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Boss lesson · The Position of Equilibrium
Exam-hall rules, one converter
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Exam-hall rules, one converter

This is the boss. No calculator, and the paper prints the mental-math forms: at 300 K take RT=25 L⋅atm/molRT = 25\ \mathrm{L \cdot atm/mol} for the pressure crossing, RT=2500 J/molRT = 2500\ \mathrm{J/mol} for the free-energy one, and ln⁡10=2.3\ln 10 = 2.3. Every concentration is pinned so KK lands on a power of ten, which is exactly why ln⁡K=2.3×(number of decades)\ln K = 2.3 \times (\text{number of decades}) is enough to finish the problem in your head. Chemists have used that shortcut for a century; today you get to.

One reaction — the contact process, 2SO2(g)+O2(g)⇌2SO3(g)2\mathrm{SO_2(g)} + \mathrm{O_2(g)} \rightleftharpoons 2\mathrm{SO_3(g)} — and every answer feeds the next: build KcK_c from the settled converter, judge QQ on the fresh one, call the shift, cross to KpK_p, let Gibbs put a number on it, and then answer the question the examiner actually asked. Write each line down. One slip in line one rolls all the way to the verdict, and the finish will show you where the cascade started.

5★ under par here is the chapter crown. Clock in.

[A][B][C][D]Kc

Kc=[C][D][A][B]K_c = \frac{[\mathrm{C}][\mathrm{D}]}{[\mathrm{A}][\mathrm{B}]}

  • KcK_c= Equilibrium constant (or quotient Q)
  • [C][\mathrm{C}]= Concentration of product C (molar concentration)
  • [D][\mathrm{D}]= Concentration of product D (molar concentration)
  • [A][\mathrm{A}]= Concentration of reactant A (molar concentration)
  • [B][\mathrm{B}]= Concentration of reactant B (molar concentration)
Equilibrium Constant Kc (A + B ⇌ C + D) solver →
a[A]b[B]c[C]Q

Q=[C]c[A]a [B]bQ = \frac{[\mathrm{C}]^{c}}{[\mathrm{A}]^{a}\,[\mathrm{B}]^{b}}

  • QQ= Reaction quotient
  • [A][\mathrm{A}]= Concentration of reactant A (molar concentration)
  • aa= Coefficient of reactant A
  • [B][\mathrm{B}]= Concentration of reactant B (molar concentration)
  • bb= Coefficient of reactant B
  • [C][\mathrm{C}]= Concentration of product C (molar concentration)
  • cc= Coefficient of product C
Reaction Quotient Q (aA + bB ⇌ cC) solver →
KpΔnKcT

Kp=Kc(RT)ΔnK_p = K_c (RT)^{\Delta n}

  • KpK_p= Pressure equilibrium constant
  • KcK_c= Concentration equilibrium constant
  • Δn\Delta n= Change in moles of gas
  • TT= Absolute temperature (temperature)
Kp from Kc (Kp = Kc(RT)^Δn) solver →
ΔG°KT

ΔG∘=−RTln⁡K\Delta G^{\circ} = -RT\ln K

  • ΔG∘\Delta G^{\circ}= Standard free energy change (molar energy)
  • KK= Equilibrium constant
  • TT= Absolute temperature (temperature)
Gibbs Free Energy and the Equilibrium Constant solver →
no calculator in the boss room — the numbers are chosen to fit in your head