Why this page. A dataset-friendly way to turn equilibrium information (K, K_sp, stability constants, cell potentials) into a dimensionless contrast e that preserves classical sign conventions and keeps everything bounded and collapse-safe.
Key idea (sign you can trust).
- Write the reaction in the forward direction you want to score.
- Use the equilibrium constant at temperature T (activity-based, dimensionless).
- Map to contrast so that K > 1 ⇒ e > 0 ⇒ RSI > 0 (forward favored).
What you can plug in (pick the forward form appropriately).
- Acid–base: dissociations (K_a) and neutralizations.
- Precipitation / dissolution: K_sp gives precipitation sign via the reverse of dissolution.
- Complex formation: stability (overall formation) constants β_n.
- Redox: standard cell potentials (ΔE°) with electrons n.
- Gas-phase equilibria: K_p built from activities/fugacities.
Practical notes (keep it honest).
- Prefer activities over raw concentrations; declare any activity corrections (e.g., Debye–Hückel).
- If environment corrections are uncertain, keep e from standard-state data and let conditions act via the calm gate g_t or small rapidity priors (never modify e with priors).
- Publish T, E_unit (and units), constants used (R, F), data sources, and rounding policy.
Plain ASCII formulas & examples (copy-ready)
General map (standard state unless declared otherwise)
# Write forward reaction as scored.
DeltaG0 = - R * T * ln(K)
e = (- DeltaG0) / E_unit = ( R * T * ln(K) ) / E_unit
# R = 8.314462618 J/(mol*K)
# Choose E_unit in J/mol (e.g., 100000 for 100 kJ/mol).
# Sign rule: K > 1 => ln(K) > 0 => e > 0 => RSI > 0.
Common lenses (forward directions as written)
1) Acid–base (dissociation):
HA -> H+ + A- with K = K_a
e_acid = ( R * T * ln(K_a) ) / E_unit
# Weak acids (small K_a) => e_acid < 0 for dissociation.
# Neutralization (net ionic): H+ + OH- -> H2O has K ≈ 1/K_w -> large +e.
2) Precipitation / dissolution:
Dissolution (std): AB(s) -> A+ + B- with K = K_sp
Precipitation forward is reverse of dissolution:
e_precip = - ( R * T * ln(K_sp) ) / E_unit
# Small K_sp => ln(K_sp) < 0 => e_precip > 0 (precip favored).
3) Complex formation:
M + n L -> ML_n with K = beta_n
e_form = ( R * T * ln(beta_n) ) / E_unit
# Large beta_n => e_form > 0 (complex favored).
4) Redox (cell potentials; standard):
DeltaG0 = - n * F * DeltaE0
e_redox = ( n * F * DeltaE0 ) / E_unit_J
# F = 96485.33212 C/mol
# E_unit_J is E_unit in J/mol.
5) Gas-phase equilibria (K_p):
e_gas = ( R * T * ln(K_p) ) / E_unit
Worked micro-examples (T = 298.15 K, E_unit = 100 kJ/mol ⇒ 100000 J/mol)
A) Precipitation (AgCl). K_sp ≈ 1.8e-10
e_precip = - ( R * T * ln(1.8e-10) ) / 100000
≈ +0.556
=> positive e => Ag+ + Cl- -> AgCl(s) favored.
B) Acid dissociation (acetic acid). K_a ≈ 1.8e-5
e_acid = ( R * T * ln(1.8e-5) ) / 100000
≈ -0.271
=> negative e => dissociation disfavored at standard state (weak acid).
C) Redox (Zn | Zn2+ || Cu2+ | Cu). n = 2, DeltaE0 ≈ 1.103 V
e_redox = ( 2 * 96485.33212 * 1.103 ) / 100000
≈ 2.128
=> positive e => spontaneous in written galvanic direction.
Guards & publication (keep bounded, collapse-safe)
# Alignment map (bounded) and RSI:
a_r = tanh( -c * e ) # clamp so |a| < 1 with eps_a
a_p = tanh( +c * e )
RSI = tanh( (V_p - U_r) / max(W_r, eps_w) )
# Conditions via unified gate:
RSI_env = g_t * RSI # 0 <= g_t <= 1 ; sign(RSI_env) = sign(RSI)
# Manifest: publish T, E_unit (and E_unit_J if used), R, F, lens choice, sources.
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