Activity (concentration convention)
Compute Activity (concentration convention) using a_i = γ_i c_i / c°.
a_i = γ_i c_i / c°Open calculator🌡️ Category
Physical Chemistry Calculators
Thermodynamics, quantum mechanics, colligative properties, nuclear decay, and statistical mechanics.
103 calculators in this category.
Activity (mole-fraction convention)
Compute Activity (mole-fraction convention) using a_i = γ_i x_i.
a_i = γ_i x_iOpen calculatorAmagat’s Law of Partial Volumes
Compute Amagat’s Law of Partial Volumes using V_total = ΣV_i.
V_total = ΣV_iOpen calculatorAmount of Substance from Mass
Compute Amount of Substance from Mass using n = m / M.
n = m / MOpen calculatorAmount of Substance from Particles
Compute Amount of Substance from Particles using n = N / N_A.
n = N / N_AOpen calculatorAverage Molecular Speed
Compute Average Molecular Speed using u_avg = √(8 R T / (π M)).
u_avg = √(8 R T / (π M))Open calculatorAverage Translational Kinetic Energy (per mole)
Compute Average Translational Kinetic Energy (per mole) using ⟨E_k⟩ = (3/2) R T.
⟨E_k⟩ = (3/2) R TOpen calculatorAverage Translational Kinetic Energy (per molecule)
Compute Average Translational Kinetic Energy (per molecule) using ⟨E_k⟩ = (3/2) k_B T.
⟨E_k⟩ = (3/2) k_B TOpen calculatorBohr Energy Levels
Compute Bohr Energy Levels using E_n = −2.178×10^−18 J · Z^2 / n^2.
E_n = −2.178×10^−18 J · Z^2 / n^2Open calculatorBohr Radius
Compute Bohr Radius using r_n = a_0 n^2 / Z.
r_n = a_0 n^2 / ZOpen calculatorBoiling-Point Elevation
Compute Boiling-Point Elevation using ΔT_b = i K_b m.
ΔT_b = i K_b mOpen calculatorBoltzmann Distribution
Compute Boltzmann Distribution using N_j / N_i = (g_j/g_i) e^(−ΔE / k_B T).
N_j / N_i = (g_j/g_i) e^(−ΔE / k_B T)Open calculatorBoltzmann Population Ratio
Solve one variable in N2/N1 = exp(-delta_E/(k*T)) for Boltzmann population distributions.
N2/N1 = exp(-delta_E / (k * T))Open calculatorBond Enthalpy Approximation
Compute Bond Enthalpy Approximation using ΔH_rxn ≈ ΣD(bonds broken) − ΣD(bonds formed).
ΔH_rxn ≈ ΣD(bonds broken) − ΣD(bonds formed)Open calculatorCalorimeter Heat
Compute Calorimeter Heat using q_cal = C_cal ΔT.
q_cal = C_cal ΔTOpen calculatorChemical Potential
Compute Chemical Potential using μ_i = (∂G/∂n_i)_(T,P,n_j).
μ_i = (∂G/∂n_i)_(T,P,n_j)Open calculatorChemical Potential from Activity
Compute Chemical Potential from Activity using μ_i = μ_i° + R T ln a_i.
μ_i = μ_i° + R T ln a_iOpen calculatorClapeyron Equation
Compute Clapeyron Equation using dP/dT = ΔS / ΔV = ΔH / (T ΔV).
dP/dT = ΔS / ΔV = ΔH / (T ΔV)Open calculatorClausius Clapeyron
Solve one variable in ln(p2/p1) = -(delta_H_vap/R) * (1/t2 - 1/t1) for phase-transition pressure-temperature changes.
ln(p2/p1) = -(delta_H_vap/R) * (1/t2 - 1/t1)Open calculatorClausius–Clapeyron Equation
Compute Clausius–Clapeyron Equation using ln(P_2/P_1) = −ΔH_phase/R (1/T_2 − 1/T_1).
ln(P_2/P_1) = −ΔH_phase/R (1/T_2 − 1/T_1)Open calculatorCompressibility Factor
Compute Compressibility Factor using Z = P V / (n R T).
Z = P V / (n R T)Open calculatorCoulomb’s Law
Compute Coulomb’s Law using F = k q_1 q_2 / r^2.
F = k q_1 q_2 / r^2Open calculatorDalton’s Law of Partial Pressures
Compute Dalton’s Law of Partial Pressures using P_total = ΣP_i.
P_total = ΣP_iOpen calculatorde Broglie Relation
Compute de Broglie Relation using λ = h / p.
λ = h / pOpen calculatorDe Broglie Wavelength
Solve lambda = h / p for wavelength or momentum in matter-wave quantum mechanics.
lambda = h / pOpen calculatorDensity
Compute Density using ρ = m / V.
ρ = m / VOpen calculatorDilution Equation
Compute Dilution Equation using C_1 V_1 = C_2 V_2.
C_1 V_1 = C_2 V_2Open calculatorElectrochemical Free Energy
Compute Electrochemical Free Energy using ΔG = −n F E.
ΔG = −n F EOpen calculatorEmpirical Formula Percent Composition
Compute Empirical Formula Percent Composition using % element = (mass of element in 1 mol compound / molar mass compound) × 100.
% element = (mass of element in 1 mol compound / molar mass compound) × 100Open calculatorEnthalpy Definition
Compute Enthalpy Definition using H = U + P V.
H = U + P VOpen calculatorEntropy Change (isothermal ideal gas expansion)
Compute Entropy Change (isothermal ideal gas expansion) using ΔS = n R ln(V_2 / V_1).
ΔS = n R ln(V_2 / V_1)Open calculatorEntropy Definition (reversible)
Compute Entropy Definition (reversible) using dS = δq_rev / T.
dS = δq_rev / TOpen calculatorEquilibrium Constant (concentration form)
Compute Equilibrium Constant (concentration form) using K_c = Π[products]^ν / Π[reactants]^ν.
K_c = Π[products]^ν / Π[reactants]^νOpen calculatorEquilibrium Constant (pressure form)
Compute Equilibrium Constant (pressure form) using K_p = Π(P_products)^ν / Π(P_reactants)^ν.
K_p = Π(P_products)^ν / Π(P_reactants)^νOpen calculatorExpectation Value
Compute Expectation Value using ⟨A⟩ = ∫ ψ* Â ψ dτ.
⟨A⟩ = ∫ ψ* Â ψ dτOpen calculatorEyring Equation
Compute Eyring Equation using k = (κ k_B T / h) e^(−ΔG‡ / R T).
k = (κ k_B T / h) e^(−ΔG‡ / R T)Open calculatorFirst Law of Thermodynamics
Compute First Law of Thermodynamics using ΔU = q + w.
ΔU = q + wOpen calculatorFormal Charge
Compute Formal Charge using FC = valence e^− − nonbonding e^− − (bonding e^− / 2).
FC = valence e^− − nonbonding e^− − (bonding e^− / 2)Open calculatorFree Energy–Equilibrium Relation
Compute Free Energy–Equilibrium Relation using ΔG° = −R T ln K.
ΔG° = −R T ln KOpen calculatorFreezing-Point Depression
Compute Freezing-Point Depression using ΔT_f = i K_f m.
ΔT_f = i K_f mOpen calculatorFreundlich Adsorption Isotherm
Compute Freundlich Adsorption Isotherm using x/m = K P^(1/n).
x/m = K P^(1/n)Open calculatorGibbs Free Energy
Solve one variable in delta_G = delta_H - T * delta_S for thermodynamic spontaneity relationships.
delta_G = delta_H - T * delta_SOpen calculatorGibbs Free Energy Change
Compute Gibbs Free Energy Change using ΔG = ΔH − T ΔS.
ΔG = ΔH − T ΔSOpen calculatorGibbs Phase Rule
Compute Gibbs Phase Rule using F = C − P + 2.
F = C − P + 2Open calculatorGibbs–Duhem Equation
Compute Gibbs–Duhem Equation using Σn_i dμ_i = −S dT + V dP.
Σn_i dμ_i = −S dT + V dPOpen calculatorHarmonic Oscillator Energy
Compute Harmonic Oscillator Energy using E_v = (v + 1/2) h ν.
E_v = (v + 1/2) h νOpen calculatorHeat Capacity at Constant Pressure
Compute Heat Capacity at Constant Pressure using C_P = (∂H/∂T)_P.
C_P = (∂H/∂T)_POpen calculatorHeat Capacity at Constant Volume
Compute Heat Capacity at Constant Volume using C_V = (∂U/∂T)_V.
C_V = (∂U/∂T)_VOpen calculatorHeat Capacity Energy
Solve one variable in q = m * c * delta_T for calorimetry and heat-capacity calculations.
q = m * c * delta_TOpen calculatorHeisenberg Uncertainty
Solve delta_x * delta_p = hbar / 2 for minimum uncertainty relationships.
delta_x * delta_p = hbar / 2Open calculatorHeisenberg Uncertainty Principle
Compute Heisenberg Uncertainty Principle using Δx Δp ≥ ħ/2.
Δx Δp ≥ ħ/2Open calculatorHelmholtz Free Energy
Compute Helmholtz Free Energy using A = U − T S.
A = U − T SOpen calculatorHenry’s Law
Compute Henry’s Law using C = k_H P.
C = k_H POpen calculatorJoule–Thomson Coefficient
Compute Joule–Thomson Coefficient using μ_JT = (∂T/∂P)_H.
μ_JT = (∂T/∂P)_HOpen calculatorKp–Kc Relation
Compute Kp–Kc Relation using K_p = K_c (R T)^Δn_gas.
K_p = K_c (R T)^Δn_gasOpen calculatorLangmuir Adsorption Isotherm
Compute Langmuir Adsorption Isotherm using θ = K P / (1 + K P).
θ = K P / (1 + K P)Open calculatorLinearized Arrhenius Equation
Compute Linearized Arrhenius Equation using ln k = ln A − E_a/(R T).
ln k = ln A − E_a/(R T)Open calculatorMayer’s Relation (ideal gas)
Compute Mayer’s Relation (ideal gas) using C_P − C_V = R.
C_P − C_V = ROpen calculatorMolality
Compute Molality using b = n_solute / m_solvent(kg).
b = n_solute / m_solvent(kg)Open calculatorMolar Heat Equation
Compute Molar Heat Equation using q = n C_m ΔT.
q = n C_m ΔTOpen calculatorMolar Mass
Compute Molar Mass using M = m / n.
M = m / nOpen calculatorMoles of Electrons
Compute Moles of Electrons using n_e = Q / F.
n_e = Q / FOpen calculatorMost Probable Speed
Compute Most Probable Speed using u_mp = √(2 R T / M).
u_mp = √(2 R T / M)Open calculatorOsmotic Pressure
Compute Osmotic Pressure using π = i M R T.
π = i M R TOpen calculatorOstwald’s Dilution Law
Compute Ostwald’s Dilution Law using K_a = c α^2 / (1 − α).
K_a = c α^2 / (1 − α)Open calculatorPartial Molar Quantity
Compute Partial Molar Quantity using M̄_i = (∂M/∂n_i)_(T,P,n_j).
M̄_i = (∂M/∂n_i)_(T,P,n_j)Open calculatorPartial Pressure from Mole Fraction
Compute Partial Pressure from Mole Fraction using P_i = x_i P_total.
P_i = x_i P_totalOpen calculatorParticle in a Box Energy
Compute Particle in a Box Energy using E_n = n^2 h^2 / (8 m L^2).
E_n = n^2 h^2 / (8 m L^2)Open calculatorParticle In Box Energy
Solve one variable in E_n = n^2 * h^2 / (8 * m * L^2) for 1D particle-in-a-box states.
E_n = n^2 * h^2 / (8 * m * L^2)Open calculatorPartition Function
Compute Partition Function using q = Σ g_i e^(−ε_i / k_B T).
q = Σ g_i e^(−ε_i / k_B T)Open calculatorPercent Error
Compute Percent Error using % error = \ | experimental − true\ | / true × 100.
% error = \ | experimental − true\ | / true × 100Open calculatorpKw Relation
Compute pKw Relation using pH + pOH = pK_w.
pH + pOH = pK_wOpen calculatorPlanck Relation
Compute Planck Relation using E = h ν.
E = h νOpen calculatorPressure–Volume Work (constant external pressure)
Compute Pressure–Volume Work (constant external pressure) using w = −P_ext ΔV.
w = −P_ext ΔVOpen calculatorRadioactive Activity
Compute Radioactive Activity using A = λ N.
A = λ NOpen calculatorRadioactive Decay Law
Compute Radioactive Decay Law using N_t = N_0 e^(−λ t).
N_t = N_0 e^(−λ t)Open calculatorRaoult’s Law
Compute Raoult’s Law using P_i = x_i P_i°.
P_i = x_i P_i°Open calculatorReaction Enthalpy from Formation Enthalpies
Compute Reaction Enthalpy from Formation Enthalpies using ΔH°_rxn = ΣνΔH°_f(products) − ΣνΔH°_f(reactants).
ΔH°_rxn = ΣνΔH°_f(products) − ΣνΔH°_f(reactants)Open calculatorReaction Free Energy
Compute Reaction Free Energy using ΔG = ΔG° + R T ln Q.
ΔG = ΔG° + R T ln QOpen calculatorReaction Heat from Calorimetry
Compute Reaction Heat from Calorimetry using q_rxn = −q_surroundings.
q_rxn = −q_surroundingsOpen calculatorReaction Quotient
Compute Reaction Quotient using Q = Πa_products^ν / Πa_reactants^ν.
Q = Πa_products^ν / Πa_reactants^νOpen calculatorReversible Adiabatic Relation
Compute Reversible Adiabatic Relation using P V^γ = constant.
P V^γ = constantOpen calculatorReversible Adiabatic Temperature–Pressure Relation
Compute Reversible Adiabatic Temperature–Pressure Relation using T P^((1−γ)/γ) = constant.
T P^((1−γ)/γ) = constantOpen calculatorReversible Adiabatic Temperature–Volume Relation
Compute Reversible Adiabatic Temperature–Volume Relation using T V^(γ−1) = constant.
T V^(γ−1) = constantOpen calculatorReversible Expansion/Compression Work (ideal gas, isothermal)
Compute Reversible Expansion/Compression Work (ideal gas, isothermal) using w = −n R T ln(V_2 / V_1).
w = −n R T ln(V_2 / V_1)Open calculatorRigid Rotor Energy
Compute Rigid Rotor Energy using E_J = J(J+1) ħ^2 / (2 I).
E_J = J(J+1) ħ^2 / (2 I)Open calculatorRoot-Mean-Square Speed
Compute Root-Mean-Square Speed using u_rms = √(3 R T / M).
u_rms = √(3 R T / M)Open calculatorRotational Constant
Compute Rotational Constant using B = h / (8 π^2 I c).
B = h / (8 π^2 I c)Open calculatorRydberg Equation
Compute Rydberg Equation using 1/λ = R_H (1/n_1^2 − 1/n_2^2).
1/λ = R_H (1/n_1^2 − 1/n_2^2)Open calculatorSchrödinger Equation (time-independent)
Compute Schrödinger Equation (time-independent) using Ĥ ψ = E ψ.
Ĥ ψ = E ψOpen calculatorSlater’s Rule / Effective Nuclear Charge
Compute Slater’s Rule / Effective Nuclear Charge using Z_eff = Z − S.
Z_eff = Z − SOpen calculatorSpecific Gravity
Compute Specific Gravity using SG = ρ_substance / ρ_reference.
SG = ρ_substance / ρ_referenceOpen calculatorSpecific Heat Equation
Compute Specific Heat Equation using q = m c ΔT.
q = m c ΔTOpen calculatorStandard Electrochemical Free Energy
Compute Standard Electrochemical Free Energy using ΔG° = −n F E°.
ΔG° = −n F E°Open calculatorvan ’t Hoff Equation
Compute van ’t Hoff Equation using ln(K_2/K_1) = −ΔH°/R (1/T_2 − 1/T_1).
ln(K_2/K_1) = −ΔH°/R (1/T_2 − 1/T_1)Open calculatorvan ’t Hoff Factor
Compute van ’t Hoff Factor using i = observed colligative property / calculated nonelectrolyte value.
i = observed colligative property / calculated nonelectrolyte valueOpen calculatorvan der Waals Equation
Compute van der Waals Equation using (P + a n^2 / V^2)(V − n b) = n R T.
(P + a n^2 / V^2)(V − n b) = n R TOpen calculatorVant Hoff
Solve one variable in ln(k2/k1) = -(delta_H/R) * (1/t2 - 1/t1) for equilibrium constant temperature dependence.
ln(k2/k1) = -(delta_H/R) * (1/t2 - 1/t1)Open calculatorVirial Equation of State
Compute Virial Equation of State using Z = 1 + B/V_m + C/V_m^2 + ....
Z = 1 + B/V_m + C/V_m^2 + ...Open calculatorVolume Percent
Compute Volume Percent using vol % = (volume solute / volume solution) × 100.
vol % = (volume solute / volume solution) × 100Open calculatorWater Ion Product
Compute Water Ion Product using K_w = [H_3O^+][OH^−].
K_w = [H_3O^+][OH^−]Open calculatorWave Equation Form of Schrödinger Equation
Compute Wave Equation Form of Schrödinger Equation using −(ħ^2/2m)∇^2ψ + Vψ = Eψ.
−(ħ^2/2m)∇^2ψ + Vψ = EψOpen calculatorWavefunction Normalization
Compute Wavefunction Normalization using ∫ \ | ψ\ | ^2 dτ = 1.
∫ \ | ψ\ | ^2 dτ = 1Open calculator