Chemistry 128

Acid-Base and pH

Web package edited Nov 12, 2002

(we use <==> for double arrow equilibrium expressions)

Acids - Bases and pH-- quick review

• We use several strong acids that undergo 100% dissociation in water
  • HCl, HNO₃, HClO₄, HBr and H₂SO₄ (first proton at least)
• Most others are weak acids, undergoing partial dissociation HA + H₂O <===> H₃O⁺ + A^-
• Several hydroxides are strong bases, undergoing 100% conversion to ions in solution
  • NaOH, KOH, Ca(OH)₂
• Weak bases, like ammonia, undergo a similar equilibrium NH₃ + H₂O <===> NH₄+ + OH^-
• Bronstead Lowry Acids are proton donors and Bases are proton acceptors
  • acids often donate H+ to water to form the Hydronium ion H₃O⁺
  • then water is acting as a Bronstead Lowry base -- a proton acceptor
• Every acid (base) has a conjugate base (acid)
  • acetic acid / acetate ion (base)
  • ammonium ion (acid) / ammonia (base)
  • We can relate the K_a of the acid to K_b of its conjugate base
    • K_a x K_b = K_w = 1.00 x 10^-14 (at 25^oC)
• Many common ions have no effect on the pH of a solution
  • Na, K, Ca, .... NO₃-, Cl^-, Br^-
  • so a solution of sodium acetate can be considered a solution of acetate ions
• pH is defined as pH = -log₁₀( [H₃O⁺])
  • pH is a convenient measure of the free H+ or H₃O⁺ level of a solution
  • pH is a convenient way to express very large and very small concentrations using a simple numerical form
  • pH basically collapses the range of H+ concentrations
    • 0.1 M H+ is pH 1.00 1x10^-5M H+ is pH 5.00 x 10^-12 is pH 12.0
    • pH 3.32 means [H+] = 10 ^-3.32 (clearly a value between 10^-3 and 10^-4M)
  • note that an acid-base titration measures the total concentration of acid (dissociated and nondissociated) , not the pH
• pH values don't follow the usual rule on significant figures
  • (only the digits behind the decimal point are treated as significant)
  • (the integer part of a pH basically sets the power of ten)
    • example pH 4.57 means H+] = 10 ^-4.57 = 2.69 x 10^-5
    • consider + 0.01 pH change
      • pH 4.56 =2.75 x 10^-5 M pH 4.58= 2.63 x 10^-5 M
    • this would be better labeled [H+] = 2.7 x 10^-5M

Measuring pH

• Acid Base Indicators change color over a pH range of about 2 pH units.
  • The indicator has an equilibrium constant, K_ind or pK_ind = - log₁₀(K_ind)
    • When pH = pK_ind, 50% of the indicator is in the acid form, 50% in base form
      • the color is the result of mixing these two species, chosen for different colors
    • When pH = pKind + 1, the ratio of the two forms is 1/10 or 10/1
      • now the color is that of the dominant species
    • We can detect intermediate colors and estimate pH to about + 0.2 pH units
  • We can often select an indicator that will let us judge pH in the region of interest
    • Bromthymol blue has a useful range of pH 6.0 to 7.6
    • This matches well the desired pH range in tropical fish tanks
  • We can mix several indicators to provide color changes over a wider pH range
    • You used a general purpose pH test paper recently (pHydrion brand)
    • This had useful color changes from pH 0 to pH 13, readable to +0.5 pH
    • This paper actually has a mixture of 7-8 different color indicators.

Electrochemical pH Measurements

• pH electrodes generate a voltage that varies with pH of a solution
• An electronic control box (meter) translates that voltage to pH and displays the value
• A typical pH meter will measure from pH 0 to pH 14 and can be read to 0.01 pH
  • note: there is nothing special about pH 0 or pH 14
  • strong acids will have negative pH at concentrations > 1 Molar
  • however, for most purposes pH ranges from 1>pH>13
• The pH electrode is based on a special form of glass that is H+ permeable
  • The electrode is in the form of a tube with a sealed end
  • Inside the tube is a solution of H+ (typically 1 M HCl)
  • Outside the tube is the H+ solution to be measured

• H+ will travel through the glass, trying to equalize the concentration
  • this is an extremely slow process ("not in your lifetime")
  • The thermodynamic drive to move charged particles causes an electrical potential
    • small difference s= small voltage, rising as the difference increases
  • we monitor the voltage difference between the inside and outside solutions
    • voltage changes by 0.059 V per pH difference

• All electrical measurements require two terminals and for practical reasons those terminals must ultimately be metallic wires.
  • Inside the pH electrode is a wire (perhaps platinum but often AgCl coated Ag)

• A second electrode is needed
  • to be effective, this electrode must be unaffected by pH

• Most commercial pH electrodes build the second electrode into the same device
  • the pH sensing electrode is a narrow tube in the center
    • it terminates in a glass bulb at the bottom
    • this bulb must, of course, be in the solution
  • The reference electrode is in a larger diameter tube
    • this electrode ends with a ring seal
    • just above the pH sensing bulb
    • the seal is slightly porous, since ions must be able to travel through it
  • this seal must also be immersed in the liquid being tested
    • inside is another wire (usually silver, coated with silver chloride)
    • inside is a solution, usually potassium chloride
      • for convenience, this is usually a thick gel so it stays in position

• The electronics / meter has three main roles
  • first, it measures the small voltage difference (0.059 volts/pH )
  • it converts that reading to a form suitable for a meter (amplified to 0.1 volt/pH)
    • it displays that reading as a pH value
  • it compensates for a small temperature effect and for the true pH
    • the electrode really only tells us the pH difference (inside/outside)
    • the inside H+ varies slightly during manufacture and storage
    • this requires a calibration before the pH meter can be used.

• we start with a calibrated buffer
  • this is a solution with a well established pH value
• we place the pH electrode in this buffer
  • we then adjust the reading to match this pH reading
  • after this, the reading will be correct at all other pH values
  • the calibration should be valid for about 2 hours
  • (many digital meters have you select the buffer value and it adjusts itself)

• 1. work in pairs
• 2. set up a pH meter and calibrate it in a standard buffer (pH 4.00 or 7.00)
• 3. verify the operation by measuring a buffer of another pH (pH 4.00, 7.00 or 10.00)
• 4. since these notes are set up as a worksheet you can record data and calculations directly on these pages and tuck into your lab notebook.

• calibration of your pH meter:
  • plug in the meter (power pack) and press the on/off button
  • rinse and blot the electrode (see precautions below)
  • place the electrode in a suitable buffer; swirl gently
  • press the button labeled CAL/MEAS until display says CAL
    • use up/down buttons to select the right buffer value
  • press CON to perform calibration (CON=confirm the selection)
  • press CAL/MEAS to return to pH measurements
  • remove the electrode, cap the buffer and rinse the electrode

• precision:
  • We will generally rely on our pH meters to a precision of +0.1 (or perhaps 0.05) pH units
    • 0.1 pH corresponds roughly to 16% uncertainty in H+
    • 0.05 pH corresponds to about 6-7% uncertainty in H+
    • (The pH meter reads to +0.01 pH and is reliable to that precision if we took additional precautions with our solutions and temperature control.)

• precautions:
  • before every use the electrode should be rinsed in a stream of distilled water (wash bottle)
  • then gently blot off the excess water with a fresh laboratory tissue (KemWipe)
  • • this is important since otherwise you can contaminate the sample
    • many samples will change pH drastically if contaminated with stronger solutions

• You probably have been brainwashed by now to expect the pH of pure water to be 7.00
• H₂O(acid) + H₂O(conj base) <===> H₃O⁺ + OH^-
• Kw = 1.00 x 10^-14

There's another problem with pure water. The pH meter needs some electrical conductivity between the two electrodes. Ultra pure water will actually not register properly. Fortunately, our water is not pure enough for that to be a problem.

experiment--measure the pH of:

• a. Distilled water from the DW tap ___________
• b. Special distilled water _______________
  • we've bubbled Helium to remove most of the CO₂
• c. Distilled water sitting near dry ice __________
  • a source of extra CO₂ (acid)
• d. Bowling Green tap water ___________
  • some dissolved limestone, CaCO₃, a base

• absence of buffering (we'll use this information later)
  • e. distilled water (50 ml + 1 drop 0.1M HCl) _________
    • pHc hanged by_____on addingHCl
  • f. distilled water(50ml + 1drop 0.1MNaOH)_________
    • pH changed by _____ on adding NaOH

Part II -- pH of Strong Acid or Strong Base Solutions

• measure the pH and compare to the expected value:
• calculations assume 100% dissociation.
• 0.050 M HCl has pH(obs)________
• -log10(0.050 ) = ______________, expected pH
• 0.15 M HCl has pH(obs) ________
• -log10( 0.15 ) = ______________, expected pH
• 0.025M NaOH has pH(obs) ________
• -log10( .025 ) = ______________, expected pOH
  • pH = 14-pOH = ____________
• 0.15 M NaOHl has pH _______
• -log10( 0.150) = ______________, expected pH
  • pH = 14-pOH = ____________

Part III - pH of a dilute weak acid

measure the pH and compare to the expected pH (approximately [Ka/conc]^1/2 )

also compute the % dissociation [H+] / [original HA]

• 0.10 M acetic acid (K_a= 1.7 x 10^-5)
  • observed pH _______________
  • calculated pH ______________
  • [H+] = ______________
  • % dissociation = _______________

• 0.020 M acetic acid
  • observed pH _______________
  • calculated pH ______________
  • [H+] = ______________
  • % dissociation = _______________

• 0.010 M Ascorbic acid (Vitamin C) Ka= ______________
  • observed pH _______________
  • calculated pH ______________
  • [H+] = ______________
  • % dissociation = _______________

Part IV-- pH of Mixed Acids (Strong acid + Weak Acid)

• the solution is 0.1M acetic acid and 0.05M HCl
• previously (part II) we found pH of 0.050 M HCl = ______________
• pH of 0.1 M Acetic acid = ___________
• the observed pH of the mixture ______________
• we expect to see the pH is very little affected by the acetic acid
  • Ka = [0.050+x]*[X]/ [0.1-x] ... where x= the H+ from acetic acid
  • with Ka= 1.7 x10-5, x= _______

Part V-- pH of a Simple Buffer

• We can make a buffer by mixing a weak acid and its conjugate base
• Here we choose Acetic Acid and Sodium Acetate
  • the sodium ion has no effect on pH
• Measure the pH of a solution
• in this case, place 50 ml into a small beaker
• 0.050 M in acetic acid0+ 0.075 M in sodium acetate ..... pH(obs) = _____________

• expected pH....

• calc [H+]= ___________
• calc pH= ___________

• now add 1-2-5 drops of 0.1 M HCl, stir and measure
  • compare to Part I- adding HCl to water
  • pH after 1 drop _________after 2 drops _______ after 5 drops ________

• repeat with another sample and add 0.1 M NaOH
  • compare to Part I- adding NaOH to water
  • pH after 1 drop _________ after 2 drops _______ after 5 drops ________

• Measure pH of a 0.050M solution of sodium acetate .. pH(obs)__________

• (acetate) + H₂O <=======> OH- + (acetic acid)
• the sodium ion has no effect on pH
• calculation:K_a (acetic acid) = 1.7 x 10-5
• so K_b(acetate)= ______________
• Kb=[OH-][HA]/[A-] = x² / 0.05

• x= [OH-] = ____________________
• pOH = -log( ) = ___________
• pH= 14.00 - pOH = ___________

• measure the pH of 0.03 N Ammonium Chloride .. pH(obs)__________

• the chloride ion has no effect on pH
• NH₄+ + H₂O <===> H₃O⁺ + NH₃
• K_b(ammonia) = 1.8 x 10^-5
• so K_a (ammonium ion) = ____________
• Ka= [H+][NH₃]/[NH₄+] = x² / 0.030

• x=[H+] = __________________
• so pH = __________________

Part VII-- pH during an Acid - Base Titration

• put 25 ml of 0.10 M acetic acid in a beaker ... pH(obs) =____________ (same as part III)
• add 10 ml of 0.1M NaOH ............. pH(obs) = ________________
• simple calculation--
  • it takes 25 ml of this base to neutralize this HCl
  • so 10 ml of base converts (10/25) of the acid to acetate ion
  • and it leaves (15/25) of the acid unreacted
  • so [acetate]/[acetic acid] = 10/15
  • pH = pKa + log10 ( 10/15) = ______________calc
• add another 15 ml of the base .... pH(obs) = ___________________
  • should now have eliminated all acid
  • this is a 0.050M solution of sodium acetate
  • we expect the pH = __________________ (computed in part VI)
    • (small errors in measurement can seriously affect this pH)

• measure the pH of 25 ml of distilled water: pH(obs)= ________
• add some solid NaCl , stir to dissolve and measure pH: pH(obs)= ________
  • this is not a very good test-- the pH of pure water would change with even small traces of added impurity.
• repeat with 0.02 M Acetic Acid or Ammonia
  • pH(originally) ________________... pH after adding salt___________

part X-- Measuring Ka by Electrical Conductivity

(we will ignore the actual units of conductivity)

• a. A dilute (0.001M solution of NaCl) has a conductivity of _____________
  • this is due to 0.001M Na+ and 0.001 M Cl-
• b. A dilute (0.001 M) solution of HCl has a conductivity of _____________
  • this is due to 0.001M H+ and 0.001M Cl-
• c. A dilute solution of Sodium Acetate has a conductivity of ____________
  • this is due to 0.001M Na+ and 0.001M acetate ion
• If you add the data for #1 and #3 and subtract #2 result = ________________
  • you get the conductivity due to 0.001M H+ and 0.001M acetate ion if they did not react to form neutral acetic acid
• If we measure the conductivity of a 0.001 M acetic acid solution ______________

• the ratio of observed / ideal = D= degree of dissociation
• %D = 100 D
• Ka= [H+][A-]/[HA] = [CoD][CoD]/Co[1-D]

• where Co is acid conc (0.001M)

at last, the end....