Elements of
Chemical Reaction Engineering
6th Edition



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Essentials of
Chemical Reaction Engineering
Second Edition

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Chapter 5: Isothermal Reactor Design: Conversion

Additional Homework Problems

CDP5-CB

The cells in your body need to obtain nutrients, hormones, growth factors, and other molecules present in very low concentrations in the fluid around them. To avoid engulfing a large quantity of this fluid and then intracellularly separating useful from useless molecules, the cells possess what are known as receptors on their surface. These receptors are able to bind interesting molecules or ligands with high affinity, thus capturing molecules for the cell's use (Figure CDP4-C).

(a) You are growing 10 6 cells/mL in a T flask containing 10 mL of media. Each cell has 10 5 receptors on its surface. The association rate constant for the binding of ligands to receptors is 10 6 M -1 min-1 . Calculate the time for 50% of the receptors to bind ligands if you add ligands at a concentration of 10 -7 M. Assume irreversible binding and perfect mixing.
(b) Show that the ligand concentration in part (a) is sufficiently in excess so that the binding could be considered pseudo-first order.

Figure CDP4-C          

(c) The binding of ligand to receptor is actually a reversible reaction. For the binding of your ligand to receptors, the dissociation rate constant k r is 0.1 min -1 . Using the approximation justified in part (b) and assuming perfect mixing, calculate the percentage of receptors bound 5 min after you add the ligand to the media. (J. Linderman, University of Michigan)

[2nd Ed. P4-34]