MCAT Equations

Average speed

Equation: 𝛥 x / 𝛥 t Units: (m/s)

Average Velocity

Equation: 𝛥 d / 𝛥 t Units: (m/s)

Acceleration

Equation: 𝛥 v / 𝛥 t Units: (m/s²)

Newton’s Second Law

Equation: Fnet = ma Units: 1 Newton = 1 kg ∙(m/s²)

Static Friction

Equation: Fmax = μ(s)F(N) Units: 1 Newton = 1 kg ∙(m/s²)

Kinetic Friction

Equation: F,f = μ(k)F(N) Units: 1 Newton = 1 kg ∙(m/s²)

Force of gravity acting perpendicular to an inclined plane

Equation: mgcosθ Units: 1 Newton = 1 kg ∙(m/s²)

Force of gravity acting parallel to an inclined plane

Equation: mgsinθ Units: 1 Newton = 1 kg ∙(m/s²)

Torque

Equation: τ = rFsinθ Units: Joule = (N ∙ m)

Work (pressure-volume curve)

Equation: W = P∆V Units: Joule = (N ∙ m)

Center of mass

Equation: x = m(1)x(1) + m(2)x(2) + m(2)x(2) / m(1) + m(2) + m(3)

Mechanical Advantage

Equation: MA = F(out) / F(in)

Power

Equation: P = W/ t and ∆E/t Units: 1 watt W = J/s

Power

Equation: P = Fv Units: 1 watt W = J/s

Kinetic Energy

Equation: KE = 1/2mv² Units: Joule = (N ∙ m)

Work-Kinetic Energy Theorem

Equation: Wnet = ∆KE = K(f) − K(i) Units: Joule = (N ∙ m)

Gravitational Potential Energy

Equation: U = mgh Units: Joule = (N ∙ m)

Elastic Potential Energy

Equation: U = 1/2kx² Units: Joule = (N ∙ m)

Hooke’s Law

Equation: F = −kx Units: 1 Newton = 1 kg ∙(m/s²)

Frequency of a wave

f = f/T Units: (Hz = 1/s)

Speed of a wave

Equation v = fλ Units = (m/s)

Density

Equation: ρ = m/V Units: (g/cm³)

Specific Gravity

ρ(object)/ρ(water)

Buoyant Force

F(B) = mg = ρ(fluid)Vg Units: 1 Newton = 1 kg ∙(m/s²)

Pascal’s Law

F(1)A(1) = F(2)/A(2)

Hydrostatic Pressure

P = P(0) + ρgz

Poiseuille’s Law

Q = πr^4∆P/8ηL

Continuity Equation

A(1)v(1) = A(1)v(1)

Bernoulli’s Equation

P(1) +1/2ρv²(1) + ρgh(1) = P(2) + 1/2pv²(2) + pgh(2)

Absolute Temperature

K = °C + 273

Pressure

P = F/A

Ideal Gas Law

PV = nRT

Boyle’s Law

P(1)V(1) = P(2)V(2)

Charles’ Law

V(1)/T(1) = V(2)/T(2)

Avogadro’s Law

n(1)/V(1) = n(2)/V(2)

Average kinetic energy of a gas particle

Equation: KE(avg) = 3/2 k(B)T Units: Joule = (N ∙ m)

Heat capacity at constant volume for an ideal monatomic gas

Equation: C(V) = 3/2 nR Units: J/K

Heat capacity at constant pressure for an ideal monatomic gas

Equation: C(P) = 5/2 nR Units: J/K

Van der Waals equation of state

P = (nRT/V − nb) − (n²a/V²)

Dalton’s Law of Partial Pressures

P(A) = X(A)P(T)

P = P(A) + P(B) + PC)

Heat transferred

Equation: q = mc∆T Units: 1(cal/g ∙ K) = 4.184 J/(g ∙ K)

Standard Heat of Reaction

ΔH = ∑H_{(bonds broken)} - ∑H_{(bonds formed)}

Standard Heat of Reaction (2)

ΔH = ∑H,f_(products) - ∑H,f_(reactants)

Change in Gibbs Free Energy

Equation: ∆G = ∆H − T∆S Units: kJ/mol

Linear Expansion (Solids)

∆L = αL∆T

Volumetric Expansions (Solids & Liquids)

∆V = βV∆T

Sound Level

Equation: β = 10log (I/I(0)) Units: dB

Sound Level (2)

β(f) = β(i) + 10log(I(f)/I(i)) Units: dB

Intensity

Equation: I = P/A Units: W/m²

Doppler Effect

Equation: f’ = f(v ± v(d)/v ∓ v(s) Units: Hz

Waves in Open Pipes

λ = 2L/n and f = v/λ = nv/2L

Waves in Closed Pipes

λ = 4L/n and f = v/λ = nv/4L

Speed of Light

Equation: c = fλ Units: m/s

Energy of Photon

E = hf

Law of Reflection

θ(1) = θ(2)

Index of Refraction

n = c/v

Snell’s Law

n(1)sinθ(1) = n(2)sinθ(2)

Critical Angle

θ[c] = sin^-1 (n(2)/n(1))

Optics Equation

1/f = 1/0 + 1/i = 2/r

Magnification

m = -i/o

Lens Power

Equation: P = 1/f Units: Diopters

Focal length of lenses in a series

1/f = 1/f(1) + 1/f(2) + 1/f(3) + 1/f(n)

Power of lenses in a series

P = P(1) + P(2) + P(3) + P(n) Units: Diopters

Magnification for a system of lenses

m = m(1) × m(2) × m(3)

Coulomb’s Law

F(e) = kq(1)q(2)/r² Units: 1 Newton = 1 kg ∙(m/s²)

Electric Field

Equation: E = F(e)/q = kQ²/r² Units: N/C or V/m

Electrical Potential Energy

Equation: U = kQq/r Units: Joule = (N ∙ m)

Electrical Potential

Equation: V = U/q = kQ/r Units 1 V = 1 J/C

Intensity of Uniform Electric Field

Equation: V/d Units: V/m

Voltage (Potential Difference)

Equation: ∆V = V(b) − V(a) = W(ab)/q Units: Volts = 1 (J/C)

Power

Equation: VI Units: W (J/s)

Power

Equation: V²/R Units: W (J/s)

Power

Equation: I²R Units: W (J/s)

Current

Equation: I = Q/t Units: 1 A = 1 C/s

Resistors in Series

R(s) = R1=(1) + R(2) + R(3) Units: Ohms (Ω)

Ohm’s Law

V = IR

Resistors in Parallel

1/R(1) = 1/R(1) + 2/R(2) + 3/R(3) Units: Ohms (Ω)

Resistivity

Equation: Q = R ∙ A / L Units: Ohm-meter (Ω ∙ m)

Capacitance

Equation: C = Q/V = ε(0) (A/d) Units: 1 F = 1 C/V

Energy of a Charged Capacitor

U = Q² / C = ½ Q∆V = ½ C(∆V)²

Capacitors in Series

Equation: 1/C(s) = 1/C(1) + 1/C(2) + 1/C(3) Units: F

Capacitors in Parallel

Equation: C(p) = C(1) + C(2) + C(3) Units: F 1(C/V)

Magnetic Force

F(B) = qvBsinθ Units: 1 Tesla = 1 (N ∙ s/m ∙ C)

Lorentz Force

F = qE + qvBsinθ

Maximum number of electrons in a shell

2n²

Kinetic Energy of a Photoelectron

Equation: hf − φ Units: eV (electron volt)

Formal Charge

FC = V − NB − 1/2 B

Dipole Moment

Equation: p = q ∙ d Units: C ∙ m

Specific rotation

Equation: [α] = α(observed)/ c × l Units: Degrees

Electrodeposition Equation

mol M = It/nF

Cell potential

cell pot. = red. pot − ox. pot

Rate law

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

Arrhenius Equation

k = Ae^-Ea/RT

Law of Mass Action

k(eq) = [C]^c [D]^d / [A}^a [B]^b

Wavenumber

Equation: 1/λ Units: cm^-1

Autoionization of water

K(w) = [H(3)O+][OH-] = 10^-14

pH

-log[H+]

pOH

− log[OH-]

Acid Dissociation Constant

k(a) = [H(3)O+][A-] / [HA]

Base Dissociation Constant

k(b) = [OH-][B+} / [BOH]