Molar Mass, Mole Conversions, and Percent Composition
Stoichiometry serves as the quantitative backbone of the OAT. At its core is the Mole Concept, where the number of moles (n) is defined as the mass of a substance divided by its molar mass (MW). Candidates must be proficient in converting between grams, moles, and the number of particles using Avogadro’s Number ($6.022 \times 10^{23}$). In a typical stoichiometry OAT practice scenario, you may be asked to determine the Empirical Formula from percent composition data. This involves assuming a 100g sample, converting the mass of each element to moles, and finding the simplest whole-number ratio by dividing by the smallest molar value.
Understanding Percent Composition by Mass is equally vital, calculated as (mass of element in 1 mole of compound / molar mass of compound) × 100. On the exam, this often appears in the context of identifying an unknown hydrate or determining the purity of a sample. You must also be prepared for Limiting Reagent problems, where the theoretical yield is dictated by the reactant that produces the least amount of product. Scoring highly requires recognizing that the coefficients in a balanced chemical equation represent molar ratios, not mass ratios. Always check if an equation is balanced before applying these ratios, as an unbalanced equation is a common distractor in multiple-choice options.
Solution Concentration Calculations (Molarity, Molality, Normality)
Solution chemistry on the OAT focuses heavily on concentration units and their specific applications. Molarity (M) is the most frequent unit, defined as moles of solute per liter of solution. It is temperature-dependent because the volume of a liquid expands or contracts with thermal changes. In contrast, Molality (m), defined as moles of solute per kilogram of solvent, is used primarily in Colligative Properties calculations, such as boiling point elevation ($ΔT_b = iK_bm$) and freezing point depression ($ΔT_f = iK_fm$), because mass does not change with temperature.
Normality (N) is another critical concept, particularly in acid-base titrations. It represents the number of equivalents of reactive species per liter of solution. For example, a 1M solution of $H_2SO_4$ is 2N because it provides two moles of hydrogen ions per liter. The relationship $N = M \times n$ (where n is the number of equivalents) is a shortcut often tested. When calculating Mole Fraction ($chi$), remember it is the moles of a specific component divided by the total moles of all components in the mixture. This unitless value is essential when applying Raoult’s Law to determine the vapor pressure of a solution.
Dilution Calculations and Titration Stoichiometry
Dilution problems are a staple of the general chemistry for OAT review process. The fundamental formula $M_1V_1 = M_2V_2$ allows you to calculate the change in concentration when a solvent is added. A common pitfall is failing to account for the total final volume ($V_2$); if a question asks how much water was added, you must subtract $V_1$ from your calculated $V_2$.
In the context of Titration Stoichiometry, the equivalence point occurs when the moles of acid equivalents equal the moles of base equivalents. This is represented by the formula $N_aV_a = N_bV_b$. If using molarity for polyprotic acids, the formula adjusts to $n_aM_aV_a = n_bM_bV_b$, where $n$ represents the number of dissociable protons or hydroxide ions. OAT questions frequently present titration curves, requiring you to identify the Equivalence Point (the steepest part of the curve) and the Half-Equivalence Point (where $pH = pK_a$). Understanding these geometric relationships on a graph is just as important as the algebraic manipulation of the formulas.
Gaseous State and Thermochemistry Equations
The Gas Laws and Kinetic Molecular Theory
The behavior of ideal gases is governed by the Ideal Gas Law, $PV = nRT$. For the OAT, you must know the value of the gas constant $R$ as $0.0821 Lcdot atm / molcdot K$. Many questions involve the Combined Gas Law, $(P_1V_1)/T_1 = (P_2V_2)/T_2$, which is used when the amount of gas $(n)$ remains constant. It is imperative to always convert temperatures to Kelvin ($K = ^circ C + 273$) to avoid calculation errors.
Kinetic Molecular Theory (KMT) provides the theoretical framework for these laws, stating that gas particles are in constant, random motion and undergo elastic collisions. You may be tested on Graham’s Law of Effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass: $Rate_1 / Rate_2 = sqrt{M_2 / M_1}$. This explains why lighter gases, such as Helium, effuse faster than heavier gases like Oxygen. Additionally, Dalton’s Law of Partial Pressures ($P_{total} = P_1 + P_2 + ...$) is frequently applied in "collecting gas over water" scenarios, where the vapor pressure of water must be subtracted from the total pressure to find the pressure of the dry gas.
Calorimetry and Enthalpy Change Calculations
Thermochemistry measures the flow of energy during chemical transformations. The heat absorbed or released by a substance is calculated using the specific heat formula $q = mcΔT$, where $c$ is the Specific Heat Capacity. In a constant-pressure calorimeter, the heat of the reaction ($q_{rxn}$) is equal to the change in Enthalpy (ΔH). If the reaction occurs at constant volume (bomb calorimetry), the heat measured reflects the change in internal energy ($ΔU$).
Hess’s Law is a frequent OAT topic, requiring you to manipulate several intermediate reactions to find the total enthalpy change of a target reaction. This relies on the principle that enthalpy is a State Function, meaning its value depends only on the initial and final states, not the path taken. You should also be comfortable using Standard Enthalpies of Formation ($ΔH^circ_f$) with the formula $ΔH^circ_{rxn} = Sigma ΔH^circ_f(products) - Sigma ΔH^circ_f(reactants)$. Note that the $ΔH^circ_f$ for any element in its standard state (e.g., $O_2(g)$, $Fe(s)$) is zero, a fact often omitted from the provided data in exam questions.
Gibbs Free Energy and Spontaneity (ΔG = ΔH - TΔS)
Predicting whether a reaction will occur without external intervention requires the Gibbs Free Energy equation: $ΔG = ΔH - TΔS$. This is one of the most high-yield thermochemistry equations OAT candidates encounter. The sign of $ΔG$ determines spontaneity: a negative $ΔG$ indicates a Spontaneous (Exergonic) reaction, while a positive $ΔG$ indicates a Non-spontaneous (Endergonic) reaction.
The relationship between enthalpy ($ΔH$) and entropy ($ΔS$) creates four distinct scenarios for spontaneity. For instance, if a reaction is exothermic ($-ΔH$) and increases in disorder ($+ΔS$), it is spontaneous at all temperatures. If both $ΔH$ and $ΔS$ are positive, the reaction is spontaneous only at high temperatures where the $TΔS$ term outweighs the $ΔH$ term. On the OAT, you may also need to relate $ΔG^circ$ to the equilibrium constant ($K$) using the formula $ΔG^circ = -RT ln K$. A large $K$ ($>1$) corresponds to a negative $ΔG^circ$, meaning the products are favored at equilibrium.
Chemical Kinetics and Rate Laws
Determining Reaction Order from Data
Chemical kinetics explores the speed of reactions and the mechanisms by which they occur. The Rate Law is expressed as $Rate = k[A]^m[B]^n$, where $k$ is the rate constant and the exponents $m$ and $n$ represent the reaction order with respect to each reactant. It is critical to remember that reaction orders must be determined experimentally and cannot be derived from the stoichiometric coefficients of the balanced equation unless the reaction is an Elementary Step.
On the OAT, you will often be presented with a table of initial rates and reactant concentrations. By comparing two experiments where only one reactant concentration changes, you can determine its order. If doubling the concentration doubles the rate, the reaction is First Order ($m=1$). If doubling the concentration quadruples the rate, it is Second Order ($m=2$). If the rate remains unchanged, it is Zero Order ($m=0$). The overall reaction order is the sum of the individual orders ($m+n$). Understanding the units of the rate constant $k$ is also a common assessment point; for a second-order reaction, the units are $M^{-1}s^{-1}$.
Integrated Rate Laws and Half-Life
While differential rate laws relate rate to concentration, Integrated Rate Laws relate concentration to time. For a first-order reaction, the natural log of the concentration decreases linearly over time: $ln[A]_t = -kt + ln[A]_0$. This linear relationship is a key identifier in graphical questions. For a second-order reaction, the plot of $1/[A]$ versus time yields a straight line with a positive slope $k$.
Half-life ($t_{1/2}$) is the time required for the concentration of a reactant to decrease by half. For the OAT, the most important formula is for first-order decay: $t_{1/2} = 0.693 / k$. Notably, the first-order half-life is independent of the initial concentration, a unique property often exploited in exam questions involving radioactive decay. Conversely, the half-life for a second-order reaction ($t_{1/2} = 1 / (k[A]0)$) and a zero-order reaction ($t{1/2} = [A]_0 / 2k$) both depend on the starting concentration. Being able to distinguish these relationships allows for quick elimination of incorrect answer choices in conceptual kinetics problems.
The Arrhenius Equation and Activation Energy
The temperature dependence of reaction rates is quantified by the Arrhenius Equation: $k = Ae^{-Ea/RT}$. This formula demonstrates that the rate constant $k$ increases exponentially with temperature and decreases as the Activation Energy ($E_a$) increases. Activation energy is the minimum kinetic energy required for molecules to collide with the correct orientation to form the Transition State or activated complex.
In a practical exam context, you might see the two-point form of the Arrhenius equation: $ln(k_2/k_1) = (E_a/R)(1/T_1 - 1/T_2)$. This allows for the calculation of $E_a$ if the rate constant is known at two different temperatures. Furthermore, the OAT frequently tests the effect of Catalysts. A catalyst increases the reaction rate by providing an alternative pathway with a lower activation energy, thereby increasing the fraction of "successful" collisions without being consumed in the process. Note that while a catalyst changes the rate ($k$), it has no effect on the equilibrium constant ($K$) or the change in free energy ($ΔG$).
Chemical Equilibrium and Acid-Base Chemistry
Equilibrium Constant Expressions (Kc, Kp, Ksp)
Dynamic equilibrium occurs when the rates of the forward and reverse reactions are equal. The Law of Mass Action defines the equilibrium constant ($K$) as the ratio of product concentrations to reactant concentrations, each raised to the power of their coefficients. For the general reaction $aA + bB
ightleftharpoons cC + dD$, the expression is $K_c = ([C]^c[D]^d) / ([A]^a[B]^b)$. It is vital to exclude pure solids and liquids from this expression, as their concentrations are considered constant.
For reactions involving gases, $K_p$ is used, relating the partial pressures of the components. The two are connected by $K_p = K_c(RT)^{Δn}$, where $Δn$ is the change in moles of gas. Another specific application is the Solubility Product Constant (Ksp), which describes the equilibrium between a solid ionic compound and its dissolved ions in a saturated solution. For a salt like $MgF_2$, $K_{sp} = [Mg^{2+}][F^-]^2$. If the ion product ($Q$) exceeds $K_{sp}$, a precipitate will form. Understanding Le Chatelier’s Principle is also fundamental; the system will shift its equilibrium position to counteract changes in concentration, pressure, or temperature.
Acid/Base Dissociation Constants (Ka, Kb) and pH/pOH Calculations
Acid-base chemistry OAT questions require fluency in the pH scale and dissociation constants. The strength of an acid is determined by its Acid Dissociation Constant (Ka); the larger the $K_a$, the stronger the acid and the lower the $pK_a$ ($pK_a = -log K_a$). The relationship between an acid and its conjugate base is given by $K_w = K_a imes K_b = 1.0 imes 10^{-14}$ at 25°C.
To calculate the pH of a strong acid, simply take the negative log of the molarity, as they dissociate completely. For weak acids, you must use an equilibrium approach, often simplified to $[H^+] = sqrt{K_a[HA]}$ when the percent ionization is low (typically $<5%$). The same logic applies to weak bases using $K_b$ to find $[OH^-]$ and subsequently the pOH. Remember the identity $pH + pOH = 14$. On the OAT, you must also be able to identify Amphoteric species like $H_2O$ or $HCO_3^-$, which can act as either an acid or a base depending on the environment.
Buffer Calculations (Henderson-Hasselbalch Equation)
A buffer solution resists changes in pH and consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). The pH of a buffer is calculated using the Henderson-Hasselbalch Equation: $pH = pK_a + log([A^-]/[HA])$. This equation is indispensable for OAT questions involving physiological systems or laboratory titrations.
The maximum Buffering Capacity occurs when the concentrations of the acid and conjugate base are equal, meaning $[A^-] = [HA]$. At this point, $pH = pK_a$, which corresponds to the half-equivalence point of a titration curve. If the ratio $[A^-]/[HA]$ is 10:1, the pH will be $pK_a + 1$; if the ratio is 1:10, the pH will be $pK_a - 1$. This logarithmic relationship allows for quick mental estimations during the exam. Candidates should also recognize that adding a small amount of strong acid or base to a buffer will slightly shift the ratio of $[A^-]$ to $[HA]$ but will not cause a drastic pH change as long as the buffer components are not exhausted.
Electrochemistry and Redox Reactions
Balancing Redox Reactions
Reduction-oxidation (redox) reactions involve the transfer of electrons. To balance these on the OAT, the Half-Reaction Method is preferred. This involves splitting the reaction into reduction and oxidation components, balancing all elements except H and O, balancing O using $H_2O$, balancing H using $H^+$, and finally balancing the charge using electrons ($e^-$). If the reaction occurs in a basic solution, you must neutralize the $H^+$ ions by adding an equal number of $OH^-$ ions to both sides.
An essential skill is assigning Oxidation Numbers. Rules to remember: elements in their elemental form are 0, Fluorine is always -1, Oxygen is usually -2 (except in peroxides), and Hydrogen is +1 when bonded to nonmetals. The sum of oxidation states must equal the overall charge of the molecule or ion. In a Galvanic Cell, oxidation occurs at the Anode (negative) and reduction occurs at the Cathode (positive), a relationship often memorized by the mnemonic "An Ox / Red Cat."
Standard Reduction Potentials and Cell Potential (E°cell)
The driving force of an electrochemical cell is the Electromotive Force (EMF), measured as the Standard Cell Potential ($E^circ_{cell}$). This is calculated using standard reduction potentials found in a table: $E^circ_{cell} = E^circ_{cathode} - E^circ_{anode}$. Note that when using this subtraction formula, you do not change the sign of the values provided in the table, as the subtraction already accounts for the oxidation process.
A positive $E^circ_{cell}$ indicates a spontaneous reaction, which corresponds to a negative $ΔG^circ$. The relationship is defined by the formula $ΔG^circ = -nFE^circ_{cell}$, where $n$ is the number of moles of electrons transferred and $F$ is Faraday’s Constant ($approx 96,500 C/mol e^-$). On the OAT, you may also encounter Electrolytic Cells, which require an external power source to drive a non-spontaneous reaction ($E^circ_{cell} < 0$). For these, you might use the formula $I = q/t$ (current = charge/time) to calculate the mass of a metal plated onto an electrode using stoichiometry and Faraday's constant.
The Nernst Equation for Non-Standard Conditions
When concentrations deviate from the standard 1.0 M or pressures differ from 1.0 atm, the cell potential ($E_{cell}$) changes. The Nernst Equation accounts for these variations: $E_{cell} = E^circ_{cell} - (0.0592 / n) log Q$ at 25°C. Here, $Q$ is the reaction quotient, calculated the same way as the equilibrium constant but using initial concentrations.
As a reaction proceeds, $Q$ increases until it equals $K$, at which point the cell is "dead" and $E_{cell} = 0$. This equation explains why a Concentration Cell—a cell with the same electrodes but different ion concentrations—can generate a voltage. The cell will produce a current until the concentrations in both compartments are equal. For the OAT, understand the qualitative shifts: if the concentration of reactants increases, $Q$ decreases, and $E_{cell}$ becomes more positive (the reaction becomes more spontaneous). Conversely, increasing product concentration will decrease the cell potential.
Atomic Structure and Periodic Trends
Photon Energy and Wavelength Calculations
Atomic structure questions on the OAT often bridge the gap between chemistry and physics. The energy of a photon is directly proportional to its frequency ($
u$) and inversely proportional to its wavelength ($lambda$), expressed as $E = h
u = hc / lambda$. In these formulas, $h$ is Planck’s Constant ($6.626 \times 10^{-34} Jcdot s$) and $c$ is the speed of light ($3.00 \times 10^8 m/s$).
You may also be required to use the Rydberg Equation to calculate the energy change when an electron transitions between energy levels in a hydrogen atom: $ΔE = R_H (1/n_i^2 - 1/n_f^2)$. When an electron drops from a higher energy level ($n_{high}$) to a lower one ($n_{low}$), energy is emitted as a photon. The OAT frequently tests the conceptual understanding that shorter wavelengths (like UV light) correspond to higher energy transitions compared to longer wavelengths (like infrared). Familiarity with the Electromagnetic Spectrum is crucial for identifying which types of transitions produce visible light (the Balmer series).
Electron Configurations and Quantum Numbers
The arrangement of electrons in an atom is described by four Quantum Numbers. The principal quantum number ($n$) indicates the energy level, the angular momentum quantum number ($l$) defines the subshell shape ($s=0, p=1, d=2, f=3$), the magnetic quantum number ($m_l$) specifies the orbital orientation, and the spin quantum number ($m_s$) indicates the electron spin ($+1/2$ or $-1/2$).
When writing Electron Configurations, you must follow three fundamental rules: the Aufbau Principle (fill lowest energy orbitals first), Hund’s Rule (place one electron in each orbital of a subshell before pairing), and the Pauli Exclusion Principle (no two electrons can have the same four quantum numbers). Be wary of transition metal exceptions, such as Chromium ($[Ar] 4s^1 3d^5$) and Copper ($[Ar] 4s^1 3d^{10}$), where a half-filled or fully-filled d-subshell provides extra stability. These exceptions are high-yield targets for OAT question writers because they deviate from the standard filling pattern.
Predicting Trends in Ionization Energy, Electronegativity, and Atomic Radius
Periodic trends are dictated by the balance between the nuclear charge and the shielding effect of inner-shell electrons, a concept known as Effective Nuclear Charge (Zeff). Atomic Radius increases as you move down a group (due to additional shells) and decreases as you move across a period from left to right (due to increased $Z_{eff}$ pulling electrons closer).
Ionization Energy (the energy required to remove an electron) and Electronegativity (the ability to attract electrons in a bond) generally follow the opposite trend: they increase across a period and decrease down a group. However, you must be aware of anomalies in Ionization Energy, such as the dip between Groups 2 and 13 (s-subshell shielding) and Groups 15 and 16 (electron-electron repulsion in p-orbitals). Electron Affinity also becomes more exothermic across a period, though noble gases are a notable exception with positive values. Mastery of these trends allows you to predict the chemical reactivity and bonding characteristics of elements without needing specific data points, a critical skill for the fast-paced OAT environment.