Chemistry Equations: Inspect, Calculate, Verify, and Learn

Arrhenius and Clausius-Clapeyron

Arrhenius uses k = A exp(-Ea/RT), with Ea converted from kJ/mol to J/mol because R = 8.314 J/(mol*K). Its two-temperature form assumes the same mechanism and effectively constant activation parameters over the interval.

Integrated Clausius-Clapeyron uses ln(P2/P1) = -(Delta Hvap/R)(1/T2 - 1/T1). Pressures may use any matching unit, temperatures must be kelvin, and constant Delta Hvap plus ideal-vapor behavior are approximations.

Example: with P1 = 1, T1 = 373.15 K, T2 = 353.15 K, and Delta Hvap = 40.7 kJ/mol, the reviewed calculation gives P2 about 0.47570 in the same pressure unit.

Beer-Lambert and Henderson-Hasselbalch

Beer-Lambert uses A = epsilon*c*l and A = -log10(I/I0). With epsilon = 15000 L/(mol*cm), c = 2.0e-5 mol/L, and l = 1 cm, A = 0.300. The linear model can fail because of concentration, scattering, stray light, chemistry, or instrument setup.

Henderson-Hasselbalch uses pH = pKa + log10([A-]/[HA]). Equal buffer components give pH = pKa; a 10:1 base-to-acid ratio gives pH = pKa + 1. It is a buffer approximation, not a universal pH solver.

Bragg diffraction and quantum wavelength

Bragg's law is n*lambda = 2*d*sin(theta). Lambda and d need the same length unit, while many XRD instruments report 2-theta rather than theta. A near-integer calculated order is a consistency check, not a complete peak assignment.

The quantum program combines de Broglie lambda = h/p, a nonrelativistic electron-voltage relation, and the Rydberg formula. Rydberg Z-squared modes describe hydrogenic one-electron species; they are not a general multi-electron atomic model.

Gibbs energy and Nernst potential

Delta G = Delta H - T*Delta S requires compatible energy units; the program converts entropy from J/(mol*K) to kJ/(mol*K). Delta G standard = -RT ln K requires a thermodynamic dimensionless K. Thermodynamic favorability does not give reaction speed.

The Nernst equation is E = E0 - (RT/nF) ln Q, with a 298 K base-10 shortcut. Q must be dimensionless and consistent with the same balanced reaction and electron count as E0. A positive complete cell voltage corresponds to galvanic direction as written; a lone half-cell number is not enough.

Michaelis-Menten and van der Waals

Michaelis-Menten uses v0 = Vmax[S]/(Km + [S]). At [S] = Km the rate is half Vmax; 90 percent requires [S] = 9Km. The model assumes initial-rate, steady-state, single-substrate behavior and omits inhibition, cooperativity, transport limits, and product buildup.

Van der Waals uses (P + a*n^2/V^2)(V - nb) = nRT with the program's litre-atmosphere unit set. V must exceed nb. Negative fitted parameters or nonpositive pressure indicate inconsistent inputs or an unsuitable state, and the model is not a precision phase-equilibrium equation.

Verification checklist

Before accepting a result, estimate its direction and order of magnitude, check that logarithm arguments and divisors are positive, confirm kelvin rather than Celsius where required, and make sure paired quantities use matching units.

Then compare a known special case: Q = 1 gives E = E0, [S] = Km gives half Vmax, equal buffer components give pH = pKa, and a = b = 0 recovers the ideal-gas pressure. Keep the unrounded value for working and report only justified precision.