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
 
Sequential reactions:
[B]=(k1/(k2-k-1)) f(t)[A]0
f(t)=exp(-k1t)-exp(-k2t)
 
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)
 
 
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
D = (1/3) vave λ
κ = (1/3) (CV,m/NA) vave Np λ
(CV,m/NA) = (3/2) kB
η = (1/3) vaveNpλm
vave = (8RT/(πM))1/2
Npλ = 1/((√2)σ),
λ = RT/(PNA(√2)σ)
Np = (N/V) = PNA/(RT)
σ = πd
xrms = (√<x2>) = √(2Dt)
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)
Note:



1.
Investigations of high power cables showed that copper atoms were assembled beyond the insulator of thickness 20 mm which created a short-circuit. Taking the diffusion coefficient of copper as 7.8 x 10-7 cm2s-1, estimate the time required for a copper atom to cross the insulator.
A.
1 month
B.
25 days
C.
5 days
D.
10 hours
E.
67 s


2.
Upon adding sugar carefully on top of a full cup of water of height 10 cm, sugar will start to diffuse slowly with a diffusion coefficient of 5.2x10-6 cm2 s-1 25°C. Determine the percent of sweet water vs unsweet water after 1 day.
A.
9.5%
B.
35%
C.
27.3%
D.
50.5%
E.
89.4%


3.
Liquids undergo a pressure drop when flowing through pipes. Assume a liquid flowing in a 6.00 mm radius tube for 1.00 m length at an average rate of 0.66 mL min-1 with a viscosity of 4.0x10-3 kg m-1 s-1 , then determine the pressure that should be applied to correct for the pressure drop.
A.
86 mPa
B.
21 Pa
C.
25 mPa
D.
68 nP
E.
55 cPa


4.
The diffusion coefficient of SF6 in SF6 gas at 573 K and 1.00 atm is 1.02 x10-7 m2/s. Calculate the collision cross section of SF6 at 573 K and 1.00 atm where the average speed of molecules is 288 m/s.
A.
52 nm2
B.
25 nm2
C.
5.2 nm2
D.
0.52 nm2
E.
0.052 nm2


5.
Determine the ratio of the thermal conductivities at constant temperature for Kr (σ = 0.52 nm2) versus Ar (σ = 0.36 nm2). Molar masses: 39.95 g/mol for Ar and 83.80 g/mol for Kr.
A.
0.48
B.
2
C.
10
D.
1.5
E.
100


6.
The electrolytic conductivity of a solution mixture of 0.1 M KCl and 0.2 M XCl (both of which are strong electrolytes) is 3.82 S m-1. Calculate λ for X+ in S m2 mol-1.
[Note: λK + = 7.4 × 10-3 ; λCl - = 7.6 × 10 -3 S m2 mol-1 and λi = κi /ci]
A.
4.00 × 10 -3 S m2 mol-1
B.
5.00 × 10 -3 S m2 mol-1
C.
6.00 × 10 -3 S m2 mol-1
D.
2.00 × 10 -3 S m2 mol-1
E.
19.1 S m2 mol-1


7.
The thermal conductivity of an ideal gas
A.
is proportional to T1/2
B.
is independent of T
C.
decreases with increasing temperature
D.
is inversely proportional to T
E.
is proportional to T


8.
The mean root square distance travelled by a He atom (molar mass 4.0 g/mol) at 25 oC and 101.324 kPa pressure through air (D = 1.256 x 10-4 m2 /s) in 10 minutes is
A.
0.39 m
B.
0.075 m2
C.
0.15 m2
D.
2.5 x 10-3 m2
E.
0.27 m


9.
The ratio of diffusion coefficients of hydrogen gas (H2) relative to deuterium gas (D2), assuming they have the same size, is
A.
more than one at the same and constant temperature and pressure
B.
less than one at the same and constant temperature and pressure
C.
equal to one at the same and constant temperature and pressure
D.
not affected by varying the temperature or pressure
E.
equal to one if collision cross section ratio of H2/D2 is equal to half


10.
The diffusion coefficient for a globular protein molecule in a solvent is 6.48 x 10-10 m2/s at 25 oC. The viscosity of the solution at 25 oC is 9.41 x 10-5 kg/ms and the density of the protein (pure solid compound) is 7.82 g/cm3. Assuming the protein molecules to be of spherical shape (globular protein) and much larger than the solvent molecules, what is the molar mass of the protein?
A.
907 kg/mol
B.
174 kg/mol
C.
90.6 g/mol
D.
17.4 g/mol
E.
0.907 g/mol


11.
The electrolytic conductivity of a 0.0312 M solution of a weak base is 1.53 x 10-4 S/cm. If the sum of the limiting molar ionic conductance for BH+ and OH- is 237.0 S cm2/mol, what is the value of the base dissociation constant Kb?
A.
1.36 x 10-5
B.
5.21 x 10-3
C.
2.63 x 10-4
D.
4.51 x 10-5
E.
1.12 x 10-5


12.
Water is transported upward in trees through channels in the trunk called xylem. An average value of xylem diameter is 2.0 x 10-7 m. What will be the maximum rise of water in the capillary xylem channels, assuming complete wetting and the water surface tension and density are 71.99 mN m-1 and 997 kg m-3, respectively?
A.
147 m
B.
0.74 m
C.
25 m
D.
0.25 m
E.
54 m


13.
The cell potential at 25°C of the cell,
Pb(s)| PbSO4(s) | H2SO4 (m = 0.100, γ = 0.265) | H2(g) (1 atm)
given that
PbSO4 (s) + 2e- → Pb(s) + SO42– (aq)    E°= –0.3505 V
is
A.
0.228 V
B.
0.814 V
C.
1.25   V
D.
2.21   V
E.
0.604 V


14.
If ΔS° for the reaction of Cu2+ + Zn →Zn2+ + Cu (E°rxn = 1.10V) at 298.15 K is –30.9 J K–1. What is E°rxn at 50°C for this reaction?
A.
1.096   V
B.
3. 512 V
C.
2. 230 V
D.
0.213   V
E.
0.762   V


15.
Given that
Pt(s) | H2 (g, aH2 = 1.00) | H+ (aq, aH+ = 1.00) || NaCl(aq, m = 0.300) | AgCl(s) | Ag(s)
Ecell = +0.260 V. Determine γCl– assuming γ± = γNa+ = γCl–.
A.
0.760
B.
0.253
C.
0.596
D.
1.23
E.
3.45


16.
What is the solubility of CaCO3 (Ksp = 3.4 ×10–9) in an aqueous solution with I = 0.0250 mol kg–1.
A.
1.22 ×10–4 mol kg–1
B.
2.44 ×10–4 mol kg–1
C.
3.62 ×10–4 mol kg–1
D.
4.17 ×10–4 mol kg–1
E.
5.21 ×10–4 mol kg–1


17.
Which of the following is true for a 0.0120 m solution of Na3PO4 at 298 K? (Assume complete dissociation)
A.
γ ± =   0.389,   a ± = 0.0106, I = 0.0720 m
B.
γ ± =   0.580,   a ± = 0.0204, I = 0.0820 m
C.
γ ± =   0.645,   a ± = 0.1063, I = 0.1420 m
D.
γ ± =   0.789,   a ± = 0.5106, I = 0.3720 m
E.
γ ± =   0.623,   a ± = 0.0106, I = 0.0720 m


18.
The equilibrium constant for the following reaction is 5.12×10–4. Calculate the extent of hydrolysis for a 0.210 m solution of (CH3)2NH that is in 0.500 m NaNO3 if γ± is 0.428.
(CH3)2NH (aq) + H2O (l) → (CH3)2NH2+ (aq) + OH–(aq)
A.
10.9%
B.
25.2%
C.
5.4%
D.
34.0%
E.
17.4%


19.
For the reaction A + B → P for different sets of initial A and B concentrations the following initial rates R0 were found:

Determine the rate of reaction with respect to A, α, and with respect to B, β.
A.
α = 1, β = 2
B.
α = 2, β = 1
C.
α = 0, β = 3
D.
α = 3, β = 0
E.
α = 3/2, β = 3/2


20.
Substance A decomposes in the atmosphere in a first order reaction
A → P
The half-life of A is 2.5 s. After what time will the initial amount of A be decomposed by 40%?
A.
1.84 s
B.
0.54 s
C.
0.303 s
D.
–1.845 s
E.
3.30 s


21.
When the activation energy of a reaction 2 (2Ea), rate constant k2, is double that of a reaction 1 (Ea), rate constant k1, what is ln(k1/k2) in terms of x=Ea/RT when both reactions have the same pre-exponential factor A at the same temperature for both reactions?
A.
x
B.
2x
C.
–x
D.
–2x
E.
3x


22.
For the Lindemann mechanism, when only reactant A is initially present in the reaction mixture (no buffer gas M), derive an expression for the concentration of the activated reactant molecules, [A*], using the steady state approximation (SSA) in case of very high reactant concentration, [A].      Mechanism:  
 
A.
[A*] = (k1/k-1)[A]
B.
[A*] = k1[A]2/( k-1[A] + k2)
C.
[A*] = (k1/k2)[A]2
D.
[A*] = k1[A]2
E.
[A*] = k1[A]


23.
Is a quantum yield of Φ = 2 for the formation of H2 consistent with the following mechanism?
HBr + hν → H- + Br-
H- + HBr → H2 + Br-
2 Br- → Br2
A.
No, because Φ = 1 for the formation of H2
B.
Yes, because Φ = 2 for the consumption of HBr
C.
Yes, because Φ = 2 for the formation of Br2
D.
No, because there is no quantum yield involved in this mechanism
E.
It is not possible to know


24.
For the enzyme catalyzed reaction CO2 + H2O HCO3- + H+ it was measured that
[CO2]0 (mM)
R0 (M/s)
1.25
2.78 x 10-5
20
1.07 x 10-4

Determine the maximum rate Rmax and the Michaelis constant Km, assuming a Michaelis-Menten mechanism.
A.
Rmax = 1.32 x 10-4 M/s, Km = 4.69 mM
B.
Rmax = 7571 M/s, Km = 4.69 M
C.
Rmax = 1.32 M/s, Km = 4.69 M
D.
Rmax = 7571 M/s, Km = 4.69 mM
E.
Rmax = 1.32 mM/s, Km = 4.69 M


25.
The densities of acetone and water at 20oC are 0.972 g/mL and 0.9982 g/mL, respectively (1 mL = 1 cm3). The viscosity of water is 1.002 x 10-3 kg/ms at this temperature. Water requires 120.5 s to flow through an Ostwald viscosimeter, while acetone requires 40.5 s. What is the viscosity of acetone?
A.
3.28 x 10-4 kg/ms
B.
2.90 x 10-3 kg/ms
C.
1.03 x 10-3 kg/ms
D.
1.00 x 10-4 kg/ms
E.
0.56 x 10-4 kg/ms


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