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Question One Percentage ionization in the stomach pH=pKa+log⁡〖(A-)/HA〗 pH-pKa= log⁡〖(A-)/HA〗
2.0-5.0= log⁡〖(A-)/HA〗
-3.0=log⁡〖(A-)/HA〗
〖antilog-3.0=〗⁡〖(A-)/HA〗
(A-)/HA=0.001
% drug ionized=100/(1+10^x(pH-pKa))
Where x= 1 if the drug is basic and x= -1 if the drug is acidic
% drug ionized=100/(1+10 ^-1(-3))
% drug ionized=0.1% Percentage ionization in the ileum pH=pKa+log⁡〖(A-)/HA〗 pH-pKa= log⁡〖(A-)/HA〗
7.2-5.0= log⁡〖(A-)/HA〗
2.2=log⁡〖(A-)/HA〗
〖antilog 2.2=〗⁡〖(A-)/HA〗
(A-)/HA=158.48
% drug ionized=100/(1+10^x(pH-pKa))
Where x= 1 if the drug is basic and x= -1 if the drug is acidic
% drug ionized=100/(1+10 ^-1(2.2))
% drug ionized=99.4%

b)
Naproxen is a aryl acetic acid non-steroidal anti-inflammatory drug. In the stomach, the pH is acidic and hence the drug does not readily ionize. Most of the drug is present in no-ionized form and as a result the drug has good absorption rate in the stomach. On the other hand, the drug readily ionizes in the ileum due to high pH. This results to most of the drug existing in an ionized form and hence it has poor absorption rate in the ileum.
Non-ionized molecules are readily absorbed across cell membrane through diffusion and filtration and hence easily cross from one compartment to another. This is because non-ionized molecules are lipid soluble hence can cross the lipid bilayer of cell membranes. This facilitates good absorption rates of a drug and high bioavailability. Ionize molecules, on the other hand, are lipid insoluble hence they do not readily cross the lipid bilayer of cell membranes. As a result, they require carriers to transport them across the cell membrane through active transport or carrier-mediated transport. This results to poor absorption rate and bioavailability of drugs that are highly ionized.
Question Two

This requires plotting a graph of log Cp vs time and extrapolating the line of the graph. From the graph above we can estimate the initial log Cp = 1.18. Therefore:
Cp=antilog 1.18=15 mg/L VD=Q/(Cp(0))
VD=(0.57g×100)/(15mg/L)

VD=57mg/(15mg/L)

VD=3.8L

Theophylline has a low volume of distribution and hence it is confined within the intravascular fluid, hence it is mainly found in the plasma compartment of the blood and the extracellular fluid matrix. This is because its molecules might be too large to leave the compartment or they prefer binding to plasma protein rather than tissue proteins. The volume of distribution differs for every drug and is affected by factors such as sex, age and body healthy. With knowledge of the volume of distribution of the drug, a prescriber can prescribe the correct dosage for a drug. For instance, the volume of a drug is different in elderly people compare to younger individuals; hence these two groups of individuals are prescribed to different dosage. With respect to theophylline its volume of distribution is altered in patients suffering from hepatic cirrhosis, uncorrected academia and in premature neonates.

Cp(0)=1.15 mg/L
Cp(1/2)=0.575 mg/L
Therefore: t(1/2)=17 1/2 hours t 1/2=VD/CL
CL=VD/(t 1/2)
CL=3.8L/17.5h
CL=0.217 L/h
CL=217ml/(60 min)
CL=3.6 ml/min Clearance is the volume of plasma that is cleared of a drug per unit time. The above clearance indicates that the 3.6 ml of plasma is cleared of theophylline per minute. This is through elimination process such as renal clearance. References
Feldman, D. (1976). Naprosyn (naproxen). [Palo Alto, Calif.]: Syntex.
Hinderling, P., Smith, E., Lefer, A. and Schrör, K. (1988). Drug distribution in the body. Stuttgart: Gustav Fischer Verlag.
Katzung, B., Masters, S. and Trevor, A. (2009). Basic & clinical pharmacology. New York: McGraw-Hill Medical.
Keldenich, J. (2004). Prediction of human clearance (CL) and volume of distribution (VD). Drug Discovery Today: Technologies, 1(4), pp.389-395.
Makino, S. and Pauwels, R. (1998). Theophylline. Oxford: Blackwell.
Pancorbo, S. (1986). Evaluation of the Effect of Variability in the Volume of Distribution of Theophylline on the Predictability of the Iterative and the Chiou Methods Using Computer Simulations. Therapeutic Drug Monitoring, 8(3), pp.269-273.