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| In [[electrochemistry]], the '''Nernst equation''' is an equation that relates the equilibrium [[reduction potential]] of a [[half-cell]] in an [[electrochemical cell]] (or the total [[voltage]] ([[electromotive force]]) for a full cell) to the [[standard electrode potential]], [[Thermodynamic temperature|temperature]], [[Thermodynamic activity|activity]], and [[reaction quotient]] of the underlying reactions and species used. It is named after the German physical chemist who first formulated it, [[Walther Nernst]].<ref name="isbn0-8412-1572-3">{{cite book |author=Orna, Mary Virginia; Stock, John |title=Electrochemistry, past and present |publisher=American Chemical Society |location=Columbus, OH |year=1989 |pages= |isbn=0-8412-1572-3 |oclc= 19124885|doi= |accessdate=}}</ref><ref name=Wahl2005>{{Cite journal | last = Wahl | year = 2005 | title = A Short History of Electrochemistry | journal = Galvanotechtnik | volume = 96 | issue = 8 | pages = 1820–1828 }}</ref>
| | There is however a trick that you must stay with if you want success. For women with endometriosis, the monthly fecundity (chance of getting pregnant) diminishes by 12 to 36%. If probable, wait to have sexual intercourse until finally you are entirely performed taking your medication. You could be the next and is definitely worth your try. The somewhat controversial study used uterine cells from both groups of women. <br><br>Incorporate nutritious foods into your meal plan and begin exercising to get your body in shape. This is your best time if youre trying to get pregnant. Yes, this is really hereditary but there are ways on how you will be able to stimulate the process of your hyperovulation which can possibly lead to having multiple births. Most of these the application is limited and therefore are of very few consciousness, they certainly usually do not teach the teens generation concerning the risk-free really like process, risk-free habits and what's more the employing of the contraceptives. The side effects for going green are allergies disappear, adult acne diminishes, weight stabilizes, you stay looking and feeling younger longer. <br><br>So it's vital to know what to consume, and what not to consume. Being water soluble also signifies that loads of it may be lost when it's cooked. This is also true for men as smoking and drinking will affects the quality of their sperm. The whole procedure is terrified and women' dissapointment and pain are so huge when they gave so so much hope and finally they failed to get pregnant. Aromatherapy and herbal medicines are also other examples of the methods you can use in getting pregnant help. <br><br>Most of the battle is usually over if one has a male partner and a willing sperm donor. All you have to do is enter your information and it will calculate when your fertile days are. Horse and Donkey - Horse can get pregnant once a year and usually in mid to late spring. But even the researchers couldn't believe just how strong an effect this chemical was having. In addition, whole grains, nuts, tofu, wheat germ, the consumption is also very useful for these products. <br><br>Miscarriages and PCOS are also linked with each other. These are effective solutions for them who are facing it. When to commence testing for ovulation with your Home-Check Instant Ovulation test Kit. If you're stressed out your body knows this, and could be working against you. For women who have a healthy diet, do not need a vitamin supplement, but if you do not feed you properly, then you will be prescribed a multivitamin tablets.<br><br>If you loved this article and you would such as to get additional info concerning [http://www.quebec-1759.info/ ways to get pregnant with a girl] kindly browse through the webpage. |
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| The Nernst equation gives a formula that relates the numerical values of the [[concentration gradient]] to the [[electric gradient]] that balances it. For example, if a concentration gradient was established by dissolving KCl in half of a divided vessel that was originally full of H<sub>2</sub>O, and then a membrane permeable to K<sup>+</sup> ions was introduced between the two halves—empirically, an equilibrium situation would arise where the chemical concentration gradient (that would normally cause ions to move from the region of high concentration to the region of low concentration) could be balanced by an electrical gradient that opposes the movement of charge.
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| ==Expression==
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| The two (ultimately equivalent) equations for these two cases (half-cell, full cell) are as follows:
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| :<math>
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| E_\text{red} = E^{\ominus}_\text{red} - \frac{RT}{zF} \ln\frac{a_\text{Red}}{a_\text{Ox}}
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| </math> (half-cell reduction potential)
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| :<math>
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| E_\text{cell} = E^{\ominus}_\text{cell} - \frac{RT}{zF} \ln Q
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| </math> (total cell potential)
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| where
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| *''E''<sub>red</sub> is the half-cell [[reduction potential]] at the temperature of interest
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| *''E''<sup><s>o</s></sup><sub>red</sub> is the [[standard electrode potential|''standard'' half-cell reduction potential]]
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| *''E''<sub>cell</sub> is the cell potential ([[electromotive force]]) at the temperature of interest
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| *''E''<sup><s>o</s></sup><sub>cell</sub> is the ''standard'' cell potential
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| *''R'' is the [[universal gas constant]]: ''R'' = 8.314 472(15) J K<sup>−1</sup> mol<sup>−1</sup>
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| *''T'' is the [[absolute temperature]]
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| *''a'' is the chemical [[activity (chemistry)|activity]] for the relevant species, where ''a''<sub>Red</sub> is the [[reductant]] and ''a''<sub>Ox</sub> is the [[oxidant]]. ''a''<sub>X</sub> = ''γ''<sub>X</sub>''c''<sub>X</sub>, where ''γ''<sub>X</sub> is the [[activity coefficient]] of species X. (Since activity coefficients tend to unity at low concentrations, activities in the Nernst equation are frequently replaced by simple concentrations.)
| |
| *''F'' is the [[Faraday constant]], the number of [[coulomb]]s per [[mole (unit)|mole]] of electrons: ''F'' = 9.648 533 99(24)×10<sup>4</sup> C mol<sup>−1</sup>
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| *''z'' is the number of moles of [[electron]]s transferred in the cell reaction or [[half-reaction]]
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| *''Q'' is the [[reaction quotient]].
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| At room temperature (25 °C), ''RT/F'' may be treated like a constant and replaced by 25.693 mV for cells.
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| | |
| The Nernst equation is frequently expressed in terms of base 10 [[logarithms]] (''i.e.'', [[common logarithm]]s) rather than [[natural logarithms]], in which case it is written, ''for a cell at 25 °C'':
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| :<math>
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| E = E^0 - \frac{0.05916\mbox{ V}}{z} \log_{10}\frac{a_\text{Red}}{a_\text{Ox}}.
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| </math>
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| The Nernst equation is used in [[physiology]] for finding the [[electric potential]] of a [[cell membrane]] with respect to one type of [[ion]].
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| ==Nernst potential==
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| {{main|Reversal potential}}
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| The Nernst equation has a physiological application when used to calculate the potential of an ion of charge ''z'' across a membrane. This potential is determined using the concentration of the ion both inside and outside the cell:
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| :<math>E = \frac{R T}{z F} \ln\frac{[\text{ion outside cell}]}{[\text{ion inside cell}]} = 2.303\frac{R T}{z F} \log_{10}\frac{[\text{ion outside cell}]}{[\text{ion inside cell}]}.</math>
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| When the membrane is in [[thermodynamic equilibrium]] (i.e., no net flux of ions), the [[membrane potential]] must be equal to the Nernst potential. However, in physiology, due to active [[Na+/K+-ATPase|ion pumps]], the inside and outside of a cell are not in equilibrium. In this case, the [[resting potential]] can be determined from the [[Goldman equation]]:
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| <math>E_{m} = \frac{RT}{F} \ln{ \left( \frac{ \sum_{i}^{N} P_{M^{+}_{i}}[M^{+}_{i}]_\mathrm{out} + \sum_{j}^{M} P_{A^{-}_{j}}[A^{-}_{j}]_\mathrm{in}}{ \sum_{i}^{N} P_{M^{+}_{i}}[M^{+}_{i}]_\mathrm{in} + \sum_{j}^{M} P_{A^{-}_{j}}[A^{-}_{j}]_\mathrm{out}} \right) }</math>
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| *<math>E_{m}</math> = The membrane potential (in [[volt]]s, equivalent to [[joule]]s per [[coulomb]])
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| *<math>P_\mathrm{ion}</math> = the permeability for that ion (in meters per second)
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| *<math>[ion]_\mathrm{out}</math> = the extracellular concentration of that ion (in [[Mole (unit)|moles]] per cubic meter, to match the other [[SI]] units, though the units strictly don't matter, as the ion concentration terms become a dimensionless ratio)
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| *<math>[ion]_\mathrm{in}</math> = the intracellular concentration of that ion (in moles per cubic meter)
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| *<math>R</math> = The [[ideal gas constant]] (joules per [[kelvin]] per mole)
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| *<math>T</math> = The temperature in [[kelvin]]
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| *<math>F</math> = [[Faraday constant|Faraday's constant]] (coulombs per mole)
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| The potential across the cell membrane that exactly opposes net diffusion of a particular ion through the membrane is called the Nernst potential for that ion. As seen above, the magnitude of the Nernst potential is determined by the ratio of the concentrations of that specific ion on the two sides of the membrane. The greater this ratio the greater the tendency for the ion to diffuse in one direction, and therefore the greater the Nernst potential required to prevent the diffusion.
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| A similar expression exists that includes r (the absolute value of the transport ratio). This takes transporters with unequal exchanges into account. See: [[Sodium-Potassium Pump]] where the transport ratio would be 2/3. The other variables are the same as above. The following example includes two ions: Potassium (K<sup>+</sup>) and sodium (Na<sup>+</sup>). Chloride is assumed to be in equilibrium.
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| <math>V_{m} = \frac{RT}{F} \ln{ \left( \frac{ rP_{K}[K]_{o} + P_{Na}[Na]_{o}}{ rP_{K}[K]_{i} + P_{Na}[Na]_{i}} \right) }</math>
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| When Chloride (Cl<sup>−</sup>) is taken into account, its part is flipped to account for the negative charge.
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| <math>V_{m} = \frac{RT}{F} \ln{ \left( \frac{ P_{K}[K]_{o} + P_{Na}[Na]_{o} + P_{Cl}[Cl]_{i}}{ P_{K}[K]_{i} + P_{Na}[Na]_{i} + P_{Cl}[Cl]_{o}} \right) }</math>
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| ==Derivation==
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| ===Using Boltzmann factors===
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| For simplicity, we will consider a solution of redox-active molecules that undergo a one-electron reversible reaction
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| :<math>\text{Ox} + e^- \rightleftharpoons \text{Red}\,</math>
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| and that have a standard potential of zero. The [[chemical potential]] <math>\mu_c</math> of this solution is the difference between the energy barriers for taking electrons from and for giving electrons to the [[Cyclic voltammetry|working electrode]] that is setting the solution's [[electrochemical potential]]. | |
| | |
| The ratio of oxidized to reduced molecules, [Ox]/[Red], is equivalent to the probability of being oxidized (giving electrons) over the probability of being reduced (taking electrons), which we can write in terms of the [[Boltzmann factor]] for these processes:
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| :<math>
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| \frac{[\mathrm{Ox}]}{[\mathrm{Red}]}
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| = \frac{\exp \left(-[\mbox{barrier for losing an electron}]/kT\right)}
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| {\exp \left(-[\mbox{barrier for gaining an electron}]/kT\right)}
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| = \exp \left(\mu_c / kT \right).
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| </math>
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| Taking the natural logarithm of both sides gives
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| :<math>
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| \mu_c = kT \ln \frac{[\mathrm{Ox}]}{[\mathrm{Red}]}.
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| </math>
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| If <math>\mu_c \ne 0</math> at [Ox]/[Red] = 1, we need to add in this additional
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| constant:
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| :<math>
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| \mu_c = \mu_c^0 + kT \ln \frac{[\mathrm{Ox}]}{[\mathrm{Red}]}.
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| </math>
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| Dividing the equation by ''e'' to convert from chemical potentials to electrode potentials, and remembering that ''kT/e'' = ''RT/F'', we obtain the Nernst equation for the one-electron process
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| <math>\mathrm{Ox} + e^- \rightarrow \mathrm{Red}</math>:
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| :<math>
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| E = E^0 + \frac{kT}{e} \ln \frac{[\mathrm{Ox}]}{[\mathrm{Red}]}
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| = E^0 - \frac{RT}{F} \ln \frac{[\mathrm{Red}]}{[\mathrm{Ox}]}.
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| </math>
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| | |
| ===Using thermodynamics (chemical potential)===
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| Quantities here are given per molecule, not per mole,
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| and so [[Boltzmann constant]] ''k'' and the electron charge ''e'' are used
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| instead of the gas constant ''R'' and Faraday's constant ''F''. To convert
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| to the molar quantities given in most chemistry textbooks, it is simply
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| necessary to multiply by Avogadro's number: <math>R = kN_A</math> and
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| <math>F = eN_A</math>.
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| The entropy of a molecule is defined as
| |
| :<math>
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| S \ \stackrel{\mathrm{def}}{=}\ k \ln \Omega,
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| </math>
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| where <math>\Omega</math> is the number of states available to the molecule.
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| The number of states must vary linearly with the volume ''V'' of the | |
| system, which is inversely proportional to the concentration ''c'', so
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| we can also write the entropy as
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| :<math>
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| S = k\ln \ (\mathrm{constant}\times V) = -k\ln \ (\mathrm{constant}\times c).
| |
| </math>
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| The change in entropy from some state 1 to another state 2 is therefore
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| :<math>
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| \Delta S = S_2 - S_1 = - k \ln \frac{c_2}{c_1},
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| </math>
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| so that the entropy of state 2 is
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| :<math>
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| S_2 = S_1 - k \ln \frac{c_2}{c_1}.
| |
| </math>
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| If state 1 is at standard conditions, in which <math>c_1</math> is unity (e.g.,
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| 1 atm or 1 M), it will merely cancel the units of <math>c_2</math>. We can, therefore,
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| write the entropy of an arbitrary molecule ''A'' as
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| :<math>
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| S(A) = S^0(A) - k \ln [A], \,
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| </math>
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| where <math>S^0</math> is the entropy at standard conditions and [''A''] denotes the
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| concentration of ''A''.
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| The change in entropy for a reaction
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| :<math>
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| aA + bB \rightarrow yY + zZ
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| </math>
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| is then given by
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| :<math>
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| \Delta S_\mathrm{rxn} = [yS(Y) + zS(Z)] - [aS(A) + bS(B)]
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| = \Delta S^0_\mathrm{rxn} - k \ln \frac{[Y]^y [Z]^z}{[A]^a [B]^b}.
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| </math> | |
| We define the ratio in the last term as the [[reaction quotient]]:
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| :<math>
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| Q = \frac{\prod_j a_j^{\nu_j}}{\prod_i a_i^{\nu_i}} \approx \frac{[Z]^z [Y]^y}{[A]^a [B]^b}.
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| </math>
| |
| | |
| where the numerator is a product of reaction product activities, ''a<sub> j</sub>'', each raised to the power of a [[stoichiometric coefficient]], ''ν<sub> j</sub>'', and the denominator is a similar product of reactant activities. All activities refer to a time ''t''. Under certain circumstances (see [[chemical equilibrium]]) each activity term such as <math>a_j^{\nu_j}</math> may be replaced by a concentration term, [''A''].
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| In an electrochemical cell, the cell potential ''E'' is the
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| chemical potential available from redox reactions (<math>E = \mu_c/e</math>).
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| ''E'' is related to
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| the [[Gibbs free energy|Gibbs energy]] change <math>\Delta G</math> only by a constant:
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| <math>\Delta G = -nFE</math>, where ''n'' is the number of electrons transferred and <math>F</math> is the Faraday constant.
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| There is a negative sign because a spontaneous reaction has a negative free energy <math>\Delta G</math> and a positive potential ''E''.
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| The Gibbs energy is related to the entropy by <math>G = H - TS</math>, where ''H'' is
| |
| the enthalpy and ''T'' is the temperature of the system. Using these | |
| relations, we can now write the change in
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| Gibbs energy,
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| :<math>
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| \Delta G = \Delta H - T \Delta S = \Delta G^0 + kT \ln Q, \,
| |
| </math>
| |
| and the cell potential,
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| :<math>
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| E = E^0 - \frac{kT}{ne} \ln Q.
| |
| </math>
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| This is the more general form of the Nernst equation.
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| For the redox reaction
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| <math>\mathrm{Ox} + ne^- \rightarrow \mathrm{Red},</math>
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| <math>Q = \frac{[\mathrm{Red}]}{[\mathrm{Ox}]}</math>, and we have:
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| :<math>
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| E = E^0 - \frac{kT}{ne} \ln \frac{[\mathrm{Red}]}{[\mathrm{Ox}]}
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| = E^0 - \frac{RT}{nF} \ln \frac{[\mathrm{Red}]}{[\mathrm{Ox}]}
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| = E^0 - \frac{RT}{nF} \ln Q.
| |
| </math>
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| The cell potential at standard conditions <math>E^0</math> is often
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| replaced by the formal potential <math>E^{0'}</math>, which includes some small
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| corrections to the logarithm and is the potential that is actually measured
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| in an electrochemical cell.
| |
| | |
| ==Relation to equilibrium==
| |
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| At equilibrium, ''E'' = 0 and ''Q'' = ''K''. Therefore
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| :<math>
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| \begin{align}
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| 0 &= E^o - \frac{RT}{nF} \ln K\\
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| \ln K &= \frac{nFE^o}{RT}
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| \end{align}
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| </math> | |
| | |
| Or at [[Standard conditions for temperature and pressure|standard temperature]],
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| :<math>\log_{10} K = \frac{nE^o}{59.2\text{ mV}} \quad\text{at }T = 298 \text{ K}.</math>
| |
| | |
| We have thus related the [[standard electrode potential]] and the [[equilibrium constant]] of a redox reaction.
| |
| | |
| ==Limitations==
| |
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| In dilute solutions, the Nernst equation can be expressed directly in terms of concentrations (since activity coefficients are close to unity). But at higher concentrations, the true activities of the ions must be used. This complicates the use of the Nernst equation, since estimation of non-ideal activities of ions generally requires experimental measurements.
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| The Nernst equation also only applies when there is no net current flow through the electrode. The activity of ions at the electrode surface changes when there is current flow, and there are additional [[overpotential]] and resistive loss terms which contribute to the measured potential.
| |
| | |
| At very low concentrations of the potential-determining ions, the potential predicted by Nernst equation approaches toward ±∞. This is physically meaningless because, under such conditions, the [[exchange current density]] becomes very low, and there is no thermodynamic equilibrium necessary for Nernst equation to hold. The electrode is called to be unpoised in such case. Other effects tend to take control of the electrochemical behavior of the system.
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| | |
| ==Significance to related scientific domains==
| |
| The equation has been involved in the scientific controversy of denying the reality of [[cold fusion]] phenomena.
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| | |
| ==See also==
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| *[[Concentration cell]]
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| *[[Electrode potential]]
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| *[[Galvanic cell]]
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| *[[Goldman equation]]
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| *[[Membrane potential]]
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| *[[Nernst-Planck equation]]
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| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| ==External links==
| |
| * [http://www.nernstgoldman.physiology.arizona.edu/ Nernst/Goldman Equation Simulator]
| |
| * [http://www.physiologyweb.com/calculators/nernst_potential_calculator.html Nernst Equation Calculator]
| |
| * [http://thevirtualheart.org/GHKindex.html Interactive Nernst/Goldman Java Applet]
| |
| * [http://www.doitpoms.ac.uk/tlplib/pourbaix/index.php DoITPoMS Teaching and Learning Package- "The Nernst Equation and Pourbaix Diagrams"]
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| | |
| [[Category:Electrochemical equations]]
| |
There is however a trick that you must stay with if you want success. For women with endometriosis, the monthly fecundity (chance of getting pregnant) diminishes by 12 to 36%. If probable, wait to have sexual intercourse until finally you are entirely performed taking your medication. You could be the next and is definitely worth your try. The somewhat controversial study used uterine cells from both groups of women.
Incorporate nutritious foods into your meal plan and begin exercising to get your body in shape. This is your best time if youre trying to get pregnant. Yes, this is really hereditary but there are ways on how you will be able to stimulate the process of your hyperovulation which can possibly lead to having multiple births. Most of these the application is limited and therefore are of very few consciousness, they certainly usually do not teach the teens generation concerning the risk-free really like process, risk-free habits and what's more the employing of the contraceptives. The side effects for going green are allergies disappear, adult acne diminishes, weight stabilizes, you stay looking and feeling younger longer.
So it's vital to know what to consume, and what not to consume. Being water soluble also signifies that loads of it may be lost when it's cooked. This is also true for men as smoking and drinking will affects the quality of their sperm. The whole procedure is terrified and women' dissapointment and pain are so huge when they gave so so much hope and finally they failed to get pregnant. Aromatherapy and herbal medicines are also other examples of the methods you can use in getting pregnant help.
Most of the battle is usually over if one has a male partner and a willing sperm donor. All you have to do is enter your information and it will calculate when your fertile days are. Horse and Donkey - Horse can get pregnant once a year and usually in mid to late spring. But even the researchers couldn't believe just how strong an effect this chemical was having. In addition, whole grains, nuts, tofu, wheat germ, the consumption is also very useful for these products.
Miscarriages and PCOS are also linked with each other. These are effective solutions for them who are facing it. When to commence testing for ovulation with your Home-Check Instant Ovulation test Kit. If you're stressed out your body knows this, and could be working against you. For women who have a healthy diet, do not need a vitamin supplement, but if you do not feed you properly, then you will be prescribed a multivitamin tablets.
If you loved this article and you would such as to get additional info concerning ways to get pregnant with a girl kindly browse through the webpage.