Laser Aided Determination of K_sp and K_stab

Description

The determination of equilibrium constants for solid/solution equilibria is difficult when a judgment is to be made about when the solid has formed. A laser is used to create Tyndall scattering from an otherwise invisible amount of precipitate. The appearance of the scattering permits determination of K_sp; disappearance of the scattering permits determination of the stability constant of the silver ammine complex.

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• Aqueous chloride ion reacts with aqueous silver ion to produce a cheesy, white precipitate identified as silver chloride:
  • Ag⁺(aq) + Cl^-(aq) AgCl(c)
  • K_sp = [Ag⁺(aq)][Cl^-(aq)]
• It is difficult to stop the reaction at a point where the precipitate formed is just visible. Since the precipitate observed incorporates some of the chloride and silver added, the equilibrium concentration is actually smaller than the concentrations calculated from the amounts of these reagents added. As a result, values for equilibrium constants obtained by these experiments tend to be too large. Laser detection lowers the amount of materials required to detect Tyndall scattering and, therefore, leads to a better result.

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1. Put about 5 mL of water in a 10-mL graduated cylinder. Record the volume. Fill a thin stem transfer pipet with distilled water. Add 50 drops of water from the transfer pipet to the graduated cylinder. Record the new volume. Use this information to determine the volume per drop.
2. Place a folded black card on the surface of a magnetic stirring device. Place a clean 100-mL beaker on the magnetic stirrer. Place a clean stirring bar in the beaker. Place a low power laser on the other side of the beaker. Line up the laser so that the laser beam passes through the beaker just above the magnetic stirring bar. Be certain that all of the light passing through the beaker is absorbed (stopped) after it emerges.
3. Place 100 mL of very high quality distilled water in the beaker. Use a calibrated thin stem plastic pipet to add 20 drops of 0.0020 M AgNO₃ to the beaker.
4. Lower the room lights until it is just possible to count drops added. Use another calibrated thin stem plastic pipet to add 0.002 M NaCl, dropwise, until a permanent 'red pencil' appears in the beaker.
5. The pencil is visible in a lighted room.
6. Calculate the K_sp of AgCl.
7. The silver ammine complex also may be studied. Add 180 drops of 0.002M AgNO₃ to the reaction mixture. Titrate to the disappearance of the red pencil by adding 0.25 M NH₃ dropwise.
8. Calculate the stability constant for Ag(NH₃)₂⁺ if appropriate.

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Name ___________________________ Class ________

Teacher__________________________

DoChem 118 Laser Aided Determination of K_sp and K_stab

Watch the movie.

Use this sample data for calculations:

Volume of 50 drops = 2.10 mL

Added 20 drops 0.0020 M AgNO₃ at outset of titration.

Required 32 drops 0.002 M NaCl to reach permanent pencil.

1. Calculate the molarity of [Ag⁺] in the beaker when the titration is stopped.
2. Calculate the molarity of [Cl^-] in the beaker when the titration is stopped.
3. Calculate the K_sp of AgCl.

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Purpose

To determine equilibrium constants.

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• 1 100-mL beaker
• 3 thin stem plastic pipet
• 1 10-mL graduated cylinder
• 5 mL 0.0020 M AgNO₃
• 5 mL 0.0020 M NaCl
• 5 mL 0.25 M NH₃
• magnetic stirring device
• low power HeNe laser
• 5 cm length of 2-cm wide black electrical tape
• black cards
• 200 mL high quality distilled water, squeeze bottle

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• Although this demonstration usually captures student interest because of the use of a magnetic stirrer and a laser, the content is usually reserved for discussion in an advanced chemistry class.

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Teacher preparation: 45 minutes

Presentation: 15-20 minutes

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Stray laser light may cause blindness. Silver nitrate causes stains.

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Wash spills immediately with water. Use only low power lasers. Use black tape or black paint on the reaction flask or beaker to absorb the laser beam (i.e., to terminate the beam).

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Save the silver solutions for silver reclamation.

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Volume of 50 drops = 2.10 mL

Added 20 drops 0.0020 M AgNO₃ at outset of titration.

Required 32 drops 0.002 M NaCl to reach permanent pencil.

Added 180 drops 0.002 M AgNO₃ to reaction mixture.

Used 25 drops 0.25 M NH₃ to eliminate red pencil.

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For these data:

• Volume 50 drops = 2.10 mL

  2.10 ml x (1 / 50 drop) = 0.042 (mL / drop)

  Added 20 drops 0.0020 M AgNO₃ to 100 mL of water, so:

  [Ag⁺] = (20 drops) x (0.042 (mL / drop)) x 0.002 (mol / L) x (1 / 100 mL)

  = 1.7 x 10^-5 M

  [Cl^-] = (32 drops) x (0.042 (mL / drop)) x 0.002 (mol / L) x (1 / 100 mL)

  = 2.7 x 10^-5 M

  K_sp = [Ag⁺] x [Cl^-] = (1.7 x 10^-5M) x (2.7 x 10^-5 M)

  = 4.6 x 10^-10

• The same technology may be used to determine the stability constant for the formation of the silver (I) ammine complex. Chemically speaking, the trick in determining the complex's stability is to: use the silver chloride equilibrium to fix the concentration of silver ion that must be present at equilibrium; add excess silver ion; and then use the ammonia to tie up the excess silver in the form of the silver ammine complex until the silver ion concentration is lowered back to the original equilibrium concentration.
• When 200 drops of silver ion solution are added for every 20 drops required to precipitate silver chloride, the net result is that 180 drops of the added silver must be complexed. That is, the ratio of silver ammine complex concentration to silver ion concentration in the mass action expression for the stability constant should become 9:1. In other words:

  [Ag(NH₃)₂⁺] / [Ag⁺] = (180 drops / 20 drops) = 9

• When this value is substituted into the mass action expression, the stability constant is given as

  K_stab = [Ag(NH₃)₂⁺] / ( [Ag⁺] [NH₃]²) = (9 / [NH₃]²)

• This ratio does not require knowledge of either the chloride ion concentration or the solubility product of silver chloride, even though it is the silver chloride equilibrium that is making an end point determination possible.

  [NH₃] = 25 drops x (0.042 (mL / drop)) x (0.25 M) x (1 / 100 mL)

  = 2.6 x 10^-3 M

  and K_stab = 9 / [NH₃]² = 9 / (2.6 x 10^-3 M)³

  = 1.3 x 10⁶

• The value of the stability constant obtained, 1.3 x 10⁶, is within an order of magnitude of the accepted value.
• Two aspects of the classroom discussion should center on the accuracy of the procedure in general, and the predicted relationship between the endpoint and the equivalence point. These can be approached by asking the class to predict whether the value of the equilibrium constant will be higher or lower than that calculated from the data obtained.

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• stability constant
• solubility product
• equilibrium
• laser
• Tyndall
• scattering

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