MCAT Essential Equations

Internal Energy of an ideal gas system (U = )

U = 3/2 nRT

Pressure (Force & area)

P = F/A

Volumetric Flow Rate (Q)

Q = Av

Rydberg Formula (wavelength of light btwn energy levels)

hf = R (1/n² final - 1/n² initial)

Potential E of charged particle in electric field

U = k Q q / r

Doppler Effect frequency

f = (v + v0) / (v - vs) f

freezing point depression

ΔTf = i kf m

magnitude of electric field via point charge

E = kQ / r²

magnetic force of a moving point charge

F = q v B sin(x)

Ohm’s law

V = IR

Heat transferred during phase change

Q = m H_L

Buoyant force

F_b = d V g = m g

Thin Lens equation

1/f = 1/d_i + 1/d_o (f: focal length)

osmotic pressure

π = i M R T

index of refraction

n = c/v

wave length with one closed end

λ = 4L/n (n= 1, 3, …)

frequency of a beat via two different frequency sound waves

f = | f₁ - f₂ |

electric potential at a point in space

V = kQ/r

magnetic force of a current carrying wire

F = i L B sin(0)

energy of photon

E = hc/λ = h/f

boiling point elevation

ΔTf = i kb m

pressure in a fluid

P = P_atm + ρ g h

Work done on by a gas by an outside force

W = - P ΔV

magnification of a lens

M = h_i / h_o = - d_i / d_o

intensity of sound

dβ = 10log (I/I_o)

Snell’s Law (incident and refracted light)

n₁ sin(0₁) = n₂ sin(0₂)

force between 2 charged particles

F = k |q1| |q2| / r²

heat released or absorbed by a system

q = mcΔT

Gibb’s Free Energy

ΔG = ΔH - TΔS

ΔH of reaction as function of product and reactant ΔH

ΔH = ΔH_product - ΔH_reactant

Ideal gas law

PV = nRT

Henderson-Hasselbalch equation

pH = pKa + log [conj. base] / [acid]

molality

m = mol/kg

dilution of a solution

M₁V₁ = M₂ V₂

mole fraction

X_A = mol_A / mol_total

period of a wave

T = 1/f

wave length of pipe with two open ends

λ = 2L / n (n = 1,2, …)

force of friction

F_friction = μF_normal

Force of gravity between two masses

F_g = GM₁M₂ / r²

Work equation

W = F d cos(0)

elastic potential energy

U = ½ kx²

potential energy of object at a certain height

U = mgh

potential gravitational energy

U = - GM₁M₂ / r

internal energy of a system

ΔU = Q - W

Capitance (with area and distance)

C = eA/d

resistance through a material

R = ρ L / A (ρ: resistivity)

voltage of an alternating current

V_rms = V_Max / √2

current when using alternating current

I_rms = I_max / √2

Avogadro’s number

6.02 × 10²³

Gas Constant

R = 8.314 J/mol K, 0.08021 L atm/mol K

Planck’s Constant (wavelength)

h = 6.626 × 10^-34 kg m² / s

speed of light

c = 3.0 × 10⁸ m/s

Faraday’s Constant

F = e = 1.60 × 10^-19 C

Newton units

N = kg m / s² , F = ma

Pascal unit

Pa = N/m²

Amp units

Amp = C / sec

Arrhenius equation

k = A e -E_a/RT

Hooke’s Law (spring)

F = -kx

Kinetic energy

KE = ½ mv²

potential energy of a capacitor

U = ½ C ΔV²

Ohm units

V/A

Farad units

C/V

Linear: Final velocity, initial velocity, acceleration, time

vf = v0 + a Δt

Linear: Final velocity, initial velocity, acceleration, displacement

vf² = v0² + 2a Δx

Linear: displacement, time, initial velocity, acceleration

Δx = v0 Δt + ½ a (Δt)²

centripetal acceleration

a_c = v² / r

centripetal force

F_c = mv² / r

initial velocity in X direction of a projectile

v_x = V₀ cos(0)

initial velocity in Y direction of a projectile

v_y= V₀ sin(0)

force of gravity (fxn of mass and acceleration)

F_g = mg

Torque equation

t = r F sin(x)

Power

P = W/t = F v cos(x)

Force of gravity on an object at an incline

F_incline = m g sin(x)

normal force on an object at an incline

F_N = m g cos(x)

force of friction on on object at an incline

F_fric = μ m g cos(x)

charge stored in capacitor (capitance and voltage)

Q = C ΔV

cell potential

E_cell = E_cath - E_anode²

Joule units

J = kg m² / s² = Nm

Volt units

J/C

Watt units

J / sec = VA

Electric field strength in a capacitor

Ecap = Q / eA = ΔV / d