Physical Constants
Other Units
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    = 96,500 C mol-1
 
c    = 2.998 x 108 m s-1
 
g    = 9.81 m s-2
 
B    = 0.51mol-1/2dm3/2
(in H2O, 25oC)
 
 
 
Sequential reactions:
 
 
[B]=(k1/(k2-k-1)) f(t)[A]0
 
f(t)=exp(-k1t)-exp(-k2t)
 
 
 
Parallel reactions:
 
Φi = ki/S
 
Where S is the sum of all rate constants of the paral-lel reactions
 
Note:
Quantum yield/efficiency = Φ = moles of product formed / moles of photons absorbed
1dm3   = 1 L
 
1dm3   = 1000 cm3
 
1 J    = 1 kg m2 s-2
 
1 atm    = 1.101325 x 105 Pa
 
1 atm    = 760 mmHg
 
1 Torr = 1 mmHg
 
1 Torr = 133.322 Pa
 
1 bar    = 105 Pa
 
1 nm    = 10-9 m
 
 
 
Eyring equation:
 
k =kBT/(hc0) x f
 
f =exp(ΔS#/R) x
 
x exp(-ΔH#/RT)
 
 
 
ln(1 - θ) = -θ
if θ << 1
 
E   = hυ
 
c   =υλ
 
PV =nRT
 
ΔG = ΔH - TΔS
 
k = A
 
k    =
 
A = e (kBT/h) exp (Δ‡S/R)
k    =
Ea = Δ≠Ho-PΔ≠Vo + RT (sol)
   = Δ≠Ho-ΣνRT + RT (gas)
 
log k = log ko+ 1.02 zAzB
log k = log ko -
ΔGo = - RT ln Kc
 
υ =

θ = KP/(1 + KP), at T=const
 
tf = (kf +kq[Q])-1,    Q is quencher
 



1.
The chlorination of methane (CH4),
CH4(g) + Cl2(g) → CH3Cl(g) + HCl(g)
follows the mechanism
Cl2 2 Cl
Cl + CH4 HCl + CH3
CH3 + Cl2 CH3Cl + Cl
2 Cl Cl2
Find the overall rate constant expression and the overall order of the rate law of the formation of CH3Cl, assuming, the steady state approximation is applicable on both (Cl and CH3) intermediates.
A.
k2 (k1/k4)1/2 and 3/2
B.
k2 (k1/k4)1/2 and 5/2
C.
k2 (k1/k4)1/3 and 5/2
D.
k2 (k1/k4)1/2 and 1/2
E.
k2 (k1/k4)1/3 and 1


2.
For the fluorescence quenching of rhodamine B in solution with the quencher hexaiodocyclobutene, C4I6, at a concentration of 1.00 nM C4I6 the fluorescence lifetime τf was 203 ns, while at 2.0 nM C4I6 the fluorescence lifetime was 145 ns. Determine the rate constant for quenching, kq, process.
A.
1.97 x 1015 M-1s-1
B.
1.97 x 106 M-1s-1
C.
1.97 x 1012 M-1s-1
D.
9.97 M-1s-1
E.
9.9 x 107 M-1s-1


3.
In a photochemical experiment, 3.5 mmol of 1,3-butadiene were converted to cyclobutene when irradiated with 95.0 W of 290 nm light for 15.3 s. All of the light was used for the conversion. What was the overall quantum yield for this process?
A.
1
B.
2
C.
0.50
D.
1000
E.
10


4.
The bimolecular reaction of chlorine monoxide can result in the formation of three different parallel reactions:



If the rate constants of these reactions are k1 = k3 and k2 = 4.8 x 106 M-1 s-1. What is the rate constant of the oxygen gas formation process when its yield is 0.30?
A.
3.6 x 106
B.
2.1 x 106
C.
2.5 x 106
D.
1.1 x 106
E.
5.8 x 106


5.
Which one of the following processes is called Phosphorescence (Note: S denotes a singlet state and T denotes a triplet state)?
A.
T1 → S0 + hν
B.
S1 → S0 + hν
C.
T1 → S0 - hν
D.
S0 → S1 - hν
E.
S1 → T1


6.
In the unimolecular isomerization of cyclobutane to butylene in the presence of a buffer gas M, the apparent rate constant values for kuni as a function of the buffer gas pressure were measured at 350K and found to be
[M] (mM)    
5.04
34.8
kuni (s-1)
9.58
11.1

Assuming that the Lindemann mechanism accurately describes this reaction and the apparent rate constant is given by
what will be the value of k1?
A.
1.19×104 M-1 s-1
B.
3.49×105 M-1 s-1
C.
2.19×104 M-1 s-1
D.
5.12×103 M-1 s-1
E.
6.59×104 M s-1


7.
Consider the following reaction mechanism that describes the formation of product P.
A
B
C
 
C               P

If only the species A is present at t = 0, what is the expression for the concentration of P as a function of time? (Apply the pre-equilibrium approximation)
A.
d[P]/dt = k3K1K2[A]
B.
d[P]/dt = k2K1-1K2[A]
C.
d[P]/dt = k3K1K2-1[A]
D.
d[P]/dt = k1(K1K2)-1[A]
E.
d[P]/dt = (k1K1K2)-1[A]


8.
The adsorption of ethyl chloride (C2H5Cl) on a sample of charcoal at 0 °C measured at several different pressures is as follows;
P of C2H5Cl (Torr)    
50
100
Vads (mL)
3.8
4.3

Using the Langmuir isotherm, determine the fractional coverage at 100 Torr.
A.
0.868
B.
0.595
C.
0.952
D.
0.754
E.
0.126


9.
The cleavage of N-acetyl-tyrosylamide (NAT) by chymotrypsin was studied and the following reaction rates versus substrate concentration were measured;
[NAT]0 (mM)
4.00
8.00
R0 (mM s-1)
0.016
0.028

What are the Michaelis constant, Km, and the limiting rate of this reaction, Rmax?
A.
Km = 24.0 mM ; Rmax = 0.112 mM s-1
B.
Km = 24.4 mM ; Rmax = 0.137   mM s-1
C.
Km = 57.3 mM ; Rmax = 0.298 mM s-1
D.
Km = 73.3 mM ; Rmax = 0.137   mM s-1
E.
Km = 98 mM     ; Rmax = 0.193   mM s-1


10.
For a system obeying the Langmuir isotherm , the slope of the plot of ln(θ/P) versus θ for very small coverage (θ << 1) is,
A.
–1
B.
+1
C.
+2
D.
–2
E.
+3


11.
Consider the following mechanism for ozone thermal decomposition.
O3(g)
O2(g) + O(g)
O3(g) +O(g)    2O2(g)
What is the rate law expression for the loss of O3(g) (use the pre-equilibrium approximation) ?
A.
Rate = k1k2 [O3]2/(k-1[O2])
B.
Rate= 2k1k2 [O3]2/(k-1[O2])
C.
Rate = k-1k2 [O3]2/(k1[O2])
D.
Rate= 2k-1k2 [O2]2/(k-1[O3])
E.
Rate = k1k2 [O2]/(k-1[O3])


12.
Which statement is true regarding the following reaction
A + 0.5B + 2C D + E
A.
The rate of change of C is 4 times the rate of change of B
B.
The rate of change of B is 4 times the rate of change of C
C.
The rate of change of A is 4 times the rate of change of C
D.
The rate of change of C is 4 times the rate of change of A
E.
The rate of change of B is 4 times the rate of change of D


13.
Consider the first order decomposition of ethane to ethene:
C2H6(g) C2H4(g) + H2(g)
How long will it take for the partial pressure of ethane to change by 30% of its initial value when the rate constant for decomposition is 3.52x10-3 s-1?
A.
101.3s
B.
110.0s
C.
342s
D.
27.5s    
E.
3.20x103s


14.
The rate of the following reaction is the rate of formation of CO2.
CaCO3(s) + 2HCl(aq) CaCl2(aq) + CO2(g) + H2O(l)
The rate of reaction will be the largest at:
A.
The beginning of the reaction because [HCl] is largest.
B.
The middle of the reaction because [CaCO3(s)] is not large.
C.
The end of the reaction because [HCl] is smallest.
D.
The end of the reaction because [CaCO3(s)] is smallest.
E.
In the middle of reaction time because then [HCl] is not too large.


15.
The following tabulated data were obtained for the reaction:
SO2 + O3 SO3 + O2
at 298 K.
[SO2], mol/L
[O3], mol/L
Initial Rate, mol/(L s)
0.25
0.60
0.284
0.25
0.40
0.189
0.75
0.40
0.567

The following describes best the rate parameters:
A.
rate = 1.89 (M-1 s-1) [SO2] [O3]
B.
rate = 1.27 (M-1 s-1) [O3]2
C.
rate = 0.56 (M-1 s-1) [O3]2
D.
rate = 2.36 (M-1 s-1) [SO2][O3]
E.
rate = 0.29 (M-1 s-1) [O3] [SO2]


16.
Nitrogen dioxide decomposes to nitric oxide and oxygen according to:
2NO2 2NO + O2

At 300 °C, NO2 drops from 0.0100 M by 50% M in 1.50 min. The rate of appearance of O2 for this period in M/s is:
A.
2.78 x 10-5
B.
1.94 x 10-5
C.
2.67 x 10-5
D.
1.74 x 10-5
E.
4.33 x 10-5


17.
For the sequential reaction:

the rate constants are k1 = 2.0 x 1012 s-1 and k2 = 3.3 x 1010 s-1. At what time does the maximum concentration of the intermediate B occur?
A.
2.09 x 10-12 s
B.
1.08 x 10-12 s
C.
3.09 x 10-11 s
D.
4.11 x 10-10 s
E.
1.28 x 10-12 s


18.
The rate constant and activation energy for the reaction of hydrogen and iodine to produce gaseous hydrogen iodide are 2.45 x 10-4 M-1 s-1 at 302 oC and 1.5 x 105 J mol-1, respectively. At what temperature the rate constant will be 100 times the rate constant at 302 oC (assume constant pre-exponential factor A)?
A.
401 oC
B.
350 oC
C.
250 oC
D.
675 oC
E.
525 oC


19.
The rate constants of the gas decomposition of urea in aqueous solution,
(NH2)2C=O (aq) + H2O(l) CO2(g) + 2 NH3(g)
at two different temperatures, 60.0 oC and 71.5 oC, are found to be 1.2 x 10-7 s-1 and 4.4 x 10-7 s-1, respectively. Use these parameters to estimate the enthalpy of activation (ΔH≠) of this reaction at 25 oC as described by the Eyring equation.
A.
105 kJ mol-1
B.
115 kJ mol-1
C.
106 kJ mol-1
D.
123 kJ mol-1
E.
101 kJ mol-1


20.
Consider the data of several systems for the conversion of reactants to products at the same temperature:
System
Activation energy,
Ea (kJ)
Enthalpy of reaction
ΔH (kJ)
1
40
–25
2
60
30
3
15
10
4
90
–55

A.
System 3 is the fastest endothermic reaction.
B.
System 1 is the fastest endothermic reaction.
C.
System 2 is the slowest exothermic reaction.
D.
Systems 1 and 4 are endothermic while 2 and 3 are exothermic reactions.
E.
Systems 1 and 2 are faster than 3 and 4 reactions.


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