Question

1) As a technician in a large pharmaceutical research firm, you need to produce 450. mL of a potassium dihydrogen phosphate buffer solution of pH = 7.04. The pKa of H2PO4− is 7.21.

You have the following supplies: 2.00 L of 1.00 M KH2PO4 stock solution, 1.50 L of 1.00 M K2HPO4 stock solution, and a carboy of pure distilled H2O.

How much 1.00 M KH2PO4 will you need to make this solution? (Assume additive volumes.)

2)

If the normal physiological concentration of HCO3− is 24 mM, what is the pH of blood if PCO2 drops to 28.0 mmHg ?

Express your answer numerically using two decimal places.

Answer 1

a)Use the Henderson -Hasselbalch equation:
pH = pKa + log([HPO4--]/[H2PO4-]),
7.04 = 7.21 + log([HPO4--]/[H2PO4-]),

Solving, log [HPO4--]/[H2PO4-] = -0.17, or

[HPO4--]/[H2PO4-] = 0.693
[HPO4--] = 0.693*[H2PO4-].
This means, for every mole of H2PO4- added, 0.693 moles of HPO4-- will have to be added. Luckily, the stock solutions and the final buffer solution will all be the same concentration (1 M), which makes things a LOT easier:
x + 0.693x =450 mL,
where x = the volume of H2PO4- solution. (This equation would be more complicated if the stock solutions were of different concentrations.) Solving, x = 265.8 mL. So, mixing 256.8 mL of 1M KH2PO4 and 193.2 mL of 1M K2PO4 will give 450 mL of 1M phosphate buffer at pH = 7.04. No added water is needed.

b) pH = pKa + log[HCO3−](0.030)(PCO2)
pH = 6.1 + log[24 mM](0.030)(28.0 mmHg)
pH = 6.1 + log(20.16)
pH = 6.1 + 1.3045
pH = 7.4045

Note:

Carbon dioxide (CO2) and bicarbonate (HCO3−) concentrations in the bloodstream are physiologically controlled to keep blood pH constant at a normal value of 7.4.
Physicians use the following modified form of the Henderson-Hasselbalch equation to track changes in blood pH:

pH=pKa+log[HCO3−](0.030)(PCO2)

where [HCO3−] is given in millimoles/liter and the arterial blood partial pressure of CO2 is given in mmHg. The pKa of carbonic acid is 6.1. Hyperventilation causes a physiological state in which the concentration of CO2 in the bloodstream drops. The drop in the partial pressure of CO2 constricts arteries and reduces blood flow to the brain, causing dizziness or even fainting.