thermodynamics

Formula for the Compressibility Factor (Z)

Z = (P * V_m) / (RT)

Formula for Molar Volume (V_m)

V_m = V / n

Formula for Z at low pressure (Real Gas)

Z = 1 - a / (V_m * RT)

Formula for Z at high pressure (Real Gas)

Z = 1 + (Pb) / (RT)

The van der Waals equation for 1 mole of gas

(P + a/Vm^2)(Vm - b) = RT

The First Law of Thermodynamics (FLOT)

ΔU = q + w

The infinitesimal form of the First Law of Thermodynamics

dU = dq + dw

General formula for Work Done (Integral form)

w = -∫ P_ext dV

Formula for Work Done at constant external pressure

w = -P_ext * ΔV

Formula for Work Done in a chemical reaction

w = -Δn_g * RT

Formula for Work Done during a reversible isothermal process

w = -nRT ln(V2/V1) = -2.303 nRT log10(V2/V1)

Formula for Work Done during an irreversible isothermal process

w = -P_ext(V2 - V1)

Formula for Work Done during a reversible adiabatic process

w = (P2V2 - P1V1) / (γ - 1) = nR(T2 - T1) / (γ - 1)

Definition of Enthalpy (H)

H = U + PV

General formula for Enthalpy change (ΔH)

ΔH = ΔU + Δ(PV)

Relation between ΔH and ΔU for a chemical reaction

ΔH = ΔU + Δn_g * RT

Formula for Heat Capacity (C)

C = q / ΔT

Formula for Molar Heat Capacity (C_m)

C_m = q / (n * ΔT)

Formula for Specific Heat Capacity (C_sp)

C_sp = q / (m * ΔT)

Mayer's Equation for 1 mole of an ideal gas

CP - CV = R

Formula for Poisson’s Ratio (γ)

γ = CP / CV

Relation between P and V in a reversible adiabatic process

PV^γ = constant

Relation between T and V in a reversible adiabatic process

TV^(γ-1) = constant

Relation between P and T in a reversible adiabatic process

P^(1-γ) * T^γ = constant

The slope of an adiabatic curve on a P-V diagram

dP/dV = -γ * (P/V)

ΔH_R° using Standard Enthalpies of Formation

ΔHR° = Σ ΔHf°(products) - Σ ΔH_f°(reactants)

ΔH_R° using Standard Enthalpies of Combustion

ΔHR° = Σ ΔHc°(reactants) - Σ ΔH_c°(products)

ΔH_R° using Bond Energies (gaseous state)

ΔH_R° = Σ BE(reactants) - Σ BE(products)

Formula for Resonance Energy

Resonance Energy = ΔHExpected - ΔHReal

Formula for Entropy Change (dS)

dS = dq_rev / T

General formula for the Entropy change of a system

ΔSsys = n * CV * ln(T2/T1) + nR * ln(V2/V1)

Formula for Entropy change during a Phase Change

ΔS = ΔHphase / Tphase

Formula for Gibbs Free Energy (G)

G = H - TS

The Gibbs-Helmholtz Equation

ΔG = ΔH - TΔS

Formula for the temperature at equilibrium (ΔG = 0)

T_eqm = ΔH / ΔS