Data Sheet:

Note: Any fact not provided here will NOT be provided during the examination, and it is the student's responsibility to memorize it (if necessary).

R = 8.314 47 J K ^-1 mol ^-1 = 8.314 47 × 10 ^-2 L bar K ^-1 mol ^-1 = 8.205 74 × 10 ^-2 L atm K ^-1 mol ^-1 = 6.236 37 × 10 ¹ L Torr K ^-1 mol ^-1.

k = 1.380 65 × 10 ^-23 J K ^-1.

g = 9.81 m s ^-2.

1 J = 1 kg m² s ^-2.

1 W = 1 J s^-1.

1 N = 1 kg m s ^-2.

1 Pa = 1 N m ^-2 = 1 kg m ^-1 s ^-2 = 1 J m ^-3.

1 atm = 101.325 kPa.

1 bar = 1.0 × 10⁵ Pa.

1 Torr = 101325/760 Pa (exactly)

w = -nRT ln(V_f / V_i).

w = -C_V ΔT.

V_iT_i ^c = V_fT_f ^c, c = C_{V, m}/R.

pV^&gamma = constant, &gamma = C_{p, m} / C_{V, m}. For monoatomic perfect gas, C_{V, m} = 3R/2. For non-linear polyatomic perfect gas, C_{V, m} = 3R.

C_{p, m} = 20.786 J K ^-1 mol ^-1 for He, Ne, Ar, Xe.

G(p_f) = G(p_i) + nRT ln(p_f/p_i).

G(p_f) = G(p_i) + V_m(p_f - p_i).

G_m = G_m* + RT ln(f/p*).

f = φ p.

(p - p*)/p* ≈ V_M ΔP/RT

dp/dT = Δ_trsS / Δ_trsV.

p = p* + (Δ_fusH/Δ_fusV)ln(T/T*).

p ≈ p* + (Δ_fusH/Δ_fusV)(T - T*).

d ln p/dT = Δ _vapH/RT².

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

dw = γ dσ.

p_in = p_out + 2γ/r.

h = 2γ/ρgr.

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

p_A = x_A p_A^*.

p_B = x_B K_B.

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.

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.

F = C - P +2

p = p_A + p_B = p*_B + (p*_A - p*_B) x_A, in terms of x_A.

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

y_A = x_Ap*_A / [p*_B + (p*_A - p*_B) x_A].

n_α l_α = n_β l_β.

k = Ae^E/RT.

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

Test Grading:

Be careful with signs! You must use the Atkins convention for the First Law (U = q + w), where w is work done on the system. The wrong sign will cause a deduction of 30%. (On a multiple choice test like the GRE or MCAT, such a mistake would be penalized with a 100% reduction)

Complete work must be shown, and the use of introduced equations explained. If you use pV = nRT, you must write that you are using the perfect gas law (as opposed to using the van der Waals or some other equation of state).

Units are an essential part of the answer, unless a unitless quantity is requested in the problem. Answers without units are WRONG, and will receive zero credit.

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© 2003 by Lawrence T. Sein. All rights reserved.

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