Chemical and Physical Equilibrium

Chemistry 128

October 25, 2002

• This week's "experiment" is a tour of equilibrium, with many separate parts.
  • there are 10-12 different parts, each illustrating a different type of equilibrium
• Some of the simpler systems involve physical equilibrium
  • phase changes such as evaporation or sublimation (and of course the reverse processes)
  • phase changes associated with solubility
    • solubility of salts
    • solubility of gases

• Then we will examine a number of examples involving reactions and chemical equilibrium
  • acid-base equilibrium
  • acid-base indicators
  • equilibrium involving solids and gases
  • equilibrium involving complex ion formation

We will generally send you and your group to various experiment work stations rather than having you work at your bench. the various experiments can be performed in any order.

This is not really a balanced list of examples. It is biased towards those processes we can monitor easily in the time available to us. We also avoid processes that are hazardous such as those involving high pressure gases. We also avoid reactions that are slow-- after all, we really only have about 15 minutes to devote to each topic.

Part 1 -- Solubility of a Salt (an ionic compound)

For an ionic compound, we would be justified treating this as a real chemical reaction. The salt is an ionic solid, but the dissolved salt is really a different species. It becomes a collection of independent cations and ions. For example, a solution of sodium sulfate contains no identifiable "sodium sulfate" species-- it is a solution of sodium ions and sulfate ions.

We will focus on a set of Calcium compounds because we have access to a calcium electrode. With the electrode we can make an accurate Calcium ion measurement in as little as 30 seconds. The concentration of Ca²⁺ can be anywhere from 0.1M to 10^-5 M and the electrode ignores almost every other chemical species in the solution.

We further simplify your experiment by providing many of the samples as saturated solutions. Waiting for solubility equilibrium to be reached would otherwise cost us a few hours.

1a. What is the solubility of a Ca salt in water?

• calcium sulfate, CaSO₄
• calcium oxalate Ca (C₂O₄)
• calcium stearate Ca(stearate.)₂
  • this is a major component of soap scum
  • a typical soap might be the potassium salt of stearic acid (from animal fat)
  • the stearate ion will react with calcium Ions in hard water
  • calcium stearate has very low solubility, so a solid (soap scum) forms
• In each case, the electrode will tell us the concentration of dissolved Ca²⁺
• Stoichiometry will give us the concentration of the anion

• The equilibrium constant is often called Ksp or the solubility product
  • A typical reaction is CaSO₄(s) -----> Ca²⁺ + SO₄2-
  • So Keq = [Ca²⁺] x [SO₄2-]
    • quantities in [ square brackets] are concentrations, moles/liter
    • the product Ca²⁺ has coefficient of 1 so its concentration is raised to the first power
    • the product SO₄2- has coefficient of 1 so its concentration is raised to the first power
    • the reactant is a solid, so it is written as 1 (one)
  • Evaluation of Ksp is easy Ksp = [Ca²⁺] [ SO₄2-]
    • we get [Ca^2+] from the electrode and a calibration curve
    • in this case, [SO₄2-] will be the same number

• Rinse the Ca electrode in distilled water and gently blot with a laboratory tissue
  • place electrode into the saturated solution.
  • record the voltage (mV) once a stable reading is established
  • determine Ca concentration from the calibration plot provided
    • determine Ksp

Experimental:

• Measure the Ca concentration of a saturated solution containing additional anion
  • for example, Solubility of CaSO₄ in 0.1 M Na₂SO₄
    • in 0.01 M Na₂SO₄
    • in 0.002M Na₂SO₄
  • In each case the Sulfate ion increases by the amount of Ca²⁺ that dissolved
    • example- if Ca+2 = 0.0015M and solvent is 0.0020M Na₂SO₄ then
    • sulfate concentration is 0.0035M
  • Evaluate K_sp as before, using the new values for the concentrations
  • We expect to get the same values for Ksp

1c. Testing the solubility product results

We can cause the reverse reaction to occur by mixing Ca²⁺ ion and SO₄2- ions until a solid appears When the solution gets cloudy.) We obviously start with solutions of much more soluble salts such as CaCl₂ and Na₂SO₄. the remaining Na⁺ and Cl^- ions have no effect on our process.

There is a serious limitation in this approach-- we won't detect the cloudiness of the solution when the first solid forms, so we will not stop the addition at the exact moment that solid appears.

• example: We start with 50 ml 0.01 M oxalate ion
  • We add drops of 0.005 M Barium ion
    • this is a 1:1 compound, Ksp = [Ba²⁺]{oxalate^2-]
  • We add 3.0 ml of the barium solution before we see a precipitate
    • final volume = 53 ml
    • oxalate concentration is 0.01 x (50/53) = .0094M
    • barium concentration is 0.005 x (3/53)=2.8 x 10^-4M
    • Ksp = 2.7 x 10^-6

2. The Solubility of a Gas in Water

The solubility of Carbon Dioxide is easier to handle and demonstrate.

• there are good sources of CO₂ solutions (carbonated beverages)
  • there is enough gas in a pop bottle to fill a small balloon for volume measurement
  • there's a convenient source of pure gas (dry ice)

• this is the pressure of the species (the partial pressure)
• don't confuse this with the total pressure, especially if air is present at 1 atm.

• Keq = [CO₂, _dissolved] / P(CO₂)
  • so increasing the CO₂ pressure will increase concentration
  • (see Henry's Law)

3. Chemical Equilibrium Involving a Solid and Gases

• Ammonium Carbonate (NH₄)₂CO₃ (s) ----> 2 NH₃ (g) + CO₂ (g) + H₂O(g)

• You can verify one aspect by sniffing a sample of solid-- you should smell NH₃
  • This compound is sometimes used as a leveling agent (gas producing) in baking
  • It is used to take the place of baking powder or sodium bicarbonate.

• This is slow but we could demonstrate a LeChatlier shift in equilibrium
  • place solid Ammonium carbonate and Calcium oxide in a sealed jar
    • (keep them separated)
  • the Ammonium Bicarbonate then evaporates until equilibrium is reached
    • Kp = P(NH₃)² x P(CO₂) x P(H₂O)
  • but the CO₂ will react with CaO to form CaCO₃
    • also, the H₂O(g) is absorbed, forming Ca(OH)₂
  • More Ammonium carbonate will decompose
    • the ammonium carbonate pile will gradually get much smaller and vanish
    • a sniff of the bottle would reveal a much higher NH₃ concentration
  • In this case, we would keep driving the process but won't reach equilibrium unless we use up all of the CaO.

4. Gas Solubility and Freezing Point Depression

• 1. CO₂ is reasonably soluble in water
• 2. dissolving anything in water lowers the freezing point
• 3. the solubility of a gas is much greater at high pressures

• We start with Seltzer water in a plastic bottle
  • (basically CO₂ dissolved in water)
  • most sugar free pop or club soda is close enough;
    • there's only a small a bit of salt, citric acid and other flavorings
    • regular pop has too much sugar to be good for you or for this demonstration
    • typically the concentration of dissolved CO₂ is ____ molal at these conditions
• Cool the bottle to about -8^oC
  • use an ice/salt bath or the freezer compartment of a refrigerator
    • (caution: most freezers get too cold)
  • note that the contents of the bottle do not freeze
  • the freezing point is -0.86^O x (solution molality) = ____^oC with the data above
• Now open the bottle and try to pour it into a glass that has been cooled in ice
  • at this point the excess CO₂ pressure is vented
  • the new solubility of CO₂ at 1 atm is _______ molal
  • as the gas comes out of solution, the liquid is now cooled below its freezing point
  • so the liquid will solidify either in the gas or in the bottle while you pour

5. Phase Transitions in Solids

• (Not really an equilibrium demonstration, but fun and informative anyway)
• Many solids exist as several different solid phases and there are transitions between them.
• Generally, we change the phase by changing temperature of the solid.
  • Other phases are produced at higher pressures, but it's hard to demonstrate this safely.
• Our solid is a synthetic rubber (the type used for "superballs" )

• We will set up an experiment to measure the degree of bounce
  • drop the ball from a height of 1 meter
  • let it hit a very solid target (we will use a steel plate)
  • measure how high the ball bounces upward
• Begin by cooling the ball in liquid nitrogen (-195^oC) or dry ice (-78^oC)
  • caution: this ball is cold and can cause frostbite / use heavy gloves, tongs or forceps.
• Every 15-30 seconds, drop and measure the rebound
  • the ball will warm over the next 5 minutes in room air
  • without giving away any secrets a plot of rebound vs. time will show you when the phase transition occurs.
  • (We will try to provide a similar ball, drilled to accept a temperature probe to help estimate the temperature.)

6. Vapor Pressure of a Pure Liquid and the Effect of Temperature

• A typical "balanced chemical equation" is H₂O (liq) -----> H₂O(g)
• The equilibrium express has P(H₂O) on the top of the fraction
  • the reactant is a pure liquid and does not appear in the equilibrium
• So Kp = P(H₂O)
• Funny as an equilibrium expression since it says...
  • at equilibrium, the pressure of water vapor is independent of all other variables
  • that is, the equilibrium vapor pressure is a constant
  • in particular, it is independent of how much liquid or vapor is present (volumes)
• Remember that P(H₂O) is the partial pressure of water vapor, not the total pressure
  • if air is present, the total pressure may be much higher
• Of course Kp varies with temperature, so we do expect the vapor pressure to vary with temperature
• A plot of ln P vs 1/T (Kelvin) should shows a straight line
  • the slope = - DHvaporization/ R
• We can measure the vapor pressure of a variety of liquids including water
  • we have an electronic pressure sensor we can use
  • it responds to the pressure of any (all) gases (including air)
  • we will work in the presence of air
    • (to avoid need for vacuum pumps, heavy walled containers, valves, etc.)

• We begin with a dry 250 ml Erlenmeyer flask
• the Pressure Gauge is located in one tube on a two hole stopper
  • the pressure will be displayed (plotted) on a computer screen
• the other hole has a tube capped with a rubber septum
  • we can inject liquid into the flask though the rubber septum
  • we use a micro-syringe and a sharp needle
  • the pressure will rise as soon as the liquid in injected
    • the pressure levels out to the equilibrium value
    • the vapor pressure of the liquid is the increase in pressure (class notes said increase in temperature, that's wrong)

• If the flask is at a controlled temperature (ice, water bath)
  • we determine the vapor pressure at the bath temperature

• Notice that we must begin each run with a clean, dry flask
  • otherwise the flask will start with some vapor and we get a smaller pressure rise

• We could take a flask with liquid and heat it, but the pressure rise will now reflect two processes
  • Charles' law for the air
  • Increased vapor pressure of the liquid

• We will limit our attention to weak acids
• Strong acids dissociate completely to ions in water and there is essentially no equilibrium
• We will use a pH meter to measure the concentration of one component, H+
  • [H+] = 10^-pH ... use the power or antilog function of a calculator or computer spreadsheet
• A typical weak acid follows this equation
  • HA + (water) ----> H+ + A-
  • you may prefer to talk about H₃O⁺ as the Hydronium ion
  • Keq = [H⁺] [A^-] / [HA]

• In our experiment we only measure the concentration of one of the three species
  • We need to be able to determine the other two species
  • We use stoichiometry to find these species
• If we make a dilution solution of a weak acid
  • some dissociated to form H+ (we measured that)
  • we must get an equal about of A- (so now we know that quantity)
  • but we must lose an equal amount of acid HA
  • we know the concentration of the original acid solution
  • subtract the amount that reacted
    • often, so little reacts that we can use the original number

• We can also look at the effect of added anion
  • this is referred to as the conjugate base of our acid
  • we can add it in the form of a sodium or potassium salt
  • if we mix known amounts of acid and conjugate base
    • pH measurement tells use H+ concentration
      • in our examples this is tiny compared to [HA] or [A-]
      • So we can fill in the equilibrium expression with initial concentrations of the others

• measure the pH of a dilution solution of acetic acid.
  • evaluate Ka
• mix this solution with a solution of sodium acetate
  • ml of acid _____, conc of acid ____ M
  • ml of salt ______, conc of salt _____M
    • final volume = _____ ml (add acid + salt)
    • final acid conc = _____________
    • final base concentration = ___________
  • evaluate Ka
    • you should get a consistent value of Ka.

8. Acid - Base Indicators and Equilibrium

• These species are colored compounds that act as weak acids
• The acid and base forms have different colors
  • thus, looking at color can help use determine pH or [H+]
• Bromcresol Green was used last week for other purposes
• In acidic solutions this is a yellow compound
• In neutral or basic solutions this is a blue species
• We will write this as HIn ----> H+ + In- HIn =yellow, In- =blue
  • Keq = [H+] [In-] / [HIn]
• Notice that the ratio {In-]/[Hin} is a good guide to the color of the solution
  • if the ratio is large , say 10 or higher, the solution is simply yellow
    • your eye won't detect the small amount of blue species present
  • if the ratio is modest, say 3:1, the solution will still be yellow with a modest contribution of blue;
    • this is a slightly greenish yellow color
  • when the ratio reaches 1 the solution has equal parts of yellow and blue
    • your eye sees this as a green solution
  • in more basic solutions the ratio decreases, say to 1/3
    • now there is three times as much blue material
    • your eye reports a blue solution, slightly greenish in color
  • by the time the ratio reaches 1/10, your eye fails to see any yellow or green tinge

• Will can simulate the appearance of mixtures by placing tubes of yellow and blue forms
  • together so you must look through both tubes.
  • We dilute the two forms so the sum of the concentrations remains constant

• Place a drop of indicator in a buffer (known pH)
  • compare the color (tint, not darkness) to the prepared samples
  • from the match, determine the ratio
  • compute Kequil for the indicator

• (We could, of course rely on a spectrophotometer to tell us each concentration at suitable wavelengths)

9. Complex Ion Equilibrium

• We used this reaction in two previous experiments:
  • Fe(II) + 2 phen ---> Fe(phen)₃ bright red complex
  • K eq = [Fe(phen)₃] / [Fe²⁺] x [phen]³
• For today's purposes phen is a poor reagent--
  • the equilibrium constant is pretty high and almost all the iron is likely to be bound
• Let's look at ligand with a weaker binding
  • Fe³⁺ + SCN^- ---> [Fe(SCN)²⁺]
  • Keq = ---> [Fe(SCN)²⁺] / [Fe³⁺ ] x [ SCN^-]

we will use a Spectrophotometer to measure the concentration of the red species [Fe(SCN)²⁺].

10. Solubility of a salt in acid

• consider CaA₂ ---> Ca²⁺ + 2A^-
• Ksp = [Ca²⁺ ] x [A^-]²

• often the anion (A-) of a salt can function as weak base
• addition of a strong acid (H+)
  • will convert some A- to HA
    • H⁺ + A^- ---> HA
  • the lost A^- no longer participates in the solubility equilibrium
  • so more salt will dissolve

• details in lab

• This is an odd example, based on the passage of CO₂ through the walls of a soap bubble
• In one respect, the soap bubble's wall acts as a selective semi-permeable membrane
  • the effect is similar to osmosis
• CO₂ will pass from regions of higher CO₂ concentration to regions of lower concentration
• As an equilibrium this is odd, but let's write the process and Keq
  • CO2 (inside) -----> CO2 (outside)
  • K_p = P_{(CO2, outside) /} P_{(CO2, inside)}
  • but the species inside and outside is identical, so Kp must be 1
  • therefore the process occurs until P(CO₂ ) is equalized.

• An air bubble, floating in a bed of CO₂ gas... will get larger and burst in 1-2 minutes
• A CO₂ filled bubble will get smaller as it stand in air... it can collapse in a few minutes

• A similar (but slower) effect is seen with ordinary rubber balloons
  • a CO₂ filled balloon shrinks over a period of an hour or two
  • if kept in a CO₂ rich atmosphere, the balloon stays inflated
  • An air filled balloon gets larger if placed in a CO₂ rich atmosphere

12. Liquid Vapor Equilibrium in Bromine or Iodine

• (liquid bromine -evaporation, or solid iodine-- sublimation)
• We have sealed samples into test tubes
  • (the vapor is too corrosive and stoppers would react)
• We place sample in a spectrometer
• the absorbance and extinction coefficient will tell us the concentration
  • PV=nRT will let us determine the pressure
• We would like to study samples at several temperatures

• additional details available in lab 10/22/02

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