Chem 131, Physical Chemistry I Lecture

Class: 6:30 PM - 9:30 PM Mondays in Room 313 Search Hall

Office Hours: 5:30 PM - 6:30 PM Monday, 5 PM - 6 PM, Wednesday, other times by arrangement. I am always accessible for questions by e-mail.

Office hours will also double as a recitation, for those students who are interested.

Required Text:

Physical Chemistry, Atkins, P. and de Paula, J. 7th Edition.

Also Required:

Each student will be required to bring to class a working, scientific calculator, that the student actually knows how to use. This means it is better to buy a simple, dependable calculator, than an excessively complicated one. Always bring your textbook to class.

Lecture Syllabus:

Part I - Thermodynamics

09/03 - Chapter 1

Boyle's Law: pV=constant; Gay-Lussac Law: V=V₀ (1 + α₀&theta), where &alpha is the coefficient of thermal expansion, and &theta is the temperature in Celsius; Ideal (Perfect) Gas Law: pV=nRT; Daltons's Law of Partial Pressures: p_total = Σ p_J; Definition of mole fraction: x_J = n_J/n, where n_J is the number of moles of J, n is the total number of moles of gas, and x_J is the mole fraction of J. Then p_J = x_J p, i.e., the partial pressure of J (p_J) is equal to the mole fraction of J (x_J) times the total pressure.

Definition of pressure (F/A). Pressure due to column of liquid = p = p_ex + ρ gh

Zeroth Law of Thermodynamics - If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C.

Critical Temperature T_c, above which a gas can not be liquified by pressure alone. Van der Waals equation. Compression factor Z = V_M/V^o_M;

pV_m=RTZ, with Z = 1 for perfect (ideal) gas. At high T and large V_m, isotherms for a real gas are similar to those of ideal gas.

Principle of Corresponding States: different gases at same reduced temperature T_R and reduced volume V_R exert the same reduced pressure p_R.

09/08 - Chapter 2

Δw _ad = U_f - U_i; q = w_ad - w; dw = -F dz; dw = -p_ex dV; for free expansion, w = 0; work against constant pressure w = -p_ex ΔV;
isothermal reversible expansion work w = -nRT ln(V_f/V_i). Compare work of reversible and irreversible isothermal expansion graphically.
Heat capacity at constant volume = (∂U/∂T)_V; dU = C_V dT (at const V); q_V = C_VΔT.
Enthalpy: H = U + pV; dH = dq (at const p, no additional work); ΔH = ΔU + Δn_gRT (perfect gas).
C_p = (∂H/∂T)_p; C_p - C_V = nR (perfect gas).

09/15 - Chapter 2 (continued)

w_ad = C_V ΔT (adiabatic); V_fT_f^c = V_iT_i^c, where c = C_{V, M}/R.
pV^γ = constant (adiabatic, where &gamma = C_{p, M} / C_{V, M}, called heat capacity ratio)

Chapter 3

State Functions = exact differential = path independent; Path functions = inexact differential = path dependent
Differential form dz = (∂z/∂x) dx + (∂z/∂y) dy
Condition for P dx + Q dy to be exact differential is (∂P/∂y) = (∂Q/∂x)
dU = (∂U/∂V) _T dV + (∂U/∂T) _V dT.
(∂U/∂T)_V = C_V, the heat capacity at constant volume.
(∂U/∂V)_T = π_T, the internal pressure, which equals zero for ideal gas.
α = V^-1 (∂V/∂T)_p, the expansion coefficient.
(∂U/∂T)_P = C_V, for perfect gas.

dH = (∂H/∂V)_T dV + (∂H/∂T)_p dT.
(∂H/∂T)_p = C_p, the heat capacity at constant pressure.
κ_T = -V^-1 (∂V/∂p)_T, the isothermal compressibility.
μ = (∂T/∂p)_H, the Joule-Thomson coefficient..

09/22 - Chapter 4

dS = dq_rev / T; dS_sur = dq_rev / T_sur; ε = 1 - (T_c/T_h).
dS ≥ -dS_sur; Clausius inequality: dS ≥ dq/T;
Spontaneous cooling: dS = |dq| (T_c ^-1 - T_h ^-1);
ΔS_trans = ΔH_trans / T_trans
Trouton's Rule : Δ_vapS ≈ 85 J K ^-1 mol ^-1
Entropy change for isothermal expansion of perfect gas: ΔS = nR ln (V_f/V_i).
Nerst Heat Theorem: S → 0 as T → 0, so long as all substances are perfectly ordered.
Gibbs energy G = H - TS; Helmholtz energy A = U - TS.

09/29 - Chapter 5

Fundamental equation: dU = T dS - p dV. dU = (∂U/∂S)_V dS + (∂U/∂V)_S dV
(∂U/∂S)_V = T; (∂U/∂V)_S = -p
Maxwell relations.
&pi:_T = T (∂p/∂T)_V - p: thermodynamic equation of state.
dG = V dp - S dT; (∂G/∂T)_p = -S; (∂G/∂p)_T = V
Gibbs-Helmholtz equation: ∂/∂T (G/T) = - H/T²

10/06 - Yom Kippur Holiday - NO LECTURE

10/13 - Examination #1 (examination will cover up to the end of Chapter 4, and first section of Chapter 5), Chapter 5

G(p_f) = G(p_i) + nRT ln(p_f/p_i): for (perfect) gases.

G(p_f) = G(p_i) + V_m(p_f - p_i): for solids and liquids.

G_m = G_m* + RT ln(f/p*): definition of fugacity.

f = φ p.

Part II - Equilibria

10/20 - Chapter 6 - 6.1 to 6.5

chemical potential μ= (∂G/∂n); (∂μ/∂T)_p = -S_m

Criterion for equilibrium: μ_α = μ_β

(∂μ/∂p)_T = V_m

Clapeyron equation: dp/dT = Δ_trsS/Δ_trsV.

10/27 - Chapter 6 (continued)

p = p* + (Δ_fusH/Δ_fusV)ln(T/T*): solid - liquid boundary.

p ≈ p* + (Δ_fusH/Δ_fusV)(T - T*): solid - liquid boundary, when T is close to T*.

Clausius-Clapeyron equation: d ln p/dT = Δ _vapH/RT².

p = p* e ^-χ, &chi =Δ_vap(T ^-1 - T* ^-1) /R.

dw = γ dσ.

Laplace equation: p_in = p_out + 2γ/r.

h = 2γ/ρgr.

11/03 - Chapter 7 - 7.1 to 7.3 only

partial molar volume V = (∂V/∂n_J) _{p, t, n'}.

dV = V = (∂V/∂n_A) _{p, t, n'} dn_A + (∂V/∂n_B) _{p, t, n'} dn_B

V= n_AV_A + n_BV_B, binary mixture.

G = n_Aμ_A + n_Bμ_B, binary mixture.

n_Adμ_A + n_Bdμ_B = 0; Σ n_Jdμ_J = 0.

Δ_mix G = nRT(x_A ln x_A + x_B ln x_B), for perfect gases

Δ_mix S = -nR(x_A ln x_A + x_B ln x_B), for perfect gases

Raoult's Law: p_A = x_A p_A^*.

Henry's Law: p_B = x_B K_B.

11/10 - Chapter 7.5; Examination #2

elevation of boiling point: μ_A*(g) = μ_A*(l) + RT x_A.

ΔT = Kx_B, K = RT*²/Δ_vapH.

ΔT = K_bb, K_b is ebullioscopic constant.

depression of freezing point: μ_A*(s) = μ_A*(l) + RT x_A.

ΔT = K'x_B, K' = RT*²/Δ_fusH.

ΔT = K_fb, K_f is cryoscopic constant.

11/17 - Chapter 8

Gibbs phase rule: F = C - P +2

Total vapour pressure of mixture: p = p_A + p_B = p*_B + (p*_A - p*_B) x_A, in terms of x_A.

Total vapour pressure of mixture: p = p_A*p_B / [p*_A + (p*_B - p*_A) y_A], in terms of y_A.

Mole fraction of A in vapour: y_A = x_Ap*_A / [p*_B + (p*_A - p*_B) x_A].

Lever rule: n_α l_α = n_β l_β.

Part III - Kinetics

method of initial rates: if v = k[A]^a, then initial rate v₀ = k[A]₀^a. Then log v₀ = log k + a log [A]₀, straight line with slope a and y-intercept log k.

For rate law v = k[A]^a[B]^b..., reaction order is a + b +...

First-order rate law: d[A]/dt = -k[A].

Second-order rate law: d[A]/dt = -k[A][B] (for elementary bimolecular reaction).

Integrated rate law for first-order reaction: [A] = [A]₀ e^-kt.

Half life of first -order reaction: t_1/2 = ln 2/k.

Arrhenius equation: k = Ae^E/RT.

Steady-state approximation: d[I]/dt = 0.

Rate law for unimolecular reaction (Lindemann-Hinshelwood mechanism): d[P]/dt = k_ak_b[A]² / (k_b + k_a'[A]).

11/24 - Chapter 25

12/01 - Chapter 26

12/08 - Review for cumulative final

Therefore, there will be two examinations, in addition to the final exam which is scheduled during the final exam week period. Each of the "mid-term" examinations will be 90-minutes long.

Some rearrangement of topics may occur, as necessary.

Policies:

Laboratory accounts for 20% of the total grade. Frequent quizzes will be given, usually in the first 10 minutes of class. The relative weighting used for the calculation of the final course grade are are follows:

Final examination - 25%
First examination - 20%
Second examination - 20%
Laboratory - 20%
Quizzes - 10%
Class participation - 5%

I have always marked and returned examinations the next week of class, so the student can legitimately expect the timely return of all examinations.

Academic Honesty:

Cheating in the class in any form will result in a final grade of F, with no exceptions

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Send questions to: lseinjr@hotmail.com