Physical Constants
Important Equations
R    = 8.314 J mol-1 K-1
     =0.08206 L atmK-1 mol-1
   = 0.08314 L bar K-1 mol-1
NA = 6.022 x 1023 mol-1
kB    = 1.381 x 10-23 J K-1
h    = 6.626 x 10-34 J s
F    = 96,485 C mol-1
c    = 2.998 x 108 m s-1
g    = 9.81 m s-2
e = 1.6022 x 10-19 C
εo = 8.854 x 10-12 C2 J-1 m-1
B    = 0.51 mol-1/2 dm3/2 (in H2O, 25oC)
 
Other Units
 
1dm3   =1 L
1dm3   =1000 cm3
1 J    = 1 kg m2 s-2
1 atm    =1.01325 x 105 Pa
1 atm    = 760 mmHg
1 Torr = 1 mmHg
1 Torr = 133.322 Pa
1 bar    = 105 Pa
E   = hυ
c   =υλ
PV   =nRT
(RT)/F = 25.6926 mV at 25oC
ln(x)/log10(x) = 2.30259 for all x
ln(1 - θ) = -θ
if θ << 1
Quadratic equation:
a x2 + b x + c = 0
solutions:
x1,2 = (1/2a)[ - b ± (b2 - 4ac)1/2 ]
RT/F = 25.70 mV(at 25oC for ln)
       = 59.16 mV(at 25oC for log10)
Michaelis - Menten equation:
(1/R0)=(1/Rmax) + (Km/Rmax)x(1/[S]0)
Lindemann mechanism:
kuni = k1k2[M](k-1[M] + k2)-1
Langmuir isotherm:
θ = KP/(1 + KP)
1/Ro = 1/Rmax + (Km/Rmax) (1/[S]o)
Sequential reactions:
[B]=(k1/(k2-k-1)) f(t)[A]0
f(t)=exp(-k1t)-exp(-k2t)
 
Note:
Quantum yield/efficiency = Φ = moles of product formed / moles of photons absorbed
, and
and
Λm = Λom - K (c/co)1/2 (strong)
1/Λm = 1/Λom + cΛm /[(Λom)2 Ka ] (weak)
ΔGosolvation =(1/εr - 1)z2e2NA/(8πεor)
ΔG = -nFE and thus ΔGo = -nFEo
ΔS = nF(dE/dt)P
a±m+n = a+ma-n for AmBn
κ = [2e2NA x (1000 L m-3)/(εokBT)]1/2 x [ρsolvent I/εr]1/2
EoAgCl/Ag = +0.222 V
k    = A
k    =
Ea    = Δ≠Ho-PΔ≠Vo + RT (sol)
   = Δ≠Ho-ΣνRT + RT (gas)
ΔG#   = ΔH#-TΔS#
t1/2 = (ln 2)/k (1st order)
fluorescence lifetime tf = (kf +kq[Q])-1
Ro = k2[S]o[E]0/([S]o + Km),
Km = (k-1 + k2)/k1
k2[E]0 = Rmax = V
D = (1/3) vave λ
κ = (1/3) (CV,m/NA) vave Np λ
PV = nRT = (N/NA)RT,
(CV,m/NA) = (3/2) kB
η = (1/3) vaveNpλm
f = 6πηr = kBT/D
vave = (8RT/(πM))1/2
Npλ = 1/((√2)σ),
λ = RT/(PNA(√2)σ)
Np = (N/V) = PNA/(RT)
σ = πd2
xrms = √(2Dt)      (1-Dimension)
rrms = √(6Dt) (3-Dimension)
Poisseuille equation: (ΔV/Δt) = (πr4/(8η)) ΔP/ ΔL
Stokes-Einstein equation: D = kBT/(6π ηr)
if r(particle) >> r(solvent molecule)
Ostwald viscosimeter: η = Aρt,
Capillary rise: h = 2γ/(ρgr)
 
 
 



1.
What is the diffusion coefficient of xenon (Xe) at 298 K and a pressure of 2.00 atm, given the collisional cross section of Xe as σ = 5.8 x 10-19 m2 and MXe = 131.29 g/mol?
A.
1.81 x 10-6 m2/s
B.
5.43 x 10-6 m2/s
C.
1.72 x 10-7 m2/s
D.
5.72 x 10-8 m2/s
E.
0.18 m2/s


2.
At the same temperature and pressure, DXe = 4.4 DRn. What is the ratio, σRn/σXe, of their collisional cross sections if MXe = 131.29 g/mol and MRn = 222 g/mol.
A.
3.38
B.
0.77
C.
5.72
D.
0.30
E.
2.60


3.
What is the ratio of the root mean square displacement in three dimensions (rrms) to that in one dimension (xrms) for a particle with D = 3.41 x 10-5 m2/s in 900 s in case of rrms and in 1800s in case of xrms?
A.
(3/2)1/2
B.
(2/3)1/2
C.
(6)1/2
D.
(1/6)1/2
E.
3/2


4.
The thermal conductivity of Helium, He, at 300 K and 1.00 atm is 0.0612 J/(K m s). What is the mean free path length of He, assuming it to behave like an ideal gas (MHe = 4.003 g/mol)?
A.
288 nm
B.
9.11 μm
C.
2.9 mm
D.
96 nm
E.
3.0 μ


5.
The flux of a property (J) is related to the gradient of the transported quantity (grad) as (α is the transport coefficient)
A.
J proportional to -grad
B.
J proportional to α2
C.
J proportional to -1/grad
D.
J proportional to 1/grad
E.
J proportional to 1/α


6.
Thermopane windows filled with krypton (Kr, MKr = 83.80 g/mol) provide a ten times better heat insulation than normal windows filled with argon (Ar, MAr = 39.95 g/mol), advertisements claim. What is the ratio of the thermal conductivity of Kr (σ = 0.52 nm2) to that of Ar (σ = 0.36 nm2) and does it fulfill the advertisment claim of a ten times better heat insulation?
A.
κ(Kr)/ κ(Ar) = 0.478, does not fulfill the advertisement
B.
κ(Kr)/ κ(Ar) = 0.478, fulfills the advertisement
C.
κ(Kr)/ κ(Ar) = 2.09, does not fulfill the advertisement
D.
κ(Kr)/ κ(Ar) = 3.03, fulfills the advertisement
E.
κ(Kr)/ κ(Ar) = 0.33, does not fulfill the advertisement


7.
Krypton (Kr) and Helium (He) are monatomic gases, and thus CV,m = 3/2 R for each. Given that σKr = 0.52 nm2 and σHe = 0.28 nm2 and that the molar mass of Kr is larger than that of He which one of the following is definitely correct?
A.
Since λKr < λHe and vave,Kr < vave,He it follows that κKr < κHe
B.
Since λKr > λHe and vave,Kr < vave,He it follows that κKr < κHe
C.
Since λKr < λHe and vave,Kr > vave,He it follows that κKr < κHe
D.
Since λKr > λHe and vave,Kr > vave,He it follows that κKr < κHe
E.
Actually κKr > κHe


8.
The adsorption of an organic compound on an adsorbent measured at 5 °C and different pressures followed the Langmuir type of isotherm and a fit of versus gave,
1/Vads = 2.662 (torr/mL) (1/P) + 0.203 (1/mL)
where is the volume of the adsorbed organic compound in mL and is its pressure in torr. The fractional coverage of charcoal at a pressure of 100 torr is,
A.
0.884
B.
0.376
C.
0.430
D.
0.203
E.
0.612


9.
The reaction,
takes place in the presence of light . The mechanism which gives a rate law that agrees with experiment is,


The rate law is:
A.
B.
C.
D.
E.


10.
The rate constant for the second order reaction between iodomethane, CH3I, and ethoxy anions, C2H5O–-, in ethanol solution is 9.86 × 10-5 mol dm-3s-1 at 25 °C and 6.17 × 10-3mol dm-3 s-1 at 65 °C. Calculate the activation energy in kJ mol –1 units.
A.
86.7
B.
116
C.
300
D.
10.4
E.
40.0


11.
The Arhenius parameters for the unimolecular isomerization of methylcyanide,
are an activation energy of 272 kJ/mol and a preexponential factor of . Which of the following choices is completely correct for the ΔΗ‡ (in kJ/mol) and ΔS‡ (in J/(K mol)) values (from left to right) at 227 °C.
A.
268, 56.4
B.
270, 63.0
C.
264, 63.0
D.
272, 435
E.
276, 240


12.
Consider the photochemical decomposition:
With light at , absorption of 3070 J of energy decomposed . The quantum yield of this reaction is:
A.
2
B.
1
C.
5
D.
106
E.
0.5


13.
If the diffusion coefficient for insulin is 8.2 x 10-11 m2 s-1 at 20 oC, estimate the mean time required for an insulin molecule to diffuse through a distance equal to the diameter of a typical living cell (~ 10 μm).
A.
0.61 s
B.
0.17 s
C.
2.1 s
D.
1.1 s
E.
3.2 s


14.
The viscosity of ethylene at 25 oC and 101.325 kPa is 9.33 x 10-6 kg m-1 s-1. Estimate the molecular diameter of the ethylene molecule (MC = 12.01 g/mol, MH = 1.008 g/mol).
A.
0.42 nm
B.
0.14 nm
C.
0.67 nm
D.
1.19 nm
E.
2.22 nm


15.
For the protein myoglobin in water at 20 oC, the sedimentation coefficient is ssed = 2.04 x 10-13 s, the diffusion coefficient is D = 1.13 x 10-10 m2 s-1, and the specific volume is 0.740 cm3 g-1. The density of water is 0.998 g cm-3 and its viscosity is 1.002 cP at the same temperature. Estimate the radius of myoglobin, assuming it to be spherical.
A.
1.897 nm
B.
3.150 nm
C.
4.115 nm
D.
5.232 nm
E.
9.114 nm


16.
The conductivity of a 0.0312 M solution of a weak base is 1.53 x 10-4 S cm-1. If the sum of the limiting ionic conductance for BH+ and OH- is 237.0 S cm2 mol-1, what is the value of the base dissociation constant Kb?
A.
1.36 x 10-5
B.
2.11 x 10-3
C.
3.21 x 10-4
D.
1.51 x 10-4
E.
2.12 x 10-6


17.
Liquid A has half the surface tension and twice the density of liquid B, at 25 oC. If the capillary rise is 0.01 m for liquid A, then in the same capillary, the capillary rise for liquid B will be (assume complete wetting)
A.
0.04 m
B.
0.01 m
C.
0.02 m
D.
0.03 m
E.
0.05 m


18.
The densities of acetone and water at 20 oC are 0.972 g cm–3 and 0.9982 g cm–3, respectively. The viscosity of water is 1.002x10-3 Pa s at 20 oC. If at 20 oC water requires 120.5 s to run between the marks on a viscometer and acetone requires 40.5 s, what is the viscosity of acetone?
A.
3.28x10-4 Pa s
B.
2.90x10-3 Pa s
C.
1.03x10-3 Pa s
D.
3.06x10-3 Pa s
E.
6.56x10-4 Pa s


19.
Which of the following statements is not correct?
A.
The viscosities of gases decrease as temperature increases.
B.
The viscosities of gases increase as temperature increases.
C.
The viscosities of liquids increase as temperature decreases.
D.
The viscosities of liquids obey a law of the Arrhenius type.
E.
For gases, viscosity is proportional to T1/2, T being the temperature in Kelvin.


20.
Water is transported upward in trees through channels in the trunk called xylem. Although the diameter of the xylem channels varies from species to species, a typical value is 2.0 x 10-7 m. If the water surface tension and density are 70.41 x 10-3 N m-1 and 997 kg m-3, what will be the maximum transport height of the water to the top in the redwood tree?
A.
144 m
B.
21.0 m
C.
45.9 m
D.
95.0 m
E.
214 m


21.
The Galvanic cell Cu(s)| Cu2+(aq)|| Ag+(aq)| Ag (s) is based on the following cell reaction:2Ag+(aq)+Cu(s)→2Ag(s)+Cu2+(aq). Note that T = 298 K and the standard electrode potentials are E0(Cu2+,Cu)=0.34V and E0(Ag+,Ag)=0.80V. Which of the following statements are correct?
(i) The silver electrode is the cathode and the copper electrode is the anode.
(ii) Two moles of electrons flow through the external circuit from anode to cathode when the cell operates.
(iii) The standard cell potential is 0.46 V.
(iv) The change in Gibbs energy for the cell reaction is -88,766 J mol-1 in the standard state.
A.
All statements are correct.
B.
(i) is correct.
C.
(i) and (ii) are correct.
D.
(iii) and (iv) are correct.
E.
All statements are not correct.


22.
Given the following Galvanic cell Zn(s)|Zn2+(aq)||Sn4+(aq),Sn2+(aq)|Pt(s). If the standard potential E0(Zn2+,Zn)= - 0.76 V and the standard cell potential E0cell = 0.91 V, then the standard potential of the Sn4+/Sn2+ redox couple is:
A.
0.15 V
B.
– 0.15 V
C.
150 V
D.
1.67 V
E.
– 1.67 V


23.
The following reaction corresponds to eletroextraction of aluminum from aluminum ore:
2/3Al2O3 -◊ 4/3Al + O2,   ΔG0 = +966 kJ mol-1
The minimum potential required to drive this reaction at 500°C is:
A.
2.5V
B.
5.0V
C.
4.5V
D.
3.0V
E.
1.2V


24.
Given that the mean activity coefficient, γ±, in a 0.100 mol kg-1 MgBr2(aq) solution is 0.524 at 25°C. Determine the percentage difference from the value predicted by the Debye-Hückel limiting law?
A.
47%
B.
11%
C.
15%
D.
17%
E.
21%


25.
The solubility product of K2SO4 is (γ± is the mean activity coefficient):
A.
4s3γ±3
B.
4s5γ±3
C.
4s3γ±2
D.
4s3γ±5
E.
4s2γ±3


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