particles after 1 hour? Provide a physical
interpretation for the trends in D and x with
increasing size. The viscosity of water at 20
o
C is
1.002 × 10
–3 Ns/m
2 .
7. Prove that the dimensions of the diffusion
coefficient are m
3 s
–1 using Equation 3.69. Take
the units of viscosity as being Ns/m
2 .
8. If the process described in Equation 3.73 was
not diffusion-controlled, but rather reactioncontrolled, show the k obs = K × k 2 , where K is
the equilibrium constant describing the formation of the AB complex.
9. Consider a reaction between two spherical
nanoparticles in aqueous solution at 50
o
C. The
average diameter of one nanoparticle is 50 nm
and the average diameter of the other is
150 nm. Assuming the reaction is diffusionlimited, calculate the diffusion-controlled rate
constant in molL
–1 s
–1 . The viscosity of water at
20
o C is 0.547 × 10
–3 Ns/m
2 .
References and recommended reading
Berry, S. R., Rice, S. A., Ross, J. Physical and Chemical
Kinetics, Oxford University Press, Oxford, UK, 2002.
Laidler, K. J. Chemical Kinetics, 3rd edition. HarperCollins,
New York, 1987.
Tinoco, I.; Sauer, K.; Wang, J. C.; Puglisi, J. D., Physical
Chemistry: Principles and Applications in Biological Sciences. 4th ed.; Prentice-Hall: Upper Saddle River, NJ,
2002.
CHAPTER 3: Kinetics and Transport in Nanoscience
94
interpretation for the trends in D and x with
increasing size. The viscosity of water at 20
o
C is
1.002 × 10
–3 Ns/m
2 .
7. Prove that the dimensions of the diffusion
coefficient are m
3 s
–1 using Equation 3.69. Take
the units of viscosity as being Ns/m
2 .
8. If the process described in Equation 3.73 was
not diffusion-controlled, but rather reactioncontrolled, show the k obs = K × k 2 , where K is
the equilibrium constant describing the formation of the AB complex.
9. Consider a reaction between two spherical
nanoparticles in aqueous solution at 50
o
C. The
average diameter of one nanoparticle is 50 nm
and the average diameter of the other is
150 nm. Assuming the reaction is diffusionlimited, calculate the diffusion-controlled rate
constant in molL
–1 s
–1 . The viscosity of water at
20
o C is 0.547 × 10
–3 Ns/m
2 .
References and recommended reading
Berry, S. R., Rice, S. A., Ross, J. Physical and Chemical
Kinetics, Oxford University Press, Oxford, UK, 2002.
Laidler, K. J. Chemical Kinetics, 3rd edition. HarperCollins,
New York, 1987.
Tinoco, I.; Sauer, K.; Wang, J. C.; Puglisi, J. D., Physical
Chemistry: Principles and Applications in Biological Sciences. 4th ed.; Prentice-Hall: Upper Saddle River, NJ,
2002.
CHAPTER 3: Kinetics and Transport in Nanoscience
94