MCAT Chemistry Equations You Need to Know

How Much Chemistry/Biochemistry is on the MCAT?

The Chemical and Physical Foundations of Biological Systems section of the MCAT is comprised of two main components: MCAT Chemistry and MCAT Physics equations.

The chemistry part of this section is designed to test the knowledge of General Chemistry, Organic Chemistry, Introductory Biology, and first semester Biochemistry, as well as MCAT Physics. The percentages are approximated to nearest 5% and can vary from one test to another test.

MCAT Chemistry and Physics Section Breakdown

“The most challenging aspect for me was definitely the application of knowledge. While I was confident in my understanding of the topics, applying the knowledge to complex scenarios presented in the questions was challenging. The questions often require applying memorized facts and concepts to analyze novel scenarios and solve problems, not just rote recall … One strategy that helped me study for these sections was breaking down the content into smaller, manageable chunks and studying consistently over time rather than cramming. I also made use of active learning techniques such as teaching the material to myself and creating concept maps to organize information.” – Dr. Cathleen Kuo, MD, SUNY Buffalo.

All the processes happening in a biological body or our surroundings are basically chemical reactions which include bond breaking, bond formation, electron transfer, etc. Understanding of elements, compounds, structural formulas, properties, chemical and physical changes in terms of reactions, controlling the speed of a reaction etc. is vital in understanding almost all chemical and biochemical processes. This section tests your understanding of these fundamentals and subsequently their application to the functioning of biosystems.

“Organic chemistry was my weakest portion of MCAT Chemistry, both content and application of knowledge … Brushing up on my content knowledge through undergraduate courses (Organic Chemistry I and II) helped. Doing passage-based questions to then apply this knowledge in MCAT-form further reinforced this. Watching relevant videos helped to keep organic chemistry ‘fun’ while working on my knowledge base. I also truncated my studying on the days I did [organic chemistry] to exclusively focus on that section and ensure I was refreshed for studying the next day.” – Dr. Neel Mistry, MD, University of Ottawa Faculty of Medicine.

Now let’s get into the MCAT chemistry equations you need to know to ace this MCAT section!

Looking for MCAT physics equations as well? Check out our video!

5A Unique Nature of Water and its Solution

Water is considered as a universal solvent. All the biochemical reactions are carried out in water as solvent. Water is also very important in maintaining buffering conditions in living system. Unique properties of water allow it to strongly interact with ions, biomolecules.

The content in this category covers solutions, solubility, acids, bases, buffers.

Acid and Bases

Both Acids and Bases can be classified either as Arrhenius or Brønsted–Lowry.

Arrhenius Acid and Bases

This definition exists only for aqueous solutions. An Arrhenius acid is a substance which increases hydronium ion concentration in water and an Arrhenius base is a substance that increases hydroxide ion concentration in water. 

ACID: HCl_(aq) ⟶ H⁺_(aq) + Cl^-_(aq)

BASE: NaOH_(aq)  ⟶ OH^-_(aq)  + Na⁺_(aq) 

Brønsted–Lowry Acid and Base

Any substance that donates a proton is a Bronsted acid and any substance that is a proton acceptor is a Bronsted base. It is not specific to aqueous solutions only.

NH_3(g) + H₂O_(l) ⇌ NH₄⁺_(aq) + OH^-_(aq)

Ammonia acts both as Arrhenius and Brønsted–Lowry Base

NH_3(g) + HCl_(aq) ⇌ NH₄⁺_(aq)+Cl⁻_(aq)

Ammonia acts as only Brønsted–Lowry Base

Autoionization of Water

Water is amphoteric in nature acting as both Brønsted–Lowry acid and base. Since acid and bases can react with each other, that implies that water molecules can react with each other. Water molecules exchange proton with each other.

H₂​O_(l)+H₂​O_(l)⇌H₃​O⁺_(aq)+OH⁻_(aq)

One molecule of water is donating a proton acting as Brønsted–Lowry acid and the other is accepting a proton thus acting as Brønsted–Lowry Base. Because water is a weak acid and a weak base, the hydronium and hydroxide ions exist in very small amount relative to that of non-ionized water and the reaction lies mostly towards the left-hand side. The equilibrium expression which is a ratio of products to reactants is therefore given as below. Remember that the concentrations of pure solids and liquids is not included in the expression.

K_w = [H₃O]⁺[OH]^-= 10^-14

The value of K_w calculated at 25^OC is 10^-14. Taking negative logarithm on both sides of the equation we get:

−logK_w​​=−log([H₃​O⁺][OH⁻])= -log 10^-14

pK_w=pH+ pOH​ = 14

pH = pOH = 7

pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution. The pH scale usually ranges from 0 to 14. Aqueous solutions at 25°C with a pH less than 7 are acidic, while those with a pH greater than 7 are basic or alkaline. 

pH = -log[H₃O⁺]

[H₃O⁺] stands for the hydrogen ion concentration in units of moles per liter solution

Conjugate Acid-Base Pair

NH_3(g) + HCl_(aq) ⇌ NH₄⁺_(aq)+Cl⁻_(aq)

With Brønsted–Lowry acids and bases, in each acid base reaction, a conjugate acid–base pair consists of two substances that differ only by the presence of a proton (H⁺). A conjugate acid is formed when a proton is added to a base, and a conjugate base is formed when a proton is removed from an acid. In the above reaction, NH₃(base) is accepting a proton to become NH₄⁺ (conjugate acid of NH₃). Similarly, HCl(acid) is donating a proton to become Cl^-(conjugate base of HCl).

Strong Acids and Bases

Strong Acids are the one which when dissolved in water dissociate completely. There are 7 strong acids known: HCl - hydrochloric acid, HNO₃ - nitric acid, H₂SO₄ - sulfuric acid (HSO₄^- is a weak acid), HBr - hydrobromic acid, HI - hydroiodic acid, HClO₄ - perchloric acid, HClO₃ - chloric acid

HCl ⟶ H ⁺ + Cl^- (complete dissociation)

Note: All the strong acids are monoprotic i.e they donate one proton(H⁺) except for H₂SO₄ which is a diprotic acid i.e donates two protons(H⁺)

Strong Bases are the one which dissociate completely when dissolved in water. Hydroxides of alkali and alkaline earth metals (NaOH, KOH, Ca(OH)₂, LiOH etc.

NaOH ⟶ Na+ + OH – (complete dissociation)

Weak Acids and Bases

All other acids are classified as weak acids. Few examples: HO₂C₂O₂H - oxalic acid, H₂SO₃ - sulfurous acid, HSO₄ ^- - hydrogen sulfate ion, H₃PO₄ - phosphoric acid, HNO₂ - nitrous acid, HF - hydrofluoric acid, C₆H₅COOH - benzoic acid, CH₃COOH - acetic acid, HCOOH - formic acid.

               CH₃COOH + H₂O ⇌ H₃O⁺ + CH₃COO^- (incomplete dissociation as shown by double sided arrow)

Weak Bases include hydroxide of group III metals, transition metal hydroxides and electron rich nitrogen containing compounds (amines). Some examples: (NH₃), Al(OH)₃, Pb(OH)₂, Fe(OH)₃, Cu(OH)₂, Zn(OH)₂, N(CH₃)₃, CH₃NH₂

Al(OH)₃ ⇌ Al⁺³ + 3OH^- (incomplete dissociation as shown by double sided arrow)

Dissociation and Weak Acid /Bases

Incomplete dissociation of weak acids and bases means that the reaction not only proceeds in the forward direction but also happens simultaneously in the backward direction. Consider a weak acid HA dissociating partially:

HA + H₂O ⇌ H₃O⁺ + A^-

In the above generic weak acid/base reaction, all the species are present in a dynamic equilibrium with each other. The equilibrium expression is a ratio of products to reactants. The equilibrium constant for a weak acid dissociation reaction is specifically known as acid dissociation constant (K_a):

K_a = [H₃O]⁺[A] ^-̸ [HA]

The acid dissociation constant Ka quantifies the extent of dissociation of a weak acid. The larger the value of Ka means more amount of acid dissociate into H⁺ and its conjugate base A^- and hence the stronger the acid, and vice versa.

Similarly for a weak base, consider a weak base dissociating partially:

B + H₂O ⇌ BH⁺ + OH^-

The equilibrium constant for a weak base dissociation reaction is specifically known as base dissociation constant (K_b):

K_b = [BH]⁺[OH]^-̸ [B]

The base dissociation constant K_b quantifies the extent of dissociation of a weak base. The larger the value of K_b means the more amount of base dissociate into OH^- and is conjugate acid BH⁺ and hence the stronger the base, and vice versa.

For conjugate acid-base pair as shown below at 25^oC:

HA + H₂O ⇌ H₃O⁺ + A^-

K_a.K_b = K_w = [H₃O]⁺[OH]^- = 10^-14

Taking negative logarithm on both sides:

pK_a​+ pK_b​=14

pK_a= -log K_a

pK_b = -logK_b

We can use these equations to determine K_b or( pK_b) of a weak base given Ka of conjugate acid. We can also calculate the K_a or(pK_a) of a weak acid given K_b of its conjugate base.

Dissociation and Weak Acid /Bases in presence of added salts

Since weak acids and bases are only partially ionized and in equilibrium, addition of salts which increases the amount of product in an equilibrium reaction can suppress the dissociation of weak acids or bases and vice versa. This is known as Common ion effect.

CH₃COOH + H₂O ⇌ H₃O⁺ + CH₃COO^-

Adding CH₃COONa (CH₃COO^- + Na⁺) shifts the equilibrium to left thus suppressing acid dissociation

Hydrolysis of salts of weak acids or bases

Salts are ionic compound. Hydrolysis of salt means reaction of salt with water. We can determine whether a salt solution will be acidic, basic, or neutral by considering the reactivity of both the cation and the anion with water. This in turn depends on the type cations and anions in a salt and its source.

Anions and Cations of the salt do NOT react with water = Neutral solution

Example includes salt coming from reaction of strong acid and strong base:

NaOH + HCl ⟶ NaCl + H₂O 

Neither Na⁺ (Group IA and group II A cations) and Cl^- (conjugate base of strong acid HCl) react with water. Since pH of water is 7 so the resulting solution is neutral.

Anion reacts with water, but Cation does NOT react with water = Basic solution

Examples include salt coming from reaction of strong base and weak acid:

Ba(OH)₂ + CH₃COOH ⟶ Ba(CH₃COO)₂ + H₂O

Ba⁺² (group II A cation) does not react with water whereas CH₃COO ^– anion (conjugate base of weak acid) reacts with water making acetic acid and OH^- therefore increasing concentration of OH^- making the solution basic.

Cation reacts with water but Anion does NOT react with water = Acidic solution

Examples include salt coming from reaction of strong acid and weak base:

HNO₃ + NH₄OH ⟶ NH₄NO₃ + H₂O

NH₄⁺ (not from group IA or group IIA) therefore reacts with water making NH₄OH and H⁺. Thus, proton concentration increases making the solution acidic. NO₃^- (conjugate base of strong acid) does not react with water.

Buffer

A buffer is a solution which resists change in pH upon addition of acidic or basic component. Buffer solutions have a working pH range and buffer capacity which indicates how much acid/base can be neutralized before pH changes, and the amount by which it will change.

Composition

Buffer can be made either by combination of:

• Weak acid and salt of its conjugate base: CH₃COOH/CH₃COONa
• The Henderson-Hasselbalch approximation allows us one method to approximate the pH of a buffer solution from a weak acid. The basic equation is as follows:

pH= pK_a+ log [A⁻] ̸ [HA]

[HA] = Concentration of weak acid

[A^-] = Concentration of Conjugate base

pKa = acid dissociation constant of weak acid

• Weak base and salt of its conjugate base: NH₃/NH₄Cl

pOH = pK_b + log[HB⁺] ̸ [B]

[HB⁺] = Concentration of conjugate acid

[B] = Concentration of weak base

pKb = base dissociation constant of weak base

Solubility

Solubility tells a limit to how much solute can be dissolved in given amount of solvent. Concentration of a solution is a quantitative measure of amount of solute dissolved in solvent/solution.

Common way to express concentration:

1. Molarity(M): moles of solute /one liter of solution
2. Molality (m): moles of solute / one kilogram of solvent
3. Mass% (m/m%): (mass of solute/mass of solution) x100
4. Volume % (v/v %): (Volume of solute/volume of solution) x100
5. Parts per million (ppm): (mass of solute/mass of solution) x100
6. Mole fraction (χ): χ_A = moles of A/ moles of all the substances

Solubility Product

The solubility product constant, K_sp, is the equilibrium constant for a solid substance dissolving in an aqueous solution. It represents the maximum level at which a solute can dissolve in solution. The more soluble a substance is, the higher the K_sp value. For a general dissolution reaction

aA _(s) ⇌ cC_(aq) + dD _(aq)

K_Sp = [C]^c/[D]^d

Note that pure solids are not included in an equilibrium expression.

5B Nature of Molecules and Intermolecular Interactions

Concept of covalent bonding

Types of covalent bonds (polar, non-polar covalent bonds). Lewis dot symbol of neutral atoms and ions Lewis electron dot diagrams use dots to represent valence electrons around an atomic symbol.

Writing the Lewis structure of a molecule

Lewis electron dot diagrams for ions have fewer (for cations) or more (for anions) dots than the corresponding atom.

Valence shell electron pair repulsion theory

The valence shell electron pair repulsion (VSEPR) theory is a model used to predict 3-D molecular geometry based on the number of valence shell electron bond pairs among the atoms in a molecule or ion. According to this model electron pairs will arrange themselves to minimize repulsion effects from one another. The molecule or polyatomic ion is given an AX_mE_n designation, where A is the central atom, X is a bonded atom, E is a nonbonding valence electron group (usually a lone pair of electrons), and m and n are integers. The number of groups is equal to the sum of m and n. Using this information, we can describe the molecular geometry around a central atom.

Resonating structures

Set of 2 or more Lewis structures which have same number of electrons and atoms but only differ in the type of connectivity between atoms.

Formal charge calculation on Lewis structure

Formal charge indicates whether a molecule is overall neutral or a charged species(ions)

FC = V-N-B/2

FC= formal charge, V= number of valence electrons, N= Number of nonbonding electrons, B= number of bonding electrons

Polar Vs non-polar bonds in a covalent compound. When bonds are formed between two similar atoms, the pull towards the shared bonding electron is same. However, the bond between two unlike atoms, which differ in their affinities for electrons (electronegativity) is said to be a polar covalent bond. When a covalent bond is formed between two atoms of different elements, the bonding pair of electrons will lie more towards the atom, which has more affinity for electrons (i.e. higher electronegativity value).

A polar covalent bond behaves as if it were partially ionic. The greater the difference in electronegativity (EN) the greater the ionic character of the bond. Remember ionic bonds are forms by complete transfer of electrons.

Dipole moments occur when there is a separation of charge. This can happen between two ions in an ionic bond or between atoms in a covalent bond (polar covalent bonds); Since dipole moments are a result of electronegativity difference, larger the difference in electronegativity, the larger the dipole moment. The distance between the charge separation is also a deciding factor into the size of the dipole moment. The dipole moment is a measure of the polarity of the molecule.

Dipole Moment (µ) = Charge (Q) * distance of separation (r)

It is measured in Debye units denoted by ‘D’. 1 D = 3.33564 × 10^-30 C.m, where C is Coulomb and m denotes a meter.

When a bond is formed, there are two different types of overlaps that occur: Sigma (σ) and Pi (π). Sigma (σ) Bonds are formed between two atoms by head-to-head overlapping or bond. Pi (π) Bonds form when two un-hybridized p-orbitals overlap. This is called "side-by-side" bond. To overlap effectively, the orbitals must match each other in energy. The process by which all of the bonding orbitals become the same in energy and bond length is called hybridization (sp, sp², sp³, sp₃d, sp₃d² etc.). We can determine the hybridization by only counting the number of bonds or lone pairs of electrons around a central atom to determine its hybridization.

When double and triple bonds are present between two atoms, there is additional bonding holding the atoms together. While a sigma(σ) bond is always the first covalent bond between two atoms, a pi (π) bond is always the second bond between two atoms.

Single bond = one sigma bond

Double bond = one sigma and one pi bond

Triple bond = one sigma and two pi bonds

Multiple bonding its effect on bond length and bond energies. Multiple bonding decreases bond length. Multiple bonding increases bond energy. Rigidity in molecular structure. Multiple bonding increases rigidity in molecular structure. Single bonds can rotate, but double and triple bonds cannot

Stereochemistry of Covalently Bonded Molecules

• Isomers: Compounds with the same formula but different arrangements of atoms
• Conformational isomers: differ by rotation around a single sigma bond They don't require bond breaking
• Configurational isomers: can only be interchanged by breaking and reforming bonds
• Stereoisomers isomers: differ in spatial arrangement of atoms, rather than order of atomic connectivity. They can be further classified cis-trans isomers, enantiomers, diastereomer
• Enantiomers isomers: non-superimposable mirror images of each other rotate equal but opposite directions in plane polarized light react differently in chiral environments
• Diastereomers: Isomers which are not mirror images of each other
• R and S nomenclature: Around the chiral carbon atom, groups can be prioritized by their atomic mass.
• Optical isomers: A molecule which has a chiral center or asymmetric carbon atom and differ in the placement of substituted group around one central atom.
• Optically active: Capability to rotate the plane of vibration of polarized light to right or left. Chiral molecules are optically active molecules. It would be useful to have a common standard for optical rotation that allows to compare samples collected under slightly different concentrations and path lengths The specific rotation of a molecule is the rotation in degrees observed upon passing polarized light through a path length of 1 decimetre (dm) at a concentration of 1 g/mL.

[α] = α_observed /c x l

[α] = specific rotation in degrees

α_observed = observed rotation

l = pathlength (dm)

c = concentration (g/mL)

Intermolecular Forces

Intermolecular forces are the forces that exist between molecules. These forces determine the physical properties of substances. For example: Density, viscosity, boiling point, melting point, thermal conductivity, thermal expansion, heat of vaporization.

Types of intermolecular forces:

1. Ion-dipole forces exist between ions and polar (dipole) molecules
2. Ion-induced dipole forces exist between ions and non-polar molecules
3. Dipole-dipole forces exist between two polar (dipole) molecules.
4. Dipole-induced dipole forces exist between a polar molecule and a non-polar molecule.
5. Induced dipole forces exist between two non-polar molecules.
6. Hydrogen bonds are a type of dipole-dipole force that occurs when a hydrogen atom is attached to a highly electronegative atom (oxygen, fluorine, nitrogen). A hydrogen atom on one molecule is attracted to the electronegative atom on a second molecule.

5C Separations and Purifications 

Complex mixtures of substances especially biomolecules (peptides, proteins), small organic molecules (chiral, achiral, enantiomers) typically requires separation of the components to be analyzed. Obtaining pure compounds is of great practical importance in chemistry. Most synthetic reactions in chemistry yield mixtures of products and it is important to have a reasonably clear idea of how mixtures of compounds can be separated. Almost all biochemical compounds occur naturally as components of very complex mixtures from which they should be separated and isolated. Many methods have been developed to accomplish this task, and the method used is dependent on the types of substances and type of intermolecular forces that exists between different components of mixtures. The topic in this category covers separation and purification methods involving extraction, chromatography, and electrophoresis. The topics and subtopics are below:

5D Structure, Function, and Reactivity of Biologically Relevant Molecules

Biological macromolecules (carbohydrates, lipids, proteins, and nucleic acids) are an important component of the cell and performs a wide array of functions. The structure and hence function of these macromolecules is governed by the type of functional groups and foundational principles of chemistry such as: covalent bonds and polarity, bond rotations and vibrations, non-covalent interactions, the hydrophobic effect and dynamic aspects of molecular structure. The content in this category covers the primary, secondary, tertiary structures of different biomolecules, their function and reactivity in various biochemical pathways.

The topic and subtopics are as follow:

Nucleic Acids and Nucleotides

• Difference between Nucleoside and Nucleotide.

• RNA and DNA (structure, function and chemistry)

Amino Acids, Peptides, Proteins

• Amino acids: Amino acids are the building blocks of proteins and hence functioning of cells.
• Structure and configuration of all twenty amino acids (alpha and beta amino acids, R or S absolute configuration)
• Classification as either Lewis acid or bases
• Classification as hydrophilic or hydrophobic
• Synthesis of alpha amino acid (amino and carboxylic group attached to the alpha carbon)
• Gabriel Synthesis: Alkylation of phthalimidomalonic ester followed by hydrolysis and decarboxylation to give amino acid
• Strecker synthesis: Just three starting components are needed. Ammonia, potassium cyanide and aldehyde or ketone to give the amino acid. Much simpler and more efficient
• Peptide and proteins: Most abundant biomolecules.
• Reactions
• Peptide linkage: Bond connecting two amino acids is called peptide bond. Condensation reaction of amino and carboxylic group.
• Sulfur linkage: Disulfide bond between sulfur containing side group of two cysteine amino acid molecules. It affects the folding and stabilization of protein structures.
• Hydrolysis: Reverse of peptide bond formation where peptide bonds are cleaved with addition of water.
• General principles of protein structure
• Primary, secondary, tertiary and quaternary structures of proteins
• Isoelectronic point: pH at which the protein is electrically neutral. Determined by isoelectric focusing.
• Three-dimensional structure of proteins
• Denaturing and folding: Most stable structure of a protein depends on its environment, intramolecular and intermolecular forces. A protein folds to minimize its intrinsic energy and to maximize the entropy of the system. Changing elements of its environment causes denaturing of the protein and hence its function.
• Hydrophobic interaction and solvation layer: Since proteins largely function in aqueous environment, folding of a protein happens in a way to sequester hydrophobic amino acids towards the inside core of protein. As a result, water molecules surrounding the folded protein (solvation layer) have favourable interactions with the exposed hydrophilic groups.
• Non-enzymatic protein functions
• Immunity
• Transportation
• Nourishment, movement and regulation
• Structural

Small Organic Biomolecules

5E Principles of Chemical Thermodynamics and Kinetics

All the reactions happening in our body, around us are dynamic in nature following the principles of thermodynamics and reaction kinetic. Thermodynamics determines the energy changes happening in a reaction and its effect on the position of chemical equilibrium. Kinetics is the study to determine the speed of reaction. Enzymes are the biological catalyst known to carry out biochemical reactions to sustain life. Without enzymes, we cannot visualize basic reactions like metabolism, anabolism, and even maintaining homeostasis. The catalysts/biocatalysts facilitate both rapid and efficient progression of a reaction under set conditions.

The content in this category covers principles of chemical thermodynamics and kinetics, including enzyme catalysts. The topics are listed as below:

Principles of Bioenergetics

Bioenergetics/thermodynamics

Free energy/Keq: When the reaction attains equilibrium, certain ratio of reactants and products is obtained. This ratio is called equilibrium constant (K_eq). It is the ratio of molar concentration of products and reactant to the exponent of their coefficients.

aA + bB ⇌ cC + dD 

K_eq = [C]^c[D]^d/[A]^a[B]^b 

From Keq, we can calculate standard energy change (∆G^o) called Gibbs free energy associated with a chemical reaction at any temperature. (molar gas constant R= 8.314Jmol^-1K^-1)

T is temperature in Kelvin

∆G^o = -RT ln Keq

Gibbs free energy is the energy available in a system to do work.

Concentration: Le Châtelier's Principle

Phosphorylation/ATP

• ATP hydrolysis ΔG << 0: Adenosine triphosphate is an energy powerhouse. The hydrolysis of three different phosphate group generating free phosphate group is an energy releasing process

ATP + H₂O → ADP +Pi + free energy

• ATP group transfers: Biological reactions having large positive Gibbs free energy, receive a portion of ATP molecule to make the reaction thermodynamically favorable and easy to proceed.

Biological oxidation–reduction

Reactions involving electron transfers.

• Half-reactions: Oxidation half reaction involving losing electrons. Reduction half reaction involving gaining electrons
• Soluble electron carriers: Small organic molecules acting as electron shuttles between oxidized and reduced species. NAD⁺( nicotinamide adenine dinucleotide) and FAD( flavin adenine dinucleotide).
• Flavoproteins: These are the proteins with FAD or FMN(flavin mononucleotide) occurring in eukaryotic and prokaryotic electron transfer systems

Energy Changes in Chemical Reactions

Thermodynamic system

Understanding of system, surroundings. Definition of state functions and concept (∆H, ∆G, ∆S)

Laws of Thermodynamics

• Zeroth Law: In case of thermal equilibrium, a system has unchanging state of temperature. If a =b and b=c then b=c
• First law of thermodynamics: States the conservation of energy. Internal energy of the system is constant. Energy cannot be created or destroyed or added or taken away from a system, it only can be transferred or converted in the form of heat and work. Units of energy are joules or kilojoules. Internal energy(U) is related to heat(q) and work(w) as

∆U = q + w

• PV diagram and work done: These are used to describe pressure volume relationship in a dynamic system. The enclosed area under the curve gives the work done in the system. Under constant pressure (atmospheric pressure) work done by system is P∆V. ∆v is the volume change. This gives:

U = q – w = q - P∆V

• Second law of thermodynamics: Entropy: The entropy (state of disorder) of a system is constantly increasing. Unit of entropy is joules per kelvin. Entropy (S) of a system depends on the heat transferred in the system (q) and its temperature(T) in kelvin. For reversible processes ΔS = q / T.

For irreversible processes ΔS > q / T.

ΔS ≥ q / T

• Relative entropy of gas, liquid and crystal states

Measurement of heat changes(calorimetry), heat capacity and specific heat

• Calorimetry is the study of transferring energy as heat resulting in temperature change. Relationship between internal energy and heat ( q= thermal energy) with no other form of energy transfer is

∆U = q

Given the temperature change of the system ∆T, measured by recording initial and final temperatures, energy transfer as heat is calculated as: C = heat capacity, m = mass of substance

Q = mC∆T

• Heat capacity (C): the amount of heat required to raise the temperature of something by 1^oC

·      Molar heat capacity: heat capacity per mole

·      Specific heat capacity: heat capacity per mass

·      It takes 4.2 J of heat energy to raise the temperature of 1 gram of water by 1 °C.

·      Some useful conversion factors: 1 calorie = 4.2 J; 1 Calorie (with capital C) = 1000 calorie = 4200 J.

Endothermic and Exothermic Reactions

Enthalpy, H, and standard heats of reaction and formation

• enthalpy or H is the heat content of a reaction. H stands for heat.
• ΔH is the change in the heat content of a reaction. + means heat is taken up, - means heat is released.
• Enthalpy changes can be measured by calculating the Standard heat of reaction, ΔHrxn, is the change in heat content for any reaction. Standard enthalpy changes refer to reactions done under standard conditions, and with everything present in their standard states. The standard state is where things are in their natural, lowest energy, state. For example, oxygen is O2 (diatomic gas) and carbon is C (solid graphite).

ΔH^o_rxn = ∑ ΔH^o _products - ∑ΔH^o_reactants

• Standard heat of formation, ΔHf, is the change in heat content a formation reaction.
• Hess’ Law of Heat Summation: If a reaction involves multiple intermediate steps, then the enthalpy of the final reaction can simply be calculated using the sum of standard enthalpies of the intermediate reactions.

Bond Dissociation Energy as Related to Heats of Formation

• Bond dissociation is the energy required to break bonds.
• ΔHrxn = Bond dissociation energy of all the bonds in reactants - bond dissociation energy of all the bonds in products.
• ΔHrxn = Enthalpy of formation of all the bonds in products - Enthalpy of formation of all the bonds in reactants.
• Bond dissociation energy is positive because energy input is required to break bonds.
• The enthalpy of formation of bonds is negative because energy is released when bonds form.

Free Energy

• Free energy, also known as Gibbs free energy(G) is the energy available that can be converted to do work. H = enthalpy, S = entropy, T is temperature in Kelvin.

ΔG = ΔH - TΔS

• Standard free energy of a reaction is given as

ΔG^o_rxn = ∑ ΔG^o _products - ∑ΔG^o_reactants

• Spontaneous reactions and ΔG°
• Coefficient of expansion
• Heat of fusion(H_fus), heat of vaporization(H_vap)

ΔH_fus = -ΔH_solid   ΔH_vap = -ΔH_condensation

ΔH_fus + ΔH_vap = ΔH_substance

• Phase diagram: pressure and temperature

Rate Processes in Chemical Reactions - Kinetics and Equilibrium

• Reaction Rates: It tells the speed of the reaction. It is measured either by decrease in the concentration of reactant or increase in concentration of products over time. For a reaction the rate is measured as:

A + 2B = 3C 

-d[A]/dt = -1/2 d[B]/dt = +1/3 d[C]/dt 

[A]. [B], [C] are the respective molar concentrations of reactants and products

• Dependence of reaction rate on concentration of reactants: As the concentration of reactant molecules is increased, the number of molecules with minimum required energy (Activation energy) increase.
• Rate law (r): Equation that relates reaction rate with the concentration or partial pressure of the reactants.

aA + bB → cC 

r = k[A]^x[B]^y

k = rate constant

[A], [B] = molar concentration of reactants A and B

x, y = vary for each reaction and are determined experimentally

• Reaction order: Tells the relation between concentration of reactants and reaction rate.
• Order of reaction is the sum of exponent x and y and is determined experimentally.
• Rate determining step: Some reactions happen in multiple steps with multiple intermediates. However, the rate of a multistep reaction depends on the slowest step also known as rate determining elementary step.
• Dependence of reaction rate upon temperature:

·      Interpretation of energy profiles showing energies of reactants, products, activation energy, and ΔH for the reaction

·      Arrhenius Equation relates the rate of a chemical equation to its activation energy, which in turn can be obtained from the heat energy from the surroundings. This equation can be used to understand how the rate of a chemical reaction depends on temperature.

k = A e ^-Ea/RT

A = frequency or pre-exponential factor

e^(-Ea/RT) = fraction of collisions that have enough energy to overcome the activation barrier

Ea = activation energy

R = universal gas constant

T = temperature

Kinetic control versus thermodynamic control of a reaction

Catalysts

• Homogeneous and heterogeneous catalysts
• Type of catalysis:

·      Covalent catalysis

·      Acid-base catalysis

·      Metal ion catalysis

·      Approximation

Equilibrium in reversible chemical reactions

• Law of mass action: Rate of any chemical reaction is proportional to the product of the masses of the reacting substances, with each mass raised to a power equal to the coefficient that occurs in the chemical equation. In a chemical equilibrium the rate of forward reaction is same as the rate of backward reaction

aA + bB ⇌ cC + dD 

rate of forward = rate of backward

k₁[A]^a[B]^b = k₂[C]^c[D]^d

k1/k2 = Keq = [A]^a[B]^b/ [C]^c[D]^d

k1 and k2 are rate constants

Keq is the equilibrium constant

• Le Châtelier’s Principle: Concept in an equilibrium reaction and its application
• Relationship of the equilibrium constant and ΔG°

ΔG° = -RTlnKeq

ΔG° = standard Gibbs free energy change

R = universal gas constant

T = temperature

Keq = equilibrium constant

Enzymes

• Classification by the type of reaction they catalyze
• Mechanism

·      Substrates and enzyme specificity

·      Active site model

·      Induced-fit model

·      Cofactors, coenzymes, and vitamins

• Kinetics
• General (catalysis)
• Michaelis–Menten: Kinetic model for examining the reaction of substrates and enzymes. Michaelis-Menten plot is obtained under two specific conditions:

o  Enzyme concentration is held constant

o  Substrate concentration is increased

o  Reaction velocity is plotted Vs substrate concentration

V_max = [E] * k_cat

Where [E] = concentration of enzyme in the experiment

k_cat = turnover number of a single enzyme

vmax as the maximum speed at which the reaction can proceed. The Michael Menten equation is given as:

V₀ = (V_max x [S]) / (K_M + [S])

V₀ = reaction velocity,how fast products are being formed.

Vmax describes the maximum reaction velocity, and

[S] is the substrate concentration.

Km is the Michaelis constant. It is equal to the substrate concentration when the reaction velocity (V) is equal to half the maximum reaction velocity, or half Vmax.

• Cooperativity
• Effects of local conditions on enzyme activity
• Inhibition: Use of Lineweaver-Burk plot (1/[S] vs 1/V_o). This plot is used to identify the type of enzyme inhibition
• Competitive inhibition
• Uncompetitive inhibition
• Mixed and non-competitive inhibition
• Regulatory enzymes
• Allosteric
• Covalently modified

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