MCAT Equations

Work, Energy, and Power - Physics

Work =

Kinetic Energy (KE) =

Work Energy Theorem =

Power =

Fdcosø

1/2mv²

∆KE

W/t =, Fv =, E/t

Gravity - Physics

Fg =

mg

Circular motion - Physics

Centripetal acceleration (ac) =

Centripetal force (Fc) =

v²/r

mac, mv²/r

Projectile Motion - Physics

Horizontal

• X =

• Vx =

• ax =

Vertical

• y =

• Vy =

• ay =

General 3 Equations =

Voxt

Vxo

0

voyt-1/2gt²

voy-gt

g

V=Vo + at

V² = Vo²+2ad

d = do + Vot + 1/2at²

Torque - Physics

τ =

Frsinø

Friction - Physics

Fs ≤

Fk =

usFn

ukFn

Magnetism - Physics

Magnetic Force F_B

• Moving charge/point =

• Current carrying wire =

Magnetic Field B

• Wire =

• Circular loop =

qvB(sinø)

LIB(sinø)

u_oI / 2πr 

u_oI/2r

Thermodynamics - Physics

1st law = ∆U =

Pressure-Volume Work =

Heat capacity in calorimeter = q =

Specific heat capacity = q =

Phase Change = q =

Q-W

P∆V

C∆T

mc∆T

mL

Fluids - Physics

Density = p =

Specific gravity = SG =

Pressure (fluids) = P =

Pascal’s law (2) =

Continuity equation =

• Continuity equation when determining number of something

Flow Rate = Q = (2)

Archimedes Principle = Fb =

• For an object floating in water (no tension), Fb = ——

Bernoulli’s principle =

Hydrostatic pressure =

m/V

p/pH2O

F/A

F1/A1 = F2/A2 and F2 = A2/A1F1

A1v1 = A2v2

Av = nAv

Av, V/t

pfluid x Vsub x g = mobject x g, mg

P1 + 1/2pv² + pgh = P2 + 1/2pv² + pgh

P = pgh

Inclined Plane - Physics

Fg parallele =

Fg perpendicular =

mgsinø

mgcosø

Circuits and Electrostatics - Physics

Ohm’s Law =

Power = P =

Equivalent Resistors

• Series

• Parallel

Voltage Total

• Series

• Parallel

Equivalent Capacitance

• Series

• Parallel

Voltage Drop (Kirchoff’s Loop Rule)

• Voltage drop across a circuit is ∑V =

• States sum of voltage gains = sum of voltage drops

• The positive voltage from the battery (V_battery) minus the total voltage drops across the resistors (V_drop) must equal zero

V = IR

IV = I²R = v²/R

Rs = R1 + R2 + … Rn

1/Rp = 1/R1 + 1/R2 + … 1/Rn

Vs = V1 + V2 + … Vn = 0

Vp = V1 = V2 = Vn

1/Cs = 1/C1 + 1/C2 + … 1/Cn

Cp + C1 + C2 + … Cn

V1 + V2 … + Vn = 0

Circuits and Electrostatics Cont’d - Physics

Current = I =

Resistance = R =

Coulomb’s Law = Fe =

• Electrostatic force between two charge points

Force by electric field = Fe =

• Force exerted on a charge by a standing electric field

Electric Field strength = E =

• Work done by E =

• E by a point charge (q) some distance (d) away = ——

• E by a plane sheet = —(2)—-

  • Where σ = surface charge density and k = Coulomb’s constant

Electric Potential/Voltage = V = (2)

Electric Potential Energy = U = (2)

Conductivity σ = and resistivity p =

Q/t

pL/A

k(q1q2/r)

qE

F/q, qE x d, kq/d², 2kπσ, 2kπ(Q/A)

W/q, Ed

qV, qEd

1/p, 1/σ

Capacitors - Physics

Capacitance = C =

Capacitance (dielectrics) =

Capacitance (parallel plate geometry) =

• Parallel plate with dielectrics = ——

Capacitor electric field = E_C =

Capacitor energy (PE) (2) =

• Where C = capacitance

Q/V

k x Co

ϵ(A/d)

kϵ(A/d)

V/d

1/2CV² and 1/2QV

Lights and Optics - Physics

Photon Energy = E = (2)

Speed of light (c ) =

Index of refraction = n =

Snell’s Law =

• More dense to less dense =

• Less dense to more dense =

Critical angle =

• When Ø1 = Ø2 = 90

• When high → low density and Ø1 > Øc =

Diffraction grating =

hf and hc/λ

3×10^8

c/v

n1sinø1 = n2sinø2, Ø1 < Ø2, Ø1 > Ø2

sin^-1(n2/n1), total internal reflection

dsinø = mλ

Lights and Optics - Physics

Magnification = m = (3)

Lens strength = S =

Lens Equation (2) =

-i/o = hi/ho = -di/do

1/f

1/o + 1/i = 1/f

1/do + 1/di = 1/f

Waves and Oscillations - Physics

Frequency and Period: f =

Velocity of any/general wave = v =

Speed of light/electromagentic wave = c =

Hooke’s Law = Felastic =

PE of Spring =

Harmonics Open Pipe/String (f and λ)

Harmonics One End Closed Pipe (f and λ)

1/T

λf

λf

kx

1/2kx²

f = nv/2L λ = 2L/n

f = nv/4L λ=4L/n

Sounds - Physics

Velocity of sound = v =

Intensity = I =

Intensity in decibels = dB =

• Io =

• For every jump in 10 dB = ten fold increase

Doppler Effect = f =

• Use — signs when source is moving TOWARDS observer

• Use —- signs when source is moving AWAY from observer

λf

P/A

10log(I/Io), 1×10^-12

fs(v ± vo / v ∓ vs)

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Moles, Concentration, Dilutions - Chemistry

Moles =

Avogadros number = 1 mol =

Mol fraction = Xa =

Molarity = M =

Molality = M =

Dilution equation =

Normality =

• Where n is the equivalence factor, number of H+ the compound possesses

mass/molecular weight

6.022×10^ 23 particles

moles a / total moles

moles / L

moles / kg

m1V1 = m2V2

M x n

Gases - Chemistry

Standard Temp and Pressure (STP) =

• T = —— ºC = —— K

• P = —-atm = —- torr = —— mmHg = ——Pa

Ideal gas law =

Boyle’s Law = (2)

Charle’s Law =

Gay-Lussac Law =

Avogadro’s Law =

Dalton’s Law of Partial Pressure

• Total Pressure =

• Partial Pressure Gas a =

Graham’s Law of Effusion =

0, 273

1, 760, 760, 1×10^5

PV = nRT

P = 1/V, P1V1 = P2V2

V1/T1 = V2/T2

P1/T1 = P2/T2

V1/n1 = V2/n2

Ptotal = P1 + P2 … + Pn

Pa = XaPtotal

rate1/rate2 = √M2/M1

Atomic Chemistry - Chemistry

Formal Charge =

#valence electrons - #bonds - #lone pair electrons

Electrochemistry

Standard Free Energy Change = ∆G =

Standard emf =

Nernst Equation = Ecell =

Free Energy Change

• Standard = ∆Gº =

• NonStandard = ∆G =

-nFEcell

Ered;cathode - Ered;anode

Eºcell - (0.0592/n)logQ

-RTlnKeq

∆Gº + RTlnQ

Thermodynamics

Kelvin to Celsius =

Farenheit to Celsius =

Specific Heat = q =

Specific Heat (phase change) = q =

• mass and specific latent heat

• moles and molar enthalpy

Enthalpy of Reaction = ∆Hrxn

• Reaction Enthalpy

• Bond Enthalpy

C + 273

9/5C + 32

mc∆T

mL , n∆Hfus/vap

∑∆Hproducts - ∑∆Hreactants

∑∆Hbonds broken - ∑∆Hbonds formed

Thermodynamics Cont’d

Free Energy Change = ∆G =

Free Energy Change (Keq) = ƼG =

Free Energy Change (Q) = ∆G = (2)

∆H-T∆S

-RTlnKeq

∆Gº + RTlnQ and RTln(Q/Keq)

Ideal Gas Equations Boltzmann Terms - Chemistry

• Ideal Gas law =

  • This time N is the total number of particles, unlike n which is the moles of the gas

• KE of an ideal gas =

• Entropy (S) of an ideal gas =

PV = NKbT

3/2KbT

KblnW

Kinetics

Rate law = Rate =

Arrhenius equation = k = (2)

Simplified Arrhenius

Michaelis Menten

k[A]^a[B]^b

Ae^(-Ea/RT), A/e^(Ea/RT)

ln(k1/k2) = Ea/R + (1/∆T)

Vo = Vmax [S] / Km + [S]

Equilibrium

Equilibrium constant = Keq =

Reaction quotient = Q =

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

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

Solutions

% composition by mass =

Mole Fraction = Xa =

Solubility Product Constant = Ksp =

• Assuming the equation Am​Bn​(s)⇌mA^n+ + nB^m−

Rault’s Law (VP depression) = Pa =

Boiling Point Elevation = ∆Tb =

Freezing Point Depression = ∆Tf =

Osmotic Pressure = π =

mass solute / mass solution x 100

moles a / total mole all species

[A^n+]^m [B^m-]^n

XaPaº

iKbm

iKfm

iMRT

Acids and Bases

pH =

pOH =

pH + pOH =

Ka =

pKa =

Kb =

pKb =

Kw = (value and equation)

Autoionization of water = Kw =

Henderson-Hasselbach =

-log[H+]

-log[OH-]

14

[H+][A-] / [HA]

-logKa

[OH-][BH+] / [B]

1×10^-14, Ka x Kb

[H3O+][OH-] = 1×10^-14

pH = pKa + log([A-] / [HA])

Probability - Biology

• Two independent events, Probability of both occurring: P(A and B) =

• Non-Mutually Exclusive events, Probability of either occurring: P(A or B) =

  • This accounts for the event that both may occur

Recombination frequency (RF) =

• For gene mapping (higher RF = more distant)

hardy-Weinberg

• Allele frequency equation:

• Genotype frequency equation:

PA x PB

PA + PB - P(A x B)

recombinant offspring / total offspring x 100%

p + q = 1, p² + 2pq + q² = 1

Nuclear Decay - Chemistry

Alpha Decay

• Unstable nucleus emits an alpha particle (4/2 He)

• — the atomic mass by ——

• — the atomic number by

Beta Minus/Electron Emission

• Neutron in an unstable nucleus converts into a proton, emitting an electron

• — the atomic number by —-

• The atomic mass number is ——

Beta Positive/Positron Emission/Electron Capture

• Proton in an unstable nucleus converts into a neutron and emits a positron and electron neutrino

• — the atomic number by —

• The atomic mass number is ——

Gamma Decay

• Nucleus emits a high energy photon an shifts from an excited state to lower energy state

• The atomic mass and number are —-

reduce, 4, reduce 2

increase 1, unchanged

decrease 1, unchanged

unchanged

Effective Nuclear Charge

• Z = total charge of nucleus (# of ——)

• S = shielding constant (number of —— electrons in the atom or ion, so total # electrons - valence electrons)

Henry’s Law of Solubility

• Where C = —-, kH is a —- that equals —— , and Pgas = —- —- at —

• Describes the equilibrium between the gas partial pressure and amount dissolved in solution

• Can plug in Boyle’s law to Pgas to get ———-

kcat =

• This is the turnover number, representing the maximum number of substrate molecules converted to product by a single enzyme molecule per second when fully saturated

• At substrate saturation, Vmax = reaction rate

Catalytic Efficiency =

Isoelectric Points

• pI for neutral/nonpolar amino acids =

• pI for acidic amino acids =

• pI for basic amino acids =

Z-S, protons, core

C = kH x Pgas, concentration, constant, 6 × 10^-3 , partial pressure, equilibrium, C = kH x 1/V

Vmax/[E]total

kcat / Km

pKa1 + pKa2 / 2

pKa (R group) + pKa (COOH) / 2

pKa (R group) + pKa (NH2) / 2

Photoelectric Effect

• The represents the minimum energy required to eject an electron from a metal’s surface

• Where f_o = threshold frequency and h = Planck’s constant

Relating WF to KE

• Where hf = energy current of incoming photon and WF = energy needed to overcome the metal’s binding force and eject an electron

• If hf < WF then NO electron is emitted (would make KE negative)

WF = f_o x h

KEmax = hf - WF

Mental Math Tricks

• ln10 =, ln 2 = , lne = , ln1 =, e =

• log(1x10^x) =

• log(m x 10ⁿ) =

• To cancel out log… 2 = log(X) so X =

• log(x^y) =

• log(x * y) =

• log(x/y) =

Log(2) =

Log(3) =

Log(5) =

Any change in one unit of a p-scale (pH, pKa, etc) constitutes a 10x change in value being “logged”

2.3, 0.693, 1, 0, 2.7

x

n + 0.m

10²

ylogx

logx + logy

logx - logy

0.3, 0.5, 0.7