Nernst Equation

The Nernst Equation enables one to determine electromotive forces (emf) of many processes, for instance the resting potential of cell membranes. We can then deduce the biological standard potentials which are important in studying biological process such as action potential during a spike of a neuron in response to a stimulus.

Introduction

The Nernst Equation is derived from the emf and the Gibbs energy under non-standard conditions.

Eo=Eoreduction−Eooxidation 

When Eo is positive, the reaction is spontaneous. When Eo is negative, the reaction is not spontaneous. Since the change in Gibbs free energy, ΔG, is also related to spontaneity of a reaction, therefore, ΔG and E are related. Specifically,

ΔG=−nFE 

where, n is # of electrons transferred in the reaction, F is the Faraday constant (96500 C/mol) and E is potential difference. Under standard conditions, this equation is then

ΔGo=−nFEo.

Since,

ΔG=ΔGo+RTlnQ(1)

Substituting ΔG=−nFE and ΔGo=−nFEo into equation (1), we have:

−nFE=−nFEo +RTlnQ

Divide both sides of the equation above by −nF, we have

E=Eo −RTnFlnQ(2)

Equation (2) can be rewritten in the form of log base 10:

E=Eo −2.303RTnFlogQ(3)

At standard temperature T = 298K, the 2.303RTF equals .0592 V, so equation (3) turns into:

E = Eo −.0592VnlogQ

The equation above indicates that the electrical potential of a cell depends upon the reaction quotient Q of the reaction. As the redox reaction proceeds, reactants are consumed, thus concentration of reactants decreases. Conversely, the products concentration increases due to the increased in products formation. As this happens, cell potential gradually decreases until the reaction is at equilibrium, at which ΔG =0.

Example 1

For the Zn-Cu redox reaction: Zn(s)+Cu2+(aq)→Zn2+(aq)+Cu(s)Eocell=+1.10V SOLUTION Initially, [Cu2+] = [Zn2+] = 1.0 M at standard T = 298K As the reaction proceeds, [Cu2+] decreases as [Zn2+] increases. Lets say after one minute, [Cu2+] = 0.05 M while [Zn2+] = 5.0 M. According to Nernst, cell potential after 1 minute is: E = Eo −0.0592VnlogQ E = 1.10V −0.0592V2log5.0M.05 M E=1.04V As you can see, the initial cell potential is E =1.10V, after 1 minute, the potential drops to 1.04 V. As the reaction continues to progress, more Cu2+ will be consumed and more Zn2+ will be generated. As a result, the cell potential continues to decrease and when the cell potential drops down to 0, the concentration of reactants and products stops changing. This is when the reaction is at equilibrium.

At equilibrium, the reaction quotient Q=Keq. Also, at equilibrium, ΔG =0 and ΔG=−nFE, so E =0.   

Therefore, substituting Q=Keq and E =0 into the Nernst equation, we have:

0=Eo−RTnFlnKeq

At standard conditions, the equation above simplifies into:

0=Eo −0.0592nlogKeq

This equation can be rearranged into: 

logKeq=nEo0.0592

The equation above indicates that the equilibrium constant K_eq is proportional to the standard potential of the reaction. Specifically, when:

• K>1,Eo>0, reaction favors products formation.
• K<1,Eo<0, reaction favors reactants formation.

This result fits Le Châtlier's Principle,which states that when a system at equilibrium experiences a change, the system will minimize that change by shifting the equilibrium in the opposite direction.

Biological Application of the Nerst Equation

The emf can be determined measuring the current in a galvanic cell. This method is important when determining the standard potential of oxidizing agents. But our interest is the biological standard potentials such as neurons firing.

Action Potential of a Neuron Cell

Perhaps the most fascinating system in our body is the nervous system. The neuron is the basic operating unit of the nervous system and its mechanism is still under a lot of research. Electrolytes Sodium and Potassium are the most prevalent electrolytes in our body. Intracellular concentrations of Potassium is higher inside the cell in comparison to extracellular. For Sodium it's the opposite more extracellular and less intracellular. This difference in concentration is the mechanics of how a neuron and other cells have resting potentials. ATPase pumps and selective membrane channels allow for the concentration gradient difference. With the Nernst Equation we can deduce the membrane potential of a neuron for our discussion. The concentration of potassium inside is 150 mM, and 15 mM outside. Plugging these values in the equation above out comes the neuron potential which can be depolarize in response to ...

  

References

1. Atkins, Peter and de Paula, Julio. Physical Chemistry for the Life Sciences. New York: W.H. Freeman and Company. p. 214-222.

Le Châtelier's Principle

This page looks at Le Châtelier's Principle and explains how to apply it to reactions in a state of dynamic equilibrium. Le Châtelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. If a chemical reaction is at equilibrium and experiences a change such as pressure, temperature, or concentration of products or reactants the equilibrium will shift in the direction to accommodate the change. It covers changes to the position of equilibrium if you change concentration, pressure or temperature and explains very briefly why catalysts have no effect on the position of equilibrium.

Introduction

An action that tends to change the temperature, pressure, or concentrations of reactants in a system at equilibrium stimulates a response that partially offsets the change while a new equilibrium condition is established (2). Hence, Le Châtelier's principle states that any change to a system at equilibrium will adjust to compensate for that change. In 1884 the French chemist and engineer Henry-Louis Le Châtelier proposed one of the central concepts of chemical equilibria, which describes what happens to a system when something briefly removes it from a state of equilibrium.

It is important in understanding that Le Châtelier's Principle is only a useful guide to help you work out what happens when you change the conditions in a reaction in dynamic equilibrium, but it does not explain the microscopic reason for the changes.

Concentration Changes

Le Châtelier's principle states that if the system is changed in a way that increases the concentration of one of the reacting species, it must favor the reaction in which that species is consumed. In other words, if there is an increase in products, the Reaction Quotient Qc is increased, making it greater than the Equilibrium Constant Kc. Suppose you have an equilibrium established between four substances A, B, C and D.

What would happen if you changed the conditions by increasing the concentration of A?

According to Le Châtelier, the position of equilibrium will move in such a way as to counteract the change. That means that the position of equilibrium will move so that the concentration of A decreases again - by reacting it with B and turning it into C + D. The equilibrium moves to the right (green arrow below).

This is a useful way of converting the maximum possible amount of B into C and D. You might use it if, for example, B was a relatively expensive material whereas A was cheap and plentiful.

Decreasing the concentration of A?

According to Le Châtelier, the position of equilibrium will move so that the concentration of A increases again. That means that more C and D will react to replace the A that has been removed. The position of equilibrium moves to the left.

This is essentially what happens if you remove one of the products of the reaction as soon as it is formed. If, for example, you removed C as soon as it was formed, the position of equilibrium would move to the right to replace it. If you kept on removing it, the equilibrium position would keep on moving rightwards - turning this into a one-way reaction.

Pressure Changes

This only applies to reactions involving gases.

Increasing the pressure

According to Le Châtelier, the position of equilibrium will move in such a way as to counteract the change. That means that the position of equilibrium will move so that the pressure is reduced again. Pressure is caused by gas molecules hitting the sides of their container. The more molecules you have in the container, the higher the pressure will be. The system can reduce the pressure by reacting in such a way as to produce fewer molecules.

In this case, there are three molecules on the left-hand side of the equation, but only 2 on the right. By forming more C and D, the system causes the pressure to reduce. Increasing the pressure on a gas reaction shifts the position of equilibrium towards the side with fewer molecules.

Example 1: Haber Process Equilibrium
N2+3H2⇌2NH3 If this mixture is transferred from a 1.5 L flask to a 5 L flask, in which direction does a net change occur to return to equilibrium? Because we are increasing volume (and therefore reducing the pressure), the shift occurs in the direction that produces more moles of gas. To restore equilibrium the shift needs to occur to the left, in the direction of the reverse reaction.

Decreasing the pressure

The equilibrium will move in such a way that the pressure increases again. It can do that by producing more molecules. In this case, the position of equilibrium will move towards the left-hand side of the reaction.

What happens if there are the same number of molecules on both sides of the equilibrium reaction?

In this case, increasing the pressure has no effect whatsoever on the position of the equilibrium. Because you have the same numbers of molecules on both sides, the equilibrium cannot move in any way that will reduce the pressure again. Again, this isn't an explanation of why the position of equilibrium moves in the ways described. You will find a rather mathematical treatment of the explanation by following detailed explanation .

Summary

Three ways to change the pressure of an equilibrium mixture are: 1. Add or remove a gaseous reactant or product, 2. Add an inert gas to the constant-volume reaction mixture or 3. Change the volume of the system. (2)

1. Adding products makes Qc larger than Kc. This creates a net change in the reverse direction, toward reactants. The opposite occurs when adding more reactants. (2)
2. Adding an inert gas into a gas-phase equilibrium at constant volume does not result in a shift. This is because the addition of a non-reactive gas does not change the partial pressures of the other gases in the container. While the total pressure of the system increases, the total pressure does not have any effect on the equilibrium constant. (1)
3. When the volume of a mixture is reduced, a net change occurs in the direction that produces fewer moles of gas. When volume is increased the change occurs in the direction that produces more moles of gas.

Temperature Changes

For this, you need to know whether heat is released or absorbed during the reaction. Assume that our forward reaction is exothermic (heat is evolved):

This shows that 250 kJ is evolved (hence the negative sign) when 1 mole of A reacts completely with 2 moles of B. For reversible reactions, the value is always given as if the reaction was one-way in the forward direction. The back reaction (the conversion of C and D into A and B) would be endothermic by exactly the same amount.

The main effect of temperature on equilibrium is in changing the value of the equilibrium constant.

Warning: It is not uncommon that textbooks and instructors to consider temperature as a independent "species" in a reaction. While this is rigorously incorrect since once cannot "add or remove temperature" to a reaction as with species, it serves as a convenient mechanism to predict the shift of reactions with changing temperature. For example, if temperature is a "reactant" (ΔH>0), then the reaction favors the formation of products at elevated temperature. Similarly, if temperature is a "product" (ΔH>0), then the reaction favors the formation of reactants. A more accurate, and hence preferred, description is discussed below.

Increasing the temperature

According to Le Châtelier, the position of equilibrium will move in such a way as to counteract the change. That means that the position of equilibrium will move so that the temperature is reduced again. Suppose the system is in equilibrium at 300°C, and you increase the temperature to 500°C. How can the reaction counteract the change you have made? How can it cool itself down again?

To cool down, it needs to absorb the extra heat that you have just put in. In the case we are looking at, the back reaction absorbs heat. The position of equilibrium therefore moves to the left. The new equilibrium mixture contains more A and B, and less C and D.

If you were aiming to make as much C and D as possible, increasing the temperature on a reversible reaction where the forward reaction is exothermic isn't a good idea!

Decreasing the temperature?

The equilibrium will move in such a way that the temperature increases again. Suppose the system is in equilibrium at 500°C and you reduce the temperature to 400°C. The reaction will tend to heat itself up again to return to the original temperature. It can do that by favouring the exothermic reaction. The position of equilibrium will move to the right with more A and B are converted into C and D at the lower temperature.

Example 2: I see you
O2 + 2H2 → 2H2O   ΔH= -125.7 kJ 1. What side of the reaction is favored? Because the heat is a product of the reaction, the reactants are favored. 2. Would the conversion of O2 and H2 to H2O be favored with heat as a product or as a reactant? Heat as a product would shift the reaction forward, creating H2O. The more heat added to the reaction, the more H2O created.

Summary

• Increasing the temperature of a system in dynamic equilibrium favors the endothermic reaction. The system counteracts the change you have made by absorbing the extra heat.
• Decreasing the temperature of a system in dynamic equilibrium favors the exothermic reaction. The system counteracts the change you have made by producing more heat.

Again, this is not in any way an explanation of why the position of equilibrium moves in the ways described. It is only a way of helping you to work out what happens.

Catalysts

Adding a catalyst makes absolutely no difference to the position of equilibrium and Le Châtelier's Principle does not apply to them. This is because a catalyst speeds up the forward and back reaction to the same extent and adding a catalyst does not affect the relative rates of the two reactions, it cannot affect the position of equilibrium. So why use a catalyst?

For a dynamic equilibrium to be set up, the rates of the forward reaction and the back reaction have to become equal. This does not happen instantly and for very slow reactions, it may take years! A catalyst only speeds up the rate at which a reaction reaches dynamic equilibrium.

A reference for "factors affecting SN2 reactions"

http://www.albany.edu/faculty/musah/achm216a/presentations/chapter6/sld019.htm

http://t.co/oLlr11LdRJ a blog to help the students

— Qaisar Abbas (@qaisar1212) March 3, 2014

Electrolytic Cells

Voltaic cells are driven by a spontaneous chemical reaction that produces an electric current through an outside circuit. These cells are important because they are the basis for the batteries that fuel modern society. But they are not the only kind of electrochemical cell. The reverse reaction in each case is non-spontaneous and requires electrical energy to occur.

Introduction

The general form of the reaction can be written as:

Spontaneous ---------->
Reactants		Products	+	Electrical Energy
<----------- Non spontaneous

It is possible to construct a cell that does work on a chemical system by driving an electric current through the system. These cells are called electrolytic cells, and operate through electrolysis.  Electrolysis is used to drive an oxidation-reduction reaction in a direction in which it does not occur spontaneously by driving an electric current through the system while doing work on the chemical system itself, and therefore is non-spontaneous.

Electrolytic cells, like galvanic cells, are composed of two half-cells--one is a reduction half-cell, the other is an oxidation half-cell. The direction of electron flow in electrolytic cells, however, may be reversed from the direction of spontaneous electron flow in galvanic cells, but the definition of both cathode and anode remain the same, where reduction takes place at the cathode and oxidation occurs at the anode. Because the directions of both half-reactions have been reversed, the sign, but not the magnitude, of the cell potential has been reversed.

Similarities and Differences Galvanic and Electrolytic Cell:

Electrolytic cells are very similar to voltaic (galvanic) cells in the sense that both require a salt bridge, both have a cathode and anode side, and both have a consistent flow of electrons from the anode to the cathode. However, there are also striking differences between the two cells. The main differences are outlined below:

Differences between a Galvanic cell and an Electrolytic cell

Electrochemical cell (Galvanic Cell)	Electrolytic cell
A Galvanic cell converts chemical energy into electrical energy.	An electrolytic cell converts electrical energy into chemical energy.
Here, the redox reaction is spontaneous and is responsible for the production of electrical energy.	The redox reaction is not spontaneous and electrical energy has to be supplied to initiate the reaction.
The two half-cells are set up in different containers, being connected through the salt bridge or porous partition.	Both the electrodes are placed in a same container in the solution of molten electrolyte.
Here the anode is negative and cathode is the positive electrode. The reaction at the anode is oxidation and that at the cathode is reduction.	Here, the anode is positive and cathode is the negative electrode. The reaction at the anode is oxidation and that at the cathode is reduction.
The electrons are supplied by the species getting oxidized. They move from anode to the cathode in the external circuit.	The external battery supplies the electrons. They enter through the cathode and come out through the anode.

 

Electrolytic Cell
To explain what happens in an electrolytic cell let us examine the decomposition of molten sodium chloride into sodium metal and chlorine gas. The reaction is written below.

---------> Non spontaneous ( electrolytic cell )
2 Na Cl (l)		2 Na (s)	+	Cl2 (g)
<--------- Spontaneous ( electrochemical cell )

If molten NaCl (l) is placed into the container and inert electrodes of C(s) are inserted , attached to the + and - terminals of a battery, an electrolytic reaction will occur.

1. Electrons from the negative terminal travel to the cathode and are used to reduce sodium ions into sodium atoms. The sodium will plate onto the cathode as it forms. The sodium ion are migrating towards the cathode.

Na +

+

e-

Na 0 (s)

2. The negative Chlorine ions migrate towards the anode and release electrons as they oxidize to form chlorine atoms. The chlorine atoms will combine together to form chlorine gas which will bubble away.

2 Cl -

Cl2 (g)

+

e-

3. Note that the site of oxidation is still the anode and the site of reduction is still the cathode, but the charge on these two electrodes are reversed. Anode is now + charged and the cathode has a - charged.

4. The conditions under which the electrolyte cell operates are very important. The substance that is the strongest reducing agent (the substance with the highest standard cell potential value in the table) will undergo oxidation. The substance that is the strongest oxidizing agent will be reduced. If a solution of sodium chloride (containing water) was used in the above system, hydrogen would undergo reduction instead of sodium, because it is a stronger reducing agent that sodium.

Electrochemical Cells

Galvanic and Electrolytic Cells

Oxidation-reduction or redox reactions take place in electrochemical cells. There are two types of electrochemical cells. Spontaneous reactions occur in galvanic (voltaic) cells; nonspontaneous reactions occur in electrolytic cells. Both types of cells containelectrodes where the oxidation and reduction reactions occur. Oxidation occurs at the electrode termed the anode and reduction occurs at the electrode called the cathode.

Electrodes & Charge

The anode of an electrolytic cell is positive (cathode is negative), since the anode attracts anions from the solution. However, the anode of a galvanic cell is negatively charged, since the spontaneous oxidation at the anode is the source of the cell's electrons or negative charge. The cathode of a galvanic cell is its positive terminal. In both galvanic and electrolytic cells, oxidation takes place at the anode and electrons flow from the anode to the cathode.

Galvanic or Voltaic Cells

The redox reaction in a galvanic cell is a spontaneous reaction. For this reason, galvanic cells are commonly used as batteries. Galvanic cell reactions supply energy which is used to perform work. The energy is harnessed by situating the oxidation and reduction reactions in separate containers, joined by an apparatus that allows electrons to flow. A common galvanic cell is the Daniell cell, shown below.

Electrolytic Cells

The redox reaction in an electrolytic cell is nonspontaneous. Electrical energy is required to induce the electrolysis reaction. An example of an electrolytic cell is shown below, in which molten NaCl is electrolyzed to form liquid sodium and chlorine gas. The sodium ions migrate toward the cathode, where they are reduced to sodium metal. Similarly, chloride ions migrate to the anode and are oxided to form chlorine gas. This type of cell is used to produce sodium and chlorine. The chlorine gas can be collected surrounding the cell. The sodium metal is less dense than the molten salt and is removed as it floats to the top of the reaction container.

Differences between a Galvanic cell and an Electrolytic cell

Electrochemical cell (Galvanic Cell)	Electrolytic cell
A Galvanic cell converts chemical energy into electrical energy.	An electrolytic cell converts electrical energy into chemical energy.
Here, the redox reaction is spontaneous and is responsible for the production of electrical energy.	The redox reaction is not spontaneous and electrical energy has to be supplied to initiate the reaction.
The two half-cells are set up in different containers, being connected through the salt bridge or porous partition.	Both the electrodes are placed in a same container in the solution of molten electrolyte.
Here the anode is negative and cathode is the positive electrode. The reaction at the anode is oxidation and that at the cathode is reduction.	Here, the anode is positive and cathode is the negative electrode. The reaction at the anode is oxidation and that at the cathode is reduction.
The electrons are supplied by the species getting oxidized. They move from anode to the cathode in the external circuit.	The external battery supplies the electrons. They enter through the cathode and come out through the anode.

Assignment

Atomic Spectroscopy

                                                     Atomic spectroscopy is the study of the electromagnetic radiation absorbed and emitted by atoms. Since unique elements have characteristic (signature) spectras, atomic spectroscopy, specifically the electromagnetic spectrum or mass spectrum, is applied for determination of elemental compositions. It can be divided by atomization source or by the type of spectroscopy used. In the latter case, the main division is between optical and mass spectrometry. Mass spectrometry generally gives significantly better analytical performance, but is also significantly more complex. This complexity translates into higher purchase costs, higher operational costs, more operator training, and a greater number of components that can potentially fail. Because optical spectroscopy is often less expensive and has performance adequate for many tasks, it is far more common Atomic absorption spectrometers are one of the most commonly sold and used analytical devices.

i) Optical Spectroscopy

                                                     Electrons exist in energy levels (i.e. atomic orbitals) within an atom. Atomic orbitals are quantized, meaning they exist as defined values instead of being continuous (see: atomic orbitals). Electrons may move between orbitals, but in doing so they must absorb or emit energy equal to the energy difference between their atom's specific quantized orbital energy levels. In optical spectroscopy, energy absorbed to move an electron to a higher energy level (higher orbital) and/or the energy emitted as the electron moves to a lower energy level is absorbed or emitted in the form of photons (light particles). Because each element has a unique number of electrons, an atom will absorb/release energy in a pattern unique to its elemental identity (e.g. Ca, Na, etc.) and thus will absorb/emit photons in a correspondingly unique pattern.

ii) Mass Spectroscopy

                                                  Atomic mass spectrometry is similar to other types of mass spectrometry in that it consists of an ion source, a mass analyzer, and a detector. Atoms' identities are determined by their mass-to-charge ratio (via the mass analyzer) and their concentrations are determined by the number of ions detected. Although considerable research has gone into customizing mass spectrometers for atomic ion sources, it is the ion source that differs most from other forms of mass spectrometry. These ion sources must also atomize samples, or an atomization step must take place before ionization. Atomic ion sources are generally modifications of atomic optical spectroscopy atom sources.

Molecular spectroscopy – the basic idea

                                                 In a spectroscopy experiment, electromagnetic radiation of a specified range of wavelengths is allowed to pass through a sample containing a compound of interest. The sample molecules absorb energy from some of the wavelengths, and as a result jump from a low energy ‘ground state’ to some higher energy ‘excited state’.  Other wavelengths are not absorbed by the sample molecule, so they pass on through.  A detector on the other side of the sample records which wavelengths were absorbed, and to what extent they were absorbed.

Here is the key to molecular spectroscopy:  a given molecule will specifically absorb only those wavelengths which have energies that correspond to the energy difference of the transition that is occurring.  Thus, if the transition involves the molecule jumping from ground state A to excited state B, with an energy difference of ΔE, the molecule will specifically absorb radiation with wavelength that corresponds to ΔE, while allowing other wavelengths to pass through unabsorbed. 

By observing which wavelengths a molecule absorbs, and to what extent it absorbs them, we can gain information about the nature of the energetic transitions that a molecule is able to undergo, and thus information about its structure. 

These generalized ideas may all sound quite confusing at this point, but things will become much clearer as we begin to discuss specific examples.

·         Difference

• Atomic spectroscopy concerns only the properties of atoms, whereas molecular spectroscopy concerns the molecules which are infinitely more numerous.
• With atomic spectroscopy you can found the nature  and the amounts of a given element in your sample. Molecular spectroscopy concerns all the interaction of electromagnetic waves with the matter and gives you much more advice than atomic spectroscopy
• Atomic absorption spectroscopy (AAS) is a spectroanalytical procedure for the quantitative determination of chemical elements using the absorption of optical radiation (light) by free atoms in the gaseous state.
• Whereas The combination of atoms into molecules leads to the creation of unique types of energetic states and therefore unique spectra of the transitions between these states. Molecular spectra can be obtained due to electron spin states (electron paramagnetic resonance), molecular rotations, molecular vibration and electronic states.