Constants, Formulas, and Unit Conversions to Know

Continually updated throughout the semester

Volume of a Sphere

V = (4/3)πr³

Volume of a Cylinder / Rod

V = πr²h

Liter to cubic meters

1 L = 0.001 m³

Angstrom to meter

1 Å = 10^-10 m

Cubic micrometer to Liter

1 µm³ = 10^-15 L

Gas Constant (R)

R = 8.314 J / mol K

Numbers of mols in a solution (n)

n = CV, where C is concentration and V is volume

Numbers of molecules in a solution (N)

N = nN_a, where n is number of mols in a solution and N_a is Avogadro’s Number (6.022×10²³)

Avogadro’s Number (N_a)

6.022×10²³

Calorie to Joules

1 cal = 4.184 J

Picometer to meter

1 pm = 10^-12 m

Inches to Meter

1 in = 0.0254 m

Axial Length (in Angstroms) of an Alpha Helix

Length = (# of Amino Acids) x (1.5)

Axial Length (in Angstroms) of a Beta-Strand

Length = (# of Amino Acids) x (7/2)

Celsius to Kelvin

K = C˚ + 273

Gibbs Free Energy from Reaction Quotient

∆G = ∆G˚’ + RTlnQ,

where R = gas constant

T = temperature

Q = reaction quotient

pH of a solution

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

Blood-buffering equation

H2O + CO2 ⇌ H+ + HCO3-

Equilibrium Constant (Keq) from Gibbs Free Energy (∆G)

Keq = e^{(-∆G / RT)}

# of Sequence Possibilities for a single-stranded DNA from # of bases

# of Sequence Possibilities = 4ⁿ, where n = # of bases

Gibbs Free Energy (∆G) from Enthalpy and Entropy

∆G = ∆H - T∆S

If ∆G < 0, process is spontaneous and favors the products

If ∆G > 0, process is non-spontaneous and favors the reactants

First Law of Thermodynamics

∆Esys + ∆Esurr = 0

Second Law of Thermodynamics

∆Suniv = ∆Ssys + ∆Ssur > 0

Entropy of universe always increases

Gibbs Free Energy (∆G) from Equilibrium Constant

∆G˚ = -RTlnKeq

Oxidation States

O.S. = # of valence Electrons — # of Electrons owned by the atom