Diabetes Monitoring
Diabetics must monitor the concentration of glucose in their blood because, as we've
seen, high blood sugar leads to excessive loss of NADPH in the reduction of glucose.
Many commercial glucose monitors are based on oxidation-reduction chemistry of the
sugar.
Outline
•
Electrochemistry
•
Reduction Potentials
•
Accu-Chek meter
•
Homework
Electrochemistry
Carrying out a reaction in an electrochemical cell rather than a flask allows us to gather more information
about the energy changes (from the potential difference) and rate of the reaction (from the current). We
can also determine the exact concentration of one reactant when the concentrations of other reactants are
known.
Electrochemical Cells
You've seen examples of the oxidation and the reduction of organic molecules, including glucose. In any
oxidation-reduction reaction, we can divide the net reaction into an oxidation half reaction and an
reduction half reaction. In an electrochemical cell, these half reactions take place in separate locations.
Below is a diagram of an electrochemical cell in which molecule A+ is reduced to A while molecule B is
oxidized to B+. The reactions take place in aqueous salt solution.
The oxidation of B takes place at the anode and releases electrons that travel through wires to the
cathode. The electrons moving into the cathode reduce A+ to A.
To balance charge, anions from the salt solution migrate from the solution around the cathode to the
solution around the anode. Cations (or protons) from the aqueous salt solution around the anode migrate
to the solution around the cathode.
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oxidation half reaction
B
B+ + ereduction half reaction
A+ + eA
net reaction
A+ + B
A + B+
Thermodynamics in Electrochemistry
The tendency of a reaction to move in the direction written is the Gibbs free energy. This is a measure of
the change in heat energy (at constant pressure) and change in disorder of the system as the reaction goes
from reactants to products. A negative value for ΔG means that, from an energy standpoint, the reaction
should proceed. Under standard conditions of temperature and pressure:
ΔG0 = ΔH0 - TΔS0
In electrochemical reactions we can measure the potential difference between the reactants. The
potential, measured in volts, is related to the Gibbs free energy. Note the minus sign in the equation
below. This means that the potential must be positive when the ΔG negative for the electrochemical
reaction to proceed as written.
If the reaction of A+ and B to A and B+ had a ΔG0 of -10 kJ/mol, the potential difference as measured by a
voltmeter should be 0.1 volt under standard conditions. This also means that we can determine ΔG0 for
any electrochemical reaction by reading E0 from the voltmeter and carrying out a simple calculation.
What are standard conditions? For an electrochemical reaction at standard conditions, the temperature
must be 25 deg C and the concentrations of all solutions are 1 M. We can find the potential at other
concentrations by using the Nernst equation:
E = E0 - (0.059/n)(log Q)
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where Q is the ratio of the concentration of reactants and products raised to the power of their
coefficients.
In this case at 25 deg:
So there is a maximum potential when all reactants and products are at the same concentrations. Then E =
E0. There is a minimum potential when the reaction mixture is at equilibrium. At equilibrium ΔG = 0 and
E = 0.
From the Nernst equation, if we know the E0 and the concentration of one of the reactants at the
beginning of the reaction, we can calculate the concentration of the other one.
Kinetics in Electrochemistry
It is particularly easy to measure the rate of an electrochemical reaction because electrons must travel
through the wire connecting the anode to the cathode. A device called an ammeter can measure the flow
of these electrons per second, and therefore the rate of the electrochemical reaction.
For the reaction of A+ and B going to A and B+, 1 electron must be transferred so the rate is proportional
to the current in the wire. The rate is also proportional to the concentrations of A+ and B.
We can also determine the concentration of A+ from current measurements if the concentration of B is
known.
Reduction Potentials
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Standard Hydrogen Electrode
Another convenient aspect of electrochemistry is that
we can measure the potential of any half cell by
coupling it with the H2/H+ half cell. This is the
standard hydrogen electrode and has an E0 of 0 volts.
At right is a diagram showing the test half cell on the
left and the standard hydrogen half cell on the right.
The standard hydrogen electrode is a piece of platinum
in a 1.0 M solution of an acid in water with hydrogen
gas at 1.0 atmosphere pressure.
It is connected to the test half cell by a salt bridge that
allows anions and cations to travel from one cell to
another to balance charge. The electrodes in the two half cells are connected by a wire. The potential
difference between the two half cells is measured by a voltmeter.
Let's imaging that the test solution contains 1.0 mol/L of A+ in an aqueous salt solution.
oxidation half reaction
1/2 H2
H+ + 1e-
assigned potential = 0.00 V
reduction half reaction
A+ + 1eA
calculated potential = 0.07 V - 0.00 V = 0.07 V
net reaction
1/2 H2 + A+
measured potential = 0.07 V
H+ + A
The standard hydrogen electrode can function in either the oxidation or reduction half reaction. It is
assigned a potential of 0.00 volts either way. We could test the potential of a solution of B in the same
way.
oxidation half reaction
B
B+ + 1e-
calculated potential = 0.03 V - 0.00 V = 0.03 V
reduction half reaction
H+ + 1e1/2 H2
assigned potential = 0.00 V
net reaction
B + H+
measured potential = 0.03 V
1/2 H2H + B+
Because the sum of an oxidation half cell potential and a reduction half cell potential gives the net
potential of the oxidation-reduction reaction, we can calculate E0 = 0.07 + 0.03 V = 0.10 V.
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Reduction Potentials
The standard half cell potentials of many molecules and ions have been measured with with the standard
hydrogen half cell. These are typically recorded in tables of standard reduction potentials. For an
oxidation half reaction, the oxidation potential is mutiplied by -1 to go to the reduction potential.
1.
Switching reactants and products causes the sign of the potential to change.
2.
Multiplying a half reaction by any factor doesn't change the potential.
A few standard reduction potentials are listed below. Others are in the table.
Accu-Chek Meter
Electrochemistry is used to determine the concentration of glucose
in the blood of diabetics.
In the first step, the person collects a drop of blood with a lancet and
adds it to the disposable collector.
The collector contains an enzyme called glucose oxidase that is a
catalyst for the oxidation of glucose to gluconic acid. It also contains
a metal complex that mediates the transfer of electrons between the
electrode and glucose/gluconic acid oxidation half reaction.
Glucose is oxidized to gluconic acid:
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Ferricyanide is the oxidizing agent:
The disposable collector is one half cell and the other is contained within the meter. Several things happen
when the disposable collector goes into the meter.
1.
The meter detects the presence
of the glucose (drop detect).
2.
There is an incubation period
where all the glucose is
oxidized to gluconic acid. Two
equivalents of [Fe(CN)6]4- are
formed for every glucose
molecule that has been
oxidized.
3.
The 2 half cells are connected
and current flows as
[Fe(CN)6]4- is oxidized to
[Fe(CN)6]3- at the anode. The
current is proportional to the
concentration of [Fe(CN)6]4- at the electrode surface.
The concentration of [Fe(CN)6]4- at the electrode is determined by the measurement and this is twice the
concentration of the glucose that was originally present.
The electrochemical measurement of blood glucose concentration is highly accurate and reproducible
under various conditions of temperature and humidity making it very useful for monitoring and regulating
the effects of diabetes.
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