MCAT Equation Guide

Avogadro’s Constant

(Constants to memorize)

6.022x10^23 entities per mole

Plank’s Constant

(Constants to memorize)

6.626x10^-34 J*s (although this is often given)

Gravity Constant

(Constants to memorize)

9.8 m/s^2

Fundamental Charge of an electron (and proton) constant:

(Constants to memorize)

eF = ∓1.6x10-19 C (Coulombs) (this is also often given)

At STP constant:

(Constants to memorize)

1 mol gas = 22.4L

Standard Unit Prefixes to Memorize

Pico

Nano

Micro

Milli

Centi

Deci

Kilo

Mega

Pico (p): 10^-12; 1 pm = 1x10^-12 meters

Nano (n): 10^-9; 1 nm = 1x10^-9 meters

Micro (µ): 10^-6, 1 µm = 1x10^-6 meters

Milli (m): 10^-3, 1 mm = 1x10^-3 meters (aka .001m)

Centi (c): 10^-2, 1 cm = 1x10^-2 meters (aka .01m)

Deci (d): 10^-1; 1 decimeter = 1x10^-1 meter 

Kilo (k): 10^3, 1 km = 1x10^3 meters (aka 1000m)

Mega (M): 10^6, 1 Megawatt = 1x10^6 Watts

Standard Unit to Memorize

Volume

Mass

Pressure/Stress

Temperature

Amount

Displacement/Distance

Velocity

Acceleration

Period/Time

Intensity

Electric Field

Magnetic Field

Current

Entropy

• Volume: Liters (L)

• Mass: kilograms (kg) in physics, grams (g) in chemistry

• Pressure/Stress: atmospheres (atm) for everything except fluids (Pascals, Pa)

• Temperature: Kelvin (K), NOT Celsius (K=C+273)

• Amount: moles (mol)

• Displacement/Distance: meters (m)

• Velocity: m/s

• Acceleration: m/s² (linear) or v²/r (centripetal/circular)

• Period/Time: seconds (s)

• Intensity: Watts/meters² (W/m²)

• Electric Field: Volts/meter (V/m) or Newtons/Coulomb (N/C)

• Magnetic Field: Teslas (T)

• Current: Amps (A), or Coulombs/second (C/s)

• Entropy: J/^OK

Detailed Standard Unit to Memorize

Frequency

Force

Work, Energy, heat, Enthalpy, and Gibbs Free Energy

Power

Pressure/Stress

Charge

Electric Potential Difference

Resistance

Capacitance

Electric Conductance

• Frequency: Hertz (Hz) = 1/s 

• Force: Newtons (N) = (kg*m)/s^2

• Work, Energy, Heat, Enthalpy, and Gibbs Free Energy:  Joules (J) = N*m = (kg*m^2)/s^2

• Power: Watts (W) = J/s = (kg*m^2)/s^3

• Pressure/Stress:  Atmospheres (atm) for everything except fluids (Pascals, Pa). For Pascal: N/m^2 = kg/(s^2*m)

• Charge: Coulombs (C) = A*s

• Electric Potential Difference (Voltage): Volts (V) = W/A = (kg*m^2)/(A*s^3)

• Resistance: Ohms (Ω) = V/A =  (kg*m^2)/(A^2*s^3)

• Capacitance: Farads (F) = C/V = (s^4*A^2)/(kg*m^2)

• Electric Conductance: Siemens (S) = A/V = (s^3*A^2)/(kg*m^2)

Conversions

Pressure:

Temperature:

Parts per million (ppm):

1 eV:

Area and Volume Conversion:

Pressure: 1 atm = 760 torr = 760 mmHg = 100 kPa (rounded!). 1 Pa = 1 N/m2 (Newtons per meters2)

Temperature: ^OK = ^OC + 273

Parts per million (ppm) = (amount of solute/amount of solvent)*106

1 eV = 1.6x10-19J; eV = electron volt (unit of energy)

Area and Volume Conversions: 1 meter = 10² cm; 1 square m = (10²)² cm²; 1 cubic m = (10²)³ cubic cm

Concentration:

(Basics - General Chemistry)

Molarity (M) = mol/L

Density

(Basics - General Chemistry)

𝜌 = m/V

Molality

m = mol_solute / kg_solvent

Mole Fraction

(Basics - General Chemistry)

X_A = n_A/n_total

n = moles

Normality (N):

(Basics - General Chemistry)

N = M*(# equivalents)

M = molarity (mol/L); # equivalents = # of reactive units per mole

Gram Equivalents

(Basics - General Chemistry)

m_eq = mass/equivalent weight

Eq Weight = molar mass/n

n = # equivalents

Dilutions:

(Basics - General Chemistry)

C₁V₁ = C₂V₂

C = Concentration = Molarity (mol/L); V = Volume (L)

Atomic Weight

(Basics - General Chemistry)

AW = m₁p₁ + m₂p₂ + …

m = mass; p: probability of isotope

Percent Yield:

(Basics - General Chemistry)

% Yield = (Actual/Theoretical)*100

Equilibrium Constant

(Equilibrium - General Chemistry)

For aA + bB ⇌ cC + dD:

K_eq = [C]^c[D]^d/[A]^a[B]^b

Keq > 1 → products favored; Keq < 1 → reactants favored; Keq = 1 → products ≈ reactants

Reaction Quotient

(Equilibrium - General Chemistry)

For aA + bB ←→ cC + dD: Q = [C]^c[D]^d/[A]^a[B]^b

When Q>K_eq, reverse rxn favored (shift left)

When Q<K_eq, forward rxn favored (shift right)

When Q=K_eq, at equilibrium

Arrhenius Equation for Rate Constant

(Kinetics- General Chemistry)

k = Ae^-Ea/RT

k = Rate Constant; A = Collision frequency; Ea = Activation Energy; R = Gas Constant; T= temperature

Do not need to do calculation but know relationship: Rate ↑ when temperature & frequency ↑ or  Ea ↓

Rate Law

(Kinetics- General Chemistry)

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

X and Y are orders of A and B; k,x,y are determined experimentally

Rate

(Kinetics- General Chemistry)

For aA + bB ⇌ cC + dD

Rate = -Δ[A]/aΔt = -Δ[B]/bΔt = Δ[C]/cΔt = Δ[D]/dΔt

Integrated Rate Laws:

(Kinetics- General Chemistry)

Zeroth: slope = -k on [A] vs time 

First: slope = -k on ln[A] vs time  

Second: slope = k on 1/[A] vs time

Internal Energy of a Molecule

(Thermodynamics - General Chemistry)

ΔU = Q − W

Q = heat; W = Work

Work done on/by Gas

(Thermodynamics - General Chemistry)

W = −PΔV

Heat (no phase change):

(Thermodynamics - General Chemistry)

q = mCΔT

q = heat energy; m = mass; C: specific heat; ΔT = temp change (kelvin)

Heat of Phase Change

(Thermodynamics - General Chemistry)

q = mL

q = heat energy; m = mass; L = latent heat

Gibbs Free Energy, ΔG

(Thermodynamics - General Chemistry)

ΔG = ΔH − TΔS

ΔH = change in enthalpy; ΔS = change in entropy; T = temperature (Kelvin)

Hess Law of Summation

(Thermodynamics - General Chemistry)

ΔH_reaction​ = ∑ΔH_f^∘​_products − ∑ΔH_f^∘​_reactants 

ΔH_reaction ​= ∑ΔH_{bonds broken} − ∑ΔH_{bonds formed}

ΔS_reaction​ = ∑ΔS_f^∘​_products − ∑ΔS_f^∘​_reactants

ΔG_reaction​ = ∑G_f^∘​_products − ∑G_f^∘​_reactants

Enthalpy

(Thermodynamics - General Chemistry)

ΔH_rxn = Q/n

Q = heat; n = number of moles

Entropy

(Thermodynamics - General Chemistry)

S = Q/T

Q = heat; T = temperature (kelvin)

Thermal Expansion

(Thermodynamics - General Chemistry)

ΔL = 𝛼LΔT

𝛼: constant, L: length; ΔT = temperature change (kelvin)

Ideal Gas Law:

(Gases - General Chemistry)

PV = nRT

Boyle’s Law:

(Gases - General Chemistry)

PV = k 

k = constant

Charle's Law:

(Gases - General Chemistry)

V/T = k 

T = temp; k = constant

Avogadro’s Law:

(Gases - General Chemistry)

n/v = k 

n = moles; v = volume; k = constant

Combined Gas Law:

(Gases - General Chemistry)

P₁V₁/n₁T₁ = P₂V₂/n₂T_2; 

Cancel out constant variables

Pressure:

(Gases - General Chemistry)

P = F/A

Absolute Hydrostatic Pressure:

(Gases - General Chemistry)

P = P₀ + ρgh

P₀ = surface pressure; ρ = fluid density; g = gravity constant (9.8 m/s^2); h = height

Dalton’s Law of Partial Pressures 

(Gases - General Chemistry)

P_A = X_AP_total

X_A = mole fraction of A; P_total = P_A + P_B + P_C + …

Raoult’s Law of Vapor Pressure:

(Gases - General Chemistry)

P_A = X_AP_A^O

X_A = mole fraction of A; P_A^O: Vapor Pressure of A

Henry’s Law (Solubility of Gas)

(Gases - General Chemistry)

C_A = kP_A, ↑P ∝ ↑C 

C: Concentration 

k: gas constant

P_A: Partial Pressure of A

Graham’s Law of Effusion

(Gases - General Chemistry)

rate₁/rate₂ = √(m₂/m₁)

m = molar mass

Internal Energy of a Gas

(Gases - General Chemistry)

U_gas = 3/2 nRT

n = # of moles; R = ideal gas constant; T = temp (Kelvin)

Kinetic Energy of a Gas

(Gases - General Chemistry)

KE = ½mv² = ³/₂kT, k is a constant

Weight:

(Gases - General Chemistry)

F_g = ρVg = mg

ρ = density; V = volume; g = gravity; m = mass

Pascal's Principle:

(Gases - General Chemistry)

F1/A1 = F2/A2

F = Force; A = Area

Poiseuille's Law:

(Gases - General Chemistry)

Q = (πr⁴ΔP)/(8ηL)

Q = flow rate; r = radius; ΔP = pressure difference; η = viscosity; L = length

Flow Rate:

(Gases - General Chemistry)

Q = v1A1 = v2A2

Q = flow rate; v = velocity; A = area

Bernoulli's Equation:

(Gases - General Chemistry)

P1 + ½ρv1² + ρgh1 = P2 + ½ρv2² + ρgh2

P = pressure; ρ = density

Solubility Constant

(Solubility- General Chemistry)

For A_xB_y ←→ xA^y+ + yB^x- : 

K_sp ​= [A^y+]^x[B^x−]^y

Big Ksp = more soluble & small Ksp = less soluble

Osmotic Pressure

(Solubility- General Chemistry)

Π = iMRT

i: van’t Hoff factor; M = molarity, R = ideal gas constant; T = temperature

Boiling Point Elevation & Freezing Point Depression

(Solubility- General Chemistry)

Boiling: ΔT = iK_bm

Freezing: ΔT = iK_fm

i = van’t Hoff factor; K_b/f: boiling/freezing constant; m: molality

Retention Factor

(Solubility- General Chemistry)

R_f = d_compound / d_solvent, d: distance

pH & pOH:

(Acids and Bases- General Chemistry)

pH = -log[H⁺] or 10^-pH = [H⁺]

pOH = -log[OH^-] or 10^-pOH = [OH^-]

pK_a and K_a & pK_b and K_b:

(Acids and Bases- General Chemistry)

pK_a = -log(K_a) or 10^-pKa = K_a

pK_b = -log(K_b) or 10^-pKb = K_b

Ionization Constant of Water

(Acids and Bases- General Chemistry)

K_aK_b = K_W = 10^-14

pH + pOH = 14

pK_a + pK_b = 14

Henderson-Hasselbalch Eq (for Buffers)

(Acids and Bases- General Chemistry)

pH = pK_a + log([conj. base = A-]/[acid = HA])

pOH = pK_b + log([conj. acid = B+]/[base = BOH])

pI of Amino Acids:

(Acids and Bases- General Chemistry)

pI = pH where net charge = 0

pI = (pK_a1 + pK_a2) / 2 

Acidic: (pK_a,carboxyl+pK_a,R-Group)/2

Basic: (pK_a,amino+pK_a,R-Group)/2

Neutral: (pK_a,carboxyl+pK_a,amino)/2

Neutralizations (and Dilutions)

(Acids and Bases- General Chemistry)

C_H+V_acid = C_OH-V_Base

Standard Reduction Potential:

(Redox Chemistry and Electrochemistry - General Chemistry)

emf°  = E°cathode - E°anode & ΔG = −nFEcell

ΔG = Gibbs free energy; n = mols; F = Faraday’s constant (96,485 C/mol)

+ Ecell or - ΔG = spontaneous 

- Ecell or + ΔG = non-spontaneous

Nernst Equation:

(Redox Chemistry and Electrochemistry - General Chemistry)

E = E^O - (RT/nF)(logQ) 

E = Actual Cell potential; E^O = Standard cell potential

R = gas constant; T = Temp; n = mol; F = Faraday’s constant (96485 C/mol)

Q = reaction quotient. [C]^c[D]^d / [A]^a[B]^b from aA + bB ⇌ cC + dD

Current caused by n electrons:

(Redox Chemistry and Electrochemistry - General Chemistry)

I = nF/t 

n = mol e^- ; F = Faraday’s constant (96485 C/mol); t = temperature

Cell Potential

(Redox Chemistry and Electrochemistry - General Chemistry)

E_Cell = E_{reduction,cathode} + E_{oxidation,anode} or E_Cell = E_{reduction,cathode} - E_{reduction,anode} (they’re the same thing)

SOH CAH TOA

(Trigonometry and Geometry - General Chemistry)

Sinθ = Opposite / Hypotenuse

Cosθ = Adjacent / Hypotenuse

Tanθ = Opposite / Adjacent

Sin/Cosine/Tan to Memorize for 0^O, 30^O, 45^O, 60^O, 90^O:

(Trigonometry and Geometry - General Chemistry)

sin: 0, 1/2, √2/2=0.71, √3/2=0.87, 1

cos: 1, √3/2=0.87, √2/2=0.71, 1/2, 0

tan: 0, 1/√3=0.58, 1, √3=1.7, undefined

Pythagorean Theorem

(Trigonometry and Geometry - General Chemistry)

A² + B² = C²

3, 4, 5 Triangles

(Trigonometry and Geometry - General Chemistry)

-Significance: If you see a vector with components of 6&8 or 30&40, you know the hypotenuse is 10 or 50

Areas

(Trigonometry and Geometry - General Chemistry)

Circle: 𝜋r²

Sphere Surface Area: 4𝜋r² 

Triangle: ½base*height

Work

(Work and Energy - General Chemistry)

W = Fd = Fdcosθ = qEd = qV  = ΔEnergy (J)

d = distance; q = charge, E = electric field strength, V =Electric potential difference (voltage)

Power

(Work and Energy - General Chemistry)

P = W/t = Fv = IV

W = Work; t = time; F= force; v = velocity; I = Current; V = Potential Difference (Voltage)

Mechanical Advantage

(Work and Energy - General Chemistry)

MA = F_Resistance/F_Effort

Efficiency

(Work and Energy - General Chemistry)

Eff = W_output/W_input = P_output/P_input

W = Work; P = Power

Kinetic Energy:

(Work and Energy - General Chemistry)

KE = ½ mv²

m = mass; v = velocity

Gravitational Potential Energy

(Work and Energy - General Chemistry)

U_g = mgh

Conservation of Energy:

(Work and Energy - General Chemistry)

U_i + KE_i = U_f + KE_f + W

U = PE; W = Work; i = initial; f = final

Momentum

(Work and Energy - General Chemistry)

p = mv

m = mass; v = volume

Force

(Work and Energy - General Chemistry)

F = ma

m = mass; a = acceleration

Force of Friction

(Work and Energy - General Chemistry)

Kinetic friction: F_f = μ_kFn

Static friction (max): F_{s, Max} = μ_sFn 

μ_k = coefficient of kinetic friction; μ_s = coefficient of static friction; Fn = normal force

Forces on an Inclined Plane

(Work and Energy - General Chemistry)

F_N = mgcosθ

F_𝜇 = 𝜇mgcosθ

F_g = mgsinθ

F_N = normal force; F_𝜇 = Friction Force; Fg = gravity force

Acceleration Pulley with Two Masses

(Work and Energy - General Chemistry)

a_net = ((m₁ - m₂)g) / (m₁ + m₂)

Center of mass

(Work and Energy - General Chemistry)

x_c = (m₁x₁ + m₂x₂ + …)/(m₁ + m₂ + …)

x = center of mass; x = position of each mass; m = mass

Gravitational Force between Two Objects

(Work and Energy - General Chemistry)

F_G = GMm/r²

G = gravitational constant (6.67 x 10^-11 N*m^2 / kg^2) → should be given

M = larger mass; m = smaller mass; r = distance center to center

Elastic Force

(Work and Energy - General Chemistry)

F_k = -kx, 

k = spring constant x = amount stretched

Elastic Potential Energy

(Work and Energy - General Chemistry)

U_k = ½kx²

k = spring constant; x = amount stretched

Torque

(Work and Energy - General Chemistry)

𝛕 = rF = rFsinθ 

Rotational Equilibrium: 𝛕₁ = 𝛕₂

r = radius; F = Force

Centripetal Force

(Work and Energy - General Chemistry)

F_c = mv²/r 

m = mass; v = velocity; r = radius

Centripetal Acceleration

(Work and Energy - General Chemistry)

a_c = v²/r

v = velocity; r = radius

Mass Defect (Nuclear Binding Energy):

(Atomic/Nuclear Physics - General Chemistry)

E = Δmc²

E = Energy; m = mass; c = speed of light (3.0x10^8 m/s)

Energy of Electron n Level

(Atomic/Nuclear Physics - General Chemistry)

E_n ​= -13.6/n²

n = energy level

Rydberg Equation (Change in n Level)

(Atomic/Nuclear Physics - General Chemistry)

E_Δn = hf = R((1/n_f²)-(1/n_i²))

R = Rydberg constant (will be given); n = energy level

Number of Half Lives

(Atomic/Nuclear Physics - General Chemistry)

N=N_o(½​)ⁿ, 

n: # of half lives

N: final amount

N_o: initial amount

Total Time of Half-Life Decay

(Atomic/Nuclear Physics - General Chemistry)

t_total = n*t_1/2

n = # of half life; t_1/2 = half life of substance

Types of Nuclear Decay

(Atomic/Nuclear Physics - General Chemistry)

Alpha:  ^A_ZX → ^A-4_Z-2X + ⁴₂He (or ⁴₂𝞪)

Beta^-: ^A_ZX → ^A_Z+1X + ⁰_-1β (or ⁰_-1e)

Beta⁺: ^A_ZX → ^A_Z-1X + ⁰₁β (or ⁰₁e)

E^- Capture: ^A_ZX + ⁰_-1β → ^A_Z-1X

Gamma: ^A_ZX → ^A_ZX + 𝜸

Max # of Electrons in n Energy Shell

(Atomic/Nuclear Physics - General Chemistry)

e^- = 2n²

Photoelectric Effect

(Atomic/Nuclear Physics - General Chemistry)

KE_electron = E_photon - W_Function

½mv_electron² = hf_photon - W_Function

E_photon = Photon Energy; W = Work; m = mass; v = velocity; h = planck constant (6.626 x 10^-34 J*s); f = frequency

Series vs Parallel Circuit:

(Atomic/Nuclear Physics - General Chemistry)

Series Circuits → Same Current

R_T = R₁ + R₂ + R₃ + ...

ΔV = V₁ + V₂ + V₃ + ...

I_T = I₁ = I₂ = I₃ = ...

Parallel Circuits → Same Voltage

1/R_T = 1/R₁ + 1/R₂ + 1/R₃ + ...

V_T = V₁ = V₂ = V₃ = ...

I_T = I₁ + I₂ + I₃ + ...

Capacitance

(Atomic/Nuclear Physics - General Chemistry)

C = Q/V = ͼ_oA/d

C = Capacitance; Q = source charge, V = Potential Difference (Voltage); ε₀ = permittivity of free space; A: Area; d= distance

Capacitance in Series vs Parallel

(Atomic/Nuclear Physics - General Chemistry)

Series: 1/Ceq = 1/C1 + 1/C2 + 1/C3 + …

Parallel: Ceq = C1 + C2 + C3 + ...