MCAT Equations to Memorize

An accumulation of different equations that might be useful to know for taking the MCAT

Michaels-Menton Equation

V = (Vmax [S])/Km+[S]

Buffer Equation & other pH equations

pH = pka + log([A^-]/[HA]) —> Base over Acid

pka = -log(ka)

pH = -log (H₃O⁺)

pOH = -log (OH^-)

ka and kb

Equals the (aqueous products)/(aqueous reactants)

ka * kb = kw or 10^-14

If ka is higher = Acid is stronger than the base

If kb is higher = Base is stronger than the acid

What does the Km tell us?

Km is the substrate concentration at ½ of the Vmax

What does the Kcat tell us?

Is the catalytic constant which is the maximum number of substrates per unit time.
Formula: Kcat = Vmax/Et

Et = Enzyme Concentration

Kinematics Equations

Vf = Vi + at

Vf² = Vi² + 2a∆t or Vf² = Vi² + 2ad

d = average v * t

∆x = ½ *(Vf + Vi)*(t)

∆x = Vi*t + ½ at²

**∆x —> is the distance

d —> displacement

Heat Energy Transfer Equation

Q = mc∆T

Q —> heat in joules

c —> specific heat

m —> mass

T —> change in temperature in Kelvin

Work and Energy Equations

∆U = Q + W

W = F*s

**∆U —> change in energy

F —> force

s —> displacement

Work (W) = Positive when work is done ON the system

Work (W) = Negative when DOING work

Newtons Law Equations

Force = acceleration * mass

Fg and/or weight = mass*g

Mass units are in ‘kg’

**g = 9.8 m/s²

Momentum Equation

p = mv

F*∆t = ∆p (change in momentum or ‘impulse’)

p —> momentum in kg*m/s

m —> mass

v —> velocity

F —> force

t —> time

Kinetic and Potential Energy Equations

KE = ½ mv²

PE = mgh

Gibbs Free Energy

Gibbs = ∆H - T∆S

∆H = E + PV

∆G = Positive means Non-spontaneous

∆G = Negative means Spontaneous

**∆H —> Enthalpy: total content of heat in a system

**∆S —> Entropy: Measure of how the energy is spread in a molecule or substance. (Measure of chaos? Number of micro-state configurations)

T —> Temp measured in Kelvin

E —> Internal energy

P —> Pressure

V —> Volume in Liters

Gibbs free energy (in biochemical reaction Equation)

∆G = ∆G⁰ + RT ln(Q)

∆G⁰ —> Constant at standard conditions

R —> Universal gas constant, 8.314 J/(mol·K)

Ideal Gas Law

PV = nRT

R Constants:

(*Most important!) pKa/atm R = 0.082057 L K^-1 mol^-1

Energy R = 8.3145 J/K^-1 mol^-1

Torr R = 62.36358 L torr K^-1 mol^-1

Bar R = 0.083145 L bar*K^-1 mol^-1

Equilibrium Partial Pressure

Kp = (Pproducts)^m/(Preactants)^n

Electromagnetism Equations

V = IR

P = IV

P = Work/∆Time

V —> Voltage in volts

P —> Power in watts

I —> Current in amps

R —> resistance in ohms

Coulomb’s Law of Electrostatic Force

F_E = k * (|q₁ * q₂| / r^2)

q —> charges of the interacting particles

r —> radius or distance of the two particles

k —> Coulomb's constant (8.9875 x 10^9 N m²/C² )

F_E —> Electrostatic Force

Molarity

number of moles/Volume

Avagodro’s Number = 6.022×10²³ (the amount of atoms in a mole of an element)

Light Particle and Light Equations

E = hf

E = (h*c)/λ

f = c/λ

c = λ*f

E = mc²

E —> energy measured in Joules

f —> Frequency in hertz (Hz)

Lambda (λ) —> wavelength

Plank’s constant (h) = 6.626×10^-34 J*s

Speed of light (c) = 3×10⁸ m/s

Rate Law and Arrhenius Equations

v = k[A]^x*[B]^y

Arrhenius Equation: k = Ae^{-E_a​​/RT}

v —> rate of reaction

k —> rate constant

A and B —> concentrations of the species of chemical

x —> order of reaction with respect to A

y —> order of reaction with respect to B

A —> Pre-exponential factor

e —> euler’s number = 2.7182818

Ea —> activation energy

R —> gas constant

T —> temperature in kelvin

Hardy-Weinberg Equilibrium Equation (Genetics)

p² + 2pq + q² = 1

p + q = 1 (when the sum of both frequencies is 100 percent)

p —> frequency of dominant allele in a population

q —> frequency of recessive allele in a population

Mirror Equation (spherical)

1/f = (1/d_o) + (1/d_i)

f —> focal length

do —> distance of the object

di —> distance of the image

di Positive = Real Image

di Negative = Virtual Image

Focal Length and Radius of Curvature

f = (R/2)

f —> focal length

R —> radius of curvature

Magnification Equation (spherical)

M = (-d_i/d^_o) AND (hi/ho)

M —> magnification

-M —> Inverted/upside down Image

+M —> Upright Image

If | M | > 1 then the image is enlarged

If | M | < 1 then the image is reduced

di is negative = image is virtual

di —> distance of image

do —> distance of object

h_i —> height of image

h_o —> height of object