mass to be converted to moles by division, or moles to mass by multiplication.

The Mole Concept

The mole is a unit used in chemistry to count very large numbers of atoms, molecules, or other particles. One mole is equal to exactly 6.022 × 10²³ particles, which is called Avogadro's number. This concept helps chemists relate the amount of a substance to the number of its particles.

Avogadro's Number

Avogadro's Number is the number 6.022 × 10²³, which represents the number of representative particles in one mole of a substance.

One Mole

One mole is the amount of substance that contains exactly 6.022 × 10²³ representative particles. It allows chemists to count particles by weighing a sample.

Subatomic Particles Classification

Subatomic particles are classified based on their charges and locations: protons have positive charge and reside in the nucleus; neutrons have no charge and also reside in the nucleus; electrons have negative charge and move around the nucleus in electron clouds.

Charge of Subatomic Particles

Subatomic particles have specific charges: protons carry a positive charge (+e, where e is elementary charge), electrons carry a negative charge (−e), and neutrons have no charge (neutral).

Chemical Kinetics

Chemical Kinetics is the study of the rates at which chemical reactions occur and the factors that influence those rates. It focuses on understanding reaction mechanisms and how temperature, concentration, and catalysts affect speed.

Rate Laws and Reaction Order

Rate laws express the relationship between the concentration of reactants and the reaction rate. Reaction order refers to the sum of the exponents in the rate law, indicating how the concentration of each reactant affects the speed of the reaction.

Rate Laws in Integrated Form

Rate laws in integrated form are equations that describe how the concentration of reactants changes over time during a chemical reaction. These forms are derived by integrating the rate law differential equations and are used to determine reaction order and calculate reaction parameters from experimental concentration versus time data.

First-Order Integrated Rate Law

The mathematical expression that relates the concentration of a reactant to time for a first-order reaction. It shows that the natural logarithm of the concentration decreases linearly with time, and is given by: ln[A] = -kt + ln[A]₀, where [A] is the concentration at time t, [A]₀ is the initial concentration, and k is the rate constant.

Writing and Interpreting Rate Laws

Writing and interpreting rate laws involves determining the mathematical expression that relates the rate of a chemical reaction to the concentrations of its reactants. The rate law shows how the speed of the reaction depends on the concentration of each reactant, usually expressed as rate = k[A]^m[B]^n, where k is the rate constant, [A] is the concentration of reactant A, [B] is the concentration of reactant B, and m and n are the reaction orders with respect to each reactant. Interpreting rate laws helps us understand which reactants affect the rate and how changes in concentration will influence the reaction speed.

Overall Reaction Order

The sum of the exponents of concentration terms in the rate law, representing the total order of the reaction.

Rate Constant (k)

The rate constant is a number that relates the rate of a reaction to the concentrations of reactants in the rate law. It is specific to a particular reaction at a given temperature and does not change with reactant concentration.

Reactant Order

Reactant order is the exponent of a reactant’s concentration in the rate law expression, indicating how changes in that concentration affect the reaction rate. It is determined experimentally and can be zero, first, second, or a fractional value, reflecting the reaction’s dependence on that reactant.

Reaction Pathways and Catalytic Processes

Reaction pathways describe the sequence of steps that occur from reactants to products during a chemical reaction. Catalytic processes involve substances called catalysts that speed up reactions by providing an alternative pathway with lower activation energy, without being consumed in the reaction.

Elementary Reactions and Molecularity

Elementary reactions are the simplest steps in a reaction mechanism that describe a single event at the molecular level. Molecularity is the number of reactant molecules that come together to react in an elementary step, which can be unimolecular, bimolecular, or termolecular.

Reaction Mechanism

A reaction mechanism is the series of individual elementary steps or events that explain how reactants convert into products in a chemical reaction.

Mechanism with a Slow Initial Step

A mechanism with a slow initial step means the first step in the reaction pathway is the slowest step. This step limits the overall reaction rate and determines the rate law.

Slow Step

The slow step in a reaction mechanism is the step that occurs at the slowest rate. It controls how fast the overall reaction proceeds and is also called the rate-determining step.

Reaction Rates and the Nature of Reactants

Reaction rates describe how fast reactants are converted into products in a chemical reaction. The nature of reactants, such as their concentration, physical state, and surface area, affects these rates by influencing how often and how effectively molecules collide.

Factors That Influence Reaction Rates

These are conditions that affect how quickly a chemical reaction occurs. Important factors include temperature, concentration of reactants, surface area of solids, and the presence of a catalyst. Each factor can change how often and how energetically particles collide, thus changing the reaction rate.

Effect of Concentration on Reaction Rate

The effect of concentration on reaction rate refers to how the amount of reactants present affects the speed of a chemical reaction. Increasing the concentration generally increases the reaction rate because more particles are available to collide and react.

Change in Concentration Over Time

Change in concentration over time refers to how the amount of reactant or product changes as the reaction proceeds, typically measured in units of molarity per second.

Particulate Nature of Matter and Reaction Rates

The particulate nature of matter refers to the idea that all matter is made up of tiny particles such as atoms and molecules. Reaction rates depend on how these particles interact during collisions, including their speed, orientation, and energy.

Reaction Rate

Reaction rate is the speed at which reactants are converted to products over time. It depends on how often and how effectively reactant particles collide.

The Arrhenius Equation and Its Components

The Arrhenius equation is a formula that shows how the rate constant of a chemical reaction depends on temperature and activation energy. It expresses that the rate constant increases with higher temperature and lower activation energy and can be represented as k = A·e⁽⁻ᴱᵃ∕ ᴿᵀ⁾. The equation includes the frequency factor (A), which represents the number of collisions with the correct orientation, the activation energy (Ea), which is the energy barrier for the reaction, the gas constant (R), and the absolute temperature (T). Logging the rate constant (k) against the inverse of temperature helps to determine Ea.

Exponential Factor

The exponential factor is the part of the Arrhenius equation expressed as e⁽⁻ᴱᵃ∕ ᴿᵀ⁾. It shows the fraction of molecules that have enough energy to overcome the activation energy barrier at a given temperature.

Limiting Reactants and Percent Yield

The limiting reactant is the substance that is completely consumed first in a chemical reaction, limiting the amount of product formed. Percent yield compares the amount of product actually obtained from a reaction to the maximum possible amount, expressing efficiency as a percentage.

Identifying the Limiting Reactant and Excess Reactant

In a chemical reaction, the limiting reactant is the substance that is completely used up first and limits the amount of product formed. The excess reactant is the substance that remains after the limiting reactant is used up because there is more of it than needed for the reaction.

Identifying Limiting Reactant

Identifying the limiting reactant involves comparing the mole ratios of reactants used with the mole ratios from the balanced chemical equation to find which reactant limits product formation.

Theoretical Yield and Percent Yield

The theoretical yield is the maximum amount of product that can be formed from given amounts of reactants based on stoichiometric calculations. Percent yield is the ratio of the actual amount of product obtained to the theoretical yield, expressed as a percentage, which shows the efficiency of the reaction.

Reaction Efficiency

Reaction efficiency refers to how effectively the starting materials are converted into the desired product. It is often expressed in terms of percent yield and indicates how successful a chemical reaction has been.

Reaction Stoichiometry and Mole-Based Relationships

Reaction stoichiometry is the calculation of the amounts of substances involved in a chemical reaction. It uses balanced chemical equations and mole relationships to determine how much of each reactant or product is needed or formed. Since chemical quantities are often measured in moles, stoichiometry converts between moles and mass or volume to predict yields or to measure reactants.

Mole Ratios in Balanced Equations

Mole ratios in balanced equations refer to the relative amounts of reactants and products in a chemical reaction, expressed in moles. These ratios come from the coefficients of each substance in the balanced chemical equation and show how many moles of one substance react with or produce a certain number of moles of another.

Coefficient Interpretation

Coefficient interpretation refers to understanding the numerical coefficients in a balanced equation as representing the relative quantities of reactants and products in moles.

Mole and Mass Calculations in Reactions

Mole and mass calculations in reactions involve using balanced chemical equations to convert between the moles of substances and their masses. These calculations help predict how much product will be made or how much reactant is needed.

Stoichiometric Conversion

Stoichiometric conversion is the process of using the mole ratios from a balanced chemical equation to convert the amount of one substance to the amount of another substance in a chemical reaction.

Writing and Balancing Chemical Equations

Writing and balancing chemical equations is the process of representing a chemical reaction using symbols and formulas. It involves writing the reactants and products, then adding coefficients to ensure the number of atoms for each element is the same on both sides. This reflects the law of conservation of mass, meaning matter is neither created nor destroyed in the reaction.

Balancing Equations by Atom Count

Balancing equations by atom count means adjusting coefficients so that each element has the same number of atoms on both sides of the chemical equation.

Atom Count in Balancing

Atom count in balancing refers to counting how many atoms of each element exist in the reactants and products. This count helps adjust coefficients to make sure the chemical equation is balanced with the same number of atoms on both sides.

Coefficients

Coefficients are the numbers placed before chemical formulas in equations. They tell how many molecules or moles of each substance are involved to keep the same number of atoms of each element on both sides of the equation.

Identifying Reactants and Products

Reactants are the starting substances in a chemical reaction that interact and change. Products are the new substances formed as a result of the reaction.