chem rate laws

ln x – ln y = ln(x/y)

Used to simplify logarithms; helpful when comparing concentrations or rate constants.

ln(xⁿ) = n ln(x)

Lets you bring exponents down in logarithmic equations; useful in kinetics rearrangements.

ln([A]t/[A]₀) = –kt

Integrated rate law for a first-order reaction; shows exponential decay of reactant.

t₁/₂ = 0.693 / k

Half-life formula for first-order reactions; constant regardless of [A]₀.

[A]t = [A]₀ – kt

Integrated rate law for zero-order reactions; concentration decreases linearly with time.

t₁/₂ = [A]₀ / (2k)

Half-life for a zero-order reaction; depends on initial concentration.

1/[A]t – 1/[A]₀ = kt

Integrated rate law for a second-order reaction.

t₁/₂ = 1 / (k[A]₀)

Half-life for a second-order reaction; depends inversely on initial concentration.

1/v = (Kₘ/Vₘₐₓ)(1/[S]) + 1/Vₘₐₓ

Lineweaver–Burk equation; used to find Vmax and Km from enzyme kinetics data.

V₀ = (Vₘₐₓ [S]) / (Kₘ + [S])

Michaelis–Menten equation; shows how enzyme rate depends on substrate concentration.

k = A e^(–Eₐ/RT)

Arrhenius equation; relates rate constant to temperature and activation energy.

ln k = –(Eₐ/R)(1/T) + ln A

Linear form of Arrhenius equation; used to find activation energy from ln k vs 1/T plot.

ln(k₁/k₂) = (Eₐ/R)(1/T₂ – 1/T₁)

Used to compare rate constants at two different temperatures.

0 K = –273 °C

Temperature conversion between Kelvin and Celsius.

R = 8.314 J·mol⁻¹·K⁻¹

Value of the universal gas constant used in the Arrhenius equation.