1 / 11

Ch 13 Chemical Equilibrium

Ch 13 Chemical Equilibrium. Partition Functions  K LeChatelier’s Principle K(T), K(p). I. Chemical Equilibrium; K = f(N). Consider gas phase rxn A(g) ↔ B(g) Equilibrium constant = K = N B /N A

phyllis-mcneil
Download Presentation

Ch 13 Chemical Equilibrium

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Ch 13 Chemical Equilibrium Partition Functions  K LeChatelier’s Principle K(T), K(p)

  2. I. Chemical Equilibrium; K = f(N) • Consider gas phase rxn A(g) ↔ B(g) • Equilibrium constant = K = NB /NA • At constant T and p, G is the thermodynamic function that characterizes equilibrium. dG = -SdT + Vdp + ΣμidNi = ΣμidNi = 0 at equilibrium or μA = μB • Eqn 11.47 defines μ = -kT ℓn (q/N)

  3. K = f(q) • A and B have their own set (ladder) of energy levels beginning at ground state energies ε0A and ε0B, respectively. Fig 13.1 • q’A = partition function = [exp(-ε0Aβ) + exp(ε1Aβ) + exp(ε2Aβ) + …] • μA = -kT ℓn (q’A/N) • qA = reduced partition fnt with ε0A factored out = exp(ε0Aβ) [exp(-ε0Aβ) + exp(-ε1Aβ) + exp(-ε2Aβ) + …] = exp(ε0Aβ) q’A

  4. K = f(q) • K = NB/NA= q’B/q’A = qB/qA exp(- [ε0B - ε0A]β) = qB/qA exp(- Δε0β) Eqn 13.10 • More complex rxn: aA +bB ↔ cC • K = NCc/[NAaNBb] = Eqn 13.18 which shows q and ε0 terms • Ex. 13.2, prob 6

  5. Vibrational Energy Reference Level • If you use bottom of the well = 0  Eqn 11.26 for qvib = exp (-hνβ/2)/[1- exp (-hνβ)]. Then energy from dissociation limit to bottom of well = - ε0 • If you use ZPE as 0  Eqn 13.21 for qvz = exp [1- exp (-hνβ)]-1. Then energy from ZPE to dissociation limit = D or D0 (T11.2)

  6. K=f(p) • K  Kp using n = pV/RT or N = pV/kT • Kp = [pCc/[pAa pBc] Eqn 13.29 = (kT)c-a-b [q0Cc/[q0Aa q0Bb] exp(ΔDβ) • q0 = q/V • μ = μ0 + kT ℓn p = std state chem pot and term that depends on p • Ex 13.3, prob 1

  7. II. LeChatelier’s Principle • Given a system at equilibrium at constant T and p, ΔG = 0 and G is at a minimum. Any disturbance on the system will increase G. • The LeChatelier Prin says that the system will return to equilibrium in a way that opposes disturbance. Note that K does not change for all perturbations. Fig 13.4

  8. II.A. K = f(T) • See Thermody. Relationships (p 2) for van’t Hoff Eqn and Gibbs-Helmholtz Eqn. • A(g) ↔ B(g) μA = μB at equilibrium or • μA = μA0 + kT ℓn pA = μB = μB0 + kT ℓn pB • ℓn (pB/pA) = ℓn Kp = -(μB0 - μA0)kT = -∆μ0/kT • ∆μ0 = ∆h0 - T∆s0 (partial molar quant) • ℓn Kp = -∆μ0/kT = [∆h0 - T∆s0]/kT

  9. Van’t Hoff Eqn • ℓn Kp = -∆μ0/kT = - [∆h0 - T∆s0]/kT • Take partial w/respect to T and assume ∆h0 and ∆s0 are independent of T. • δ ℓn Kp /δT = - δ{[∆h0 - T∆s0]/kT}/δT = ∆h0/kT2 Eqn 13.37 • Or δ ℓn Kp /δ(1/T) = - ∆h0/k Eqn 13.38 • Plot ℓn Kp vs 1/T and slope = - ∆h0/k • Ex 13.4, Prob 5

  10. Gibbs-Helmholtz Eqn; G(T) • δ (G/T)/δT = - H(T)/T2 Eqn 13.43; see also p 2 of Thermodynamic Relationships • Recall ∆G = -RT ℓn K

  11. II.B. K = f(p) • (δ ℓn K/δp)T = - ∆v/kT PMV • Ex 13.6

More Related