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Concentration dependency of E

Concentration Dependency of E E o values are based on standard conditions. The E value will vary if any of the concentration vary from standard conditions Theoretically Predicted by the Nernst Equation

The Nernst Equation For aA + ne -  bB

Example Equilibrium constant and E o Find the equilibrium constant for the reaction Cu (s) + 2Fe 3+ 2Fe 2+ + Cu 2+

Example Find the voltage of the cell Half reaction Ag (s) into a solution of 0.50 M AgNO 3 (aq) The other half-reaction Cd (s) is immersed into a M Cd(NO 3 ) 2 (aq) Metals are connected by wires Solution connected with salt bridge

0.50 M AgNO M Cd(NO 3 ) 2 Find the voltage of the cell

Potentiometric Methods

Basis of Method The difference b/w the E (not E o ) values for two halves of a cell give rise to E overall., If one half reaction is known and held constant, we can measure the concentration of species on the other side!!!

Reference Indicating electrode – The part of the cell that contains the solutions we are interested in measuring

Electrodes The previous cell would be difficult to use for many systems. We would like something that can be placed in the solution we wish to measure The electrodes in the following slides have that goal in mind but THEY STILL represent a complete electrochemical cell when used

Reference Electrodes Ag/AgCl

Reference Electrodes Calomel Electrode (SCE) Very Common Hg|Hg 2 Cl 2 (sat), KCl|| Chloride is used to maintain constant ionic strength

Reference Electrodes The SCE (Saturated Calomel Electrode) Different KCl concentrations can (and are used) 0.1 M – least temperature sensitive Saturated – easier to make and maintain. E ref = Reaction E o (V) Hg 2 Cl 2 + 2e - ->2Hg(l) + 2Cl V

Hg 2 Cl 2 + 2e - ->2Hg(l) + 2Cl AgCl (s) + e - ->Ag(s) + Cl

Sensing electrodes Several types Simple Metal Solid State Electrodes Glass Membrane Etc. Let’s look at some examples.

Sensing electrodes Several types Simple Metal Solid State Electrodes Glass Membrane Etc. Let’s look at some examples.

Simple metal electrodes A bare metal in contact with a solution. General Form: M n+ + ne - -> M(s)

Simple Metal Electrodes A bare metal in contact with a solution of its cation. Ag + + 1e - -> Ag(s) V General form M n+ + ne - -> M(s)

Example A potential of V was measured vs. SCE. What is the concentration of Ag + ? Hg 2 Cl 2 + 2e -  2Hg(l) + 2 Cl - E o = 0.241V Ag + + e -  Ag(s)E o = 0.799V Using a simple metal electrode (Ag) and a reference electrode (Calomel), the voltage determined from this potentiometric set-up provides us with a direct measure of concentration no calibration plot required!!

Simple Metal Electrodes Example Silver sensing electrode

Example (cont’d)

Simple Metal Electrodes For some metals, a good electrode can’t be made or no metals are involved – just ions or gas! An inert indicating electrode is used (graphite or Pt). This type only measures the ratios of ions. No quantitation but suitable for titrations! No quantitation but suitable for titrations!

Simple Metal Electrodes For some metals, a good electrode can’t be made or no metals are involved – just ions or gas! An inert indicating electrode is used (graphite or Pt). This type only measures the ratios of ions. No quantitation but suitable for titrations! Calomel (Hg 2 Cl 2 )

Simple Metal Electrodes E overall = E ox + E red Calomel (Hg 2 Cl 2 ) Constant = V Reduction at Platinum Electrode: Reaction E o Fe e - -> Fe V

Simple Metal Electrodes For some metals, a good electrode can’t be made or no metals are involved – just ions or gas! This type only measures the ratios of ions. No direct quantitation but suitable for titrations! Calomel (Hg 2 Cl 2 ) Ce 4+

REDOX titrations “Your titrant is commonly an oxidizing agent although reducing titrants can be used.” Consider: Ce 4+ + Fe 2+  Ce 3+ + Fe 3+ General form: A ox + B red  A red + B ox

Determination of the Equivalence Point The equivalence point is based on the concentration of the oxidized and reduced form of all species involved Use Nernst Equation to find E eq.

Equivalence Point Since at equilibrium, [A red ] = [B ox ] and [B red ] = [A ox ] we massage the two general equations to yield: Nernst Equation for A Nernst Equation for B

Equivalence Point Note: This expression only works for simple REDOX TITRATIONS: Simple redox titrations: Only A ox, B ox, A red, B red are involved in the reaction …

Two examples Determine E eq for the following reactions: Fe 2+ + Ce 4+ -> Fe 3+ + Ce 3+ Sn Ce 4+ -> Sn Ce 3+

Titration curves What does a titration curve look like for an acid/base titration?

REDOX Titrations E cell OverTitration

Just like Acid/Base Titrations There are four significant regions, The Start The Start The Buffer Region The Buffer Region The equivalence Point The equivalence Point Overtitration Overtitration Let’s Use our simple example: Fe 2+ + Ce 4+  Fe 3+ + Ce 3+ Fe 2+ + Ce 4+  Fe 3+ + Ce 3+

Our simple example Let’s Use our simple example: Fe 2+ + Ce 4+  Fe 3+ + Ce 3+ Fe 2+ + Ce 4+  Fe 3+ + Ce 3+ Titrate 50 mL of 0.05 M Fe 2+ with 0.10 M Ce 4+

0% Titration Unlike acid/base titrations, we can’t find this point exactly. While some Fe 3+ must be present, we can only guess what the concentration is. No Ce 4+ or Ce 3+ present, so we don’t have a complete reaction

0% Titration NO … some of the iron is oxidized by air to give some Fe 3+ … how much ? We generally estimate that less Than one in 1000 are oxidized.

“Buffer Region” Fe 2+ + Ce 4+  Fe 3+ + Ce ml of Ce 4+ is added Goes to completion … Excess Fe 2+ pushes equilibrium to the right. Thus E is not dependent on Ce 3+ /Ce 4+, but only on Iron.

“Buffer Region”

Closer look at the “buffer” region Fe 2+ /Fe 3+ E

Equivalence Point From Before E eq = 1.24 V What volume? 25 ml

Excess Ce 4+ (post titration) Fe 2+ + Ce 4+  Fe 3+ + Ce 3+ Fe 2+ + Ce 4+  Fe 3+ + Ce 3+ The predominate change is that Ce 4+ is being added and diluted into a solution of Ce 3+. The predominate change is that Ce 4+ is being added and diluted into a solution of Ce 3+. All Fe 2+ has been converted to Fe 3+ and no longer figures into the calculations All Fe 2+ has been converted to Fe 3+ and no longer figures into the calculations We just need to keep track of the amounts of Ce 3+ and Ce 4+ as well as the VOLUME of the system. We just need to keep track of the amounts of Ce 3+ and Ce 4+ as well as the VOLUME of the system.

Excess Ce 4+ (post titration) At 30.0 mL Ce 4+ V t = 30.0 mL mL

Excess Ce 4+ (post titration) Fe 2+ + Ce 4+  Fe 3+ + Ce 3+ Fe 2+ + Ce 4+  Fe 3+ + Ce 3+ Ce 3+ /Ce 4+

Excess Ce 4+ (post titration)

Redox Indicators General Specific

General Redox Indicators Varies as a function of E cell Rely on a color change with Ind ox and Ind red being different colors. Ind ox + ne -  Ind red

General Redox Indicators In order to see a color change, you typically need approximately a 10% conversion from one form to another.

General Redox Indicators Examples Consider 1,10 phenanthrolene-Fe + e - BLUERED E o = 1.06 V

General Redox Indicators Examples Consider Diphenylamine sulphonic acid Used with the iron in the dichromate method E o = 0.80V

SPECIFIC INDICATORS Example from lab Starch Starch + I 3 -  blue complex It is easy to detect and color change is rapid!! This interaction explains why we use iodine as a titrant even though it is a very weak oxidant.

Common Titrants Usually oxidizing agents. Cr 2 O need an indicator Very stable E=1.44 V MnO 4 - Solutions must be standardized Reagent slowly degrades No indicator needed excess reagent is pink - E=1.51 V Ce 4+ - Example in Class

Common titrants Reducing Titrants Fe 2+ Usually Fe(NH 4 ) 2 (SO 4 ) 2. 6H 2 O in 1M H 2 SO 4 Solution must be standardized each day I - Indirect method Your lab was an excellent example

Sensing electrodes Several types Simple Metal Glass Membrane Solid State Electrodes Etc. Let’s look at some examples.

Membrane Electrodes A potential difference is created across a membrane that can be measured. THERE IS NO CHANGE IN THE SOLUTIONS “These electrodes are fundamentally different from metal electrodes in that they DO NOT involve redox reactions!! These Electrodes ‘selectively bind’ the ion of interest

Membrane electrodes pH Electrode First Discovered in early 1900’s! Refined through the 1950’s Probably the most important Relies on a Glass Membrane H 3 O + selectively binds to glass membrane Na + sluggishly transported across Potential is measured across the membrane!

pH membrane Special Glass (72% SiO 2 ) Doped with Na 2 O (22%) and CaO (6%) Si O Cation Key

Membrane Electrodes In order to work the Glass must be hydrated To allow for diffusion of H + and Na + H 3 O + populates BOTH side of the electrode BUT DOES NOT cross the membrane To perform an electrical measurement - Must be a complete circuit! But Na + ‘sluggishly’ crosses the membrane. Na + transport ~ salt bridge Membranes resistance ~ 1x 

Membrane Electrodes While H 3 O + causes a response, other ions also ‘interfere’. Alkali Error Many alkali metals (Li +, Na +, K +) Severe interference result when Alkali ion is in greater concentration than H 3 O + This false response is called Alkaline Error b/c of error associated when measuring solutions of sodium hydroxide. (NaOH) Note – the electrode shows little interference with OH -. Why?

Membrane Electrodes Acid Error Too many of the Si-O - sites are saturated with H 3 O + and no more sites are available for protonation. The response of real glass electrodes is described by the following equation: B is the electromotive efficiency (ideally =1, usually > 0.98)

Sensing electrodes Several types Simple Metal Glass Membrane Solid State Electrodes Etc. Let’s look at some examples.

Solid State Electrodes The F - ISE The original solid state electrode Works due to defects in a LaF 3 crystal. Other Solid state electrodes work based on the presence of primary absorbed ion. LaF 3 /Eu

F - Inorganic Crystal The solid state electrode is a very popular type of ISE. As easy to maintain as a pH electrode (sometimes easier).

Solid State Electrodes Our TISAB the pH was 5-6 and the ionic strength was held constant. Why? F - and OH - are about the same size AND same CHARGE!! LaF 3 /Eu 2+ doped crystal selects for size and charge Thus, OH - will cause a response.

Solid State Electrodes Our TISAB the pH was 5-6 and the ionic strength was held constant. Why? Constant

Conclusions Several types Simple Metal – Using Metal associated with Ion  Direct Quantitation Using Inert Electrode  Yields Information on Ratio of concentrations Glass Membrane pH Electrode Two reference electrodes (Constant Potential) Measuring the ‘junction’ potential Alkali Error Solid State Electrodes Flouride ISE Measuring junction potential Acid and Base Error Interferences are based on similar size and charge for Membrane electrodes and SS Electrodes Detection limits are between M and M