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Copyright Brian J. Kirby. With questions, contact Prof. Kirby here. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.

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Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

B.7 Exercises [water properties top]

Assume dilute solution results throughout.

  1. Derive the Henderson-Hasselbach equation.

  2. Show that Equation B.12 is approximately correct at room temperature.

  3. Consider two separate systems: one which is 100 mL of pure water at and one with 100 mL containing 100 mM each of KH2PO4 and K2HPO4. What is the resulting pH if 1 mL of 1 N HCl is added to each solution? What does this tell you about the buffering action of the phosphate ions?

  4. Given its molecular weight (32.04 gmol) and density (791 kgm3), calculate the molarity of pure methanol.

  5. Calculate the pH of the following solutions:

    1. M HCl
    2. .02 M H2SO4
    3. 10 mM KOH
  6. 0.1 mol of a weak acid, HA, is added to pure water, and the resulting pH of the system is measured to be 2.2. What is the pKa of the weak acid?

  7. mol of a weak acid, HA, is added to pure water, and the resulting pH of the system is measured to be 4.15. What is the pKa of the weak acid?

  8. 25 mmol of a weak acid, HA, is added to pure water, and the resulting pH of the system is measured to be 5.9. What is the pKa of the weak acid?

  9. Phosphoric acid (H3PO4) has three protons that systematically dissociate with pKa’s of 2.1, 7.2, and 12.3 to form H2PO4-, HPO4-2, and PO4-3. Thus we can write three equilibrium equations:
    microfluidics textbook nanofluidics textbook Brian Kirby Cornell
    (B.21)

    microfluidics textbook nanofluidics textbook Brian Kirby Cornell
    (B.22)

    microfluidics textbook nanofluidics textbook Brian Kirby Cornell
    (B.23)

    If a phosphate ion exists in the form PO4-3, we would say that three protons have dissociated. If it existed in the form HPO4-2, we would say that two protons have dissociated, and so on. At any given pH, there is a statistical distribution of the four possible dissociation states of phosphate and thus an average number of protons that have dissociated. So we can define the concentration of dissociated protons as
    microfluidics textbook nanofluidics textbook Brian Kirby Cornell
    (B.24)

    and the total concentration of phosphate ions (in all forms) is
    microfluidics textbook nanofluidics textbook Brian Kirby Cornell
    (B.25)

    Calculate and plot (as a function of pH) the average number of protons that have dissociated per phosphate ion.

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Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

Copyright Brian J. Kirby. Please contact Prof. Kirby here with questions or corrections. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.


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