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00:00Hello everyone. Welcome to this exciting lecture series on electrochemistry.
00:07In this video, we are going to explore one of the cornerstones of electrochemistry, which is the non-set equations.
00:19This equation is essential when studying how electropotentials vary under different conditions, especially when concentrations are non-standard.
00:29It also helps us predict voltage in real-world electrochemical systems like batteries and the fuel cells.
00:37So, the non-set equation is a fundamental equation in electrochemistry.
00:43It is used to predict the voltage at which an electrochemical reaction takes place.
00:48This predictability is crucial for understanding how redox reactions proceed under real-world conditions where the environment is rarely ideal.
00:58It is especially important because it calculates the standard electrode potential of an electrochemical cell and also determines the voltage of an galvanic cell under non-standard conditions.
01:12For instance, if the ion concentration is not exactly 1 molar or if the temperature varies from 298 Kelvin or 25 degree centigrade, the non-standard equation let us calculate accurately and it will predict how that non-idule conditions affect the voltage.
01:34Talking about the importance of this equation, it is also significant in energy systems, as the equation also helps in predicting the behavior of electrochemical cells, including everyday applications like batteries and fuel cells.
01:53Engineers and scientists rely only to evaluate performance and efficiency under changing the operational conditions.
02:02Finally, the non-set equation also provides a direct relationship between the concentration of ions and the electrode potential.
02:12This means that it helps us understand how shifting concentration impacts the cell voltage.
02:19That insight is vital for managing and optimizing redox reactions in both theoretical and practical domains, from research to real-life applications.
02:31So, next, we see that this equation is given by E is equal to E0 minus RT divided by NF multiplied by logarithm of R natural log of Q.
02:42Here, we see that E is the observed electrode potential, this one, E0 is the standard electrode potential.
02:50Here, R is the general gas constant, T is the temperature in Kelvin, N is the number of electrons transferred in reaction, F is the Faraday's constant,
03:00and L and Q is the natural logarithm of the reaction quotient, okay?
03:05So, this is the final form of the non-set equation.
03:08Next, in this slide, let us now look at the derivation of the non-set equation, which connects the thermodynamic with the electrochemistry.
03:21We begin with the fundamental thermodynamic identity that Gibbs free energy of a cellular reaction can be expressed as
03:31delta G is equal to delta G0 plus RT multiplied by L and Q.
03:36This shows how free energy, which is the delta G, changes under non-standard conditions depending on the reaction quotient, temperature, and the universal gas constant.
03:47So, this is for the Gibbs free energy.
03:52Now, we know from the electrochemical principles that the standard Gibbs free energy change, that is delta G0, it can be related to the standard electrode potential E0 value as follows.
04:06So, delta G is equal to minus NFE0.
04:09Here, in this equation, N is the number of electrons transferred in the electroredox reaction, and F is the Faraday's constant.
04:18So, we see that if we substitute the value of delta G0 from this equation to the original equation for the Gibbs free energy, then we get this equation.
04:31Delta G is equal to NFE0 plus RT multiplied by L and Q.
04:37Solving for the observed electrode potential.
04:41Okay.
04:42So, if we want to calculate the value for the observed potential, then here is the step.
04:47We know that E is equal to delta G divided by minus NFE0.
04:53So, from this equation, if we simply put for the simple electrode potential, we do not put the standard values, we put the values for the observed potential.
05:06So, this equation becomes this one.
05:08E will be equal to minus NFE0 divided by NFE plus RT multiplied by L and Q.
05:17So, this one is obtained by putting the value of delta G.
05:21We put the value of delta G from this equation to here, and it will be divided by the same factor, which is the minus NFE.
05:30Rearranging the equation, we get as E is equal to E0 minus RT divided by NFE multiplied by L and Q.
05:39So, this is basically our non-set equation.
05:43Next, we will see some of the modification in the non-set equation.
05:52So, we can actually calculate the half-cell potential using this equation.
05:56So, we see that for an oxidation half-cell reaction, when a metal electrode, which is denoted by M, gives N plus sign to convert into M plus sign.
06:08Then, we have a general equation, M goes to M plus sign, giving some of the electrons.
06:15So, we see that the non-set equation takes this form, E is equal to E0 minus 2.303RT divided by NFE multiplied by log MN plus divided by M.
06:27So, here, as we have replaced natural log with this log base of 10, then we will multiply this by 2.303.
06:36So, this 2.303 corresponds to the natural logarithm value.
06:42So, this is basically the non-set equation for this.
06:46As we have remembered that in the original equation, we have the log for the quotient of equation.
06:53So, this basically corresponds to the quotient of the equation.
06:56M plus divided by M.
06:57And both of the concentrations are divided.
07:00And the logarithm will be taken.
07:03So, we see that the concentration of the solid metal M is equal to 0.
07:08Therefore, the non-set equation can be written as this one.
07:13E is equal to E0 minus 2.303RT divided by NFE multiplied by log MN plus.
07:19The concentration of M is equal to 0 because we assume that M has been converted into its positive winds.
07:27So, substituting the value of the R, F and T at 25 degrees centigrade.
07:34We get the value of the quantity 2.30T multiplied by RT divided by NF.
07:40It comes out to be 0.0591.
07:42So, putting R as 8.303 and T at 25 degrees centigrade or 298 degrees Kelvin
07:51because we have to use some absolute values.
07:54Number of electrons is, I think, in this equation is 1.
07:59Okay.
08:00So, whatever the number of equation is.
08:02And putting the value of this F as 96,485 which is the value for the Faraday's constant.
08:13So, the equation will become as E is equal to E0 minus 0.0591 divided by N.
08:18As you see that we have not put the value of 10 because we don't know the number of fines that the metal M have removed or lost.
08:27So, this is the final form of the NUNFET equation which can be used to calculate the half cell potential.
08:33Okay.
08:34So, this is the equation for a half cell reaction in which oxidation occurs.
08:40In case it is a reduction reaction, the sign of the E will have to be reversed.
08:45Okay.
08:46So, we just reverse the sign and it will give the value for the reduction reaction.
08:51Also, based on the half cell reaction, we can also calculate the cell potential.
08:59The NUNFET equation is also applicable to the cell potential as well.
09:03Thus, E of the cell will be equal to E0 cell divided by 0.0591 divided by N multiplied by log K.
09:12So, in this equation, K is the equilibrium constant of the redox cell reaction.
09:17E0 is the value which has been measured at the standard condition by comparing it with the standard reduction electrode.
09:26Also, we can calculate the value of the equilibrium constant with the help of this equation.
09:35By rearranging the equation, we can calculate the equilibrium constant as K is equal to E raised to the power E0 minus E divided by RT divided by N.
09:45So, the original equation, the first equation that we have studied in the second slide, that was rearranged to find the equilibrium constant.
09:56So, now we are going to explore some of the important applications of this equation.
10:09This equation is most commonly used in electrochemistry.
10:15It allows us to calculate the potential of an electrolyte in a cell even when the conditions are not standard.
10:22As we have seen in the previous slide using some of the equations.
10:26This is actually essential for determining how the concentration of reactants and the products affect the cell voltage.
10:33It is especially helpful in designing batteries, understanding fuel cells and predicting the outcome of a redox reaction.
10:41Talking about the biochemistry, this equation finds important applications in biology as well.
10:47It can be used in biochemistry to calculate the potential of an ion channel in the biological membrane.
10:54This is crucial in understanding nerve impulses, muscle contractions and ion transport across the membranes.
11:02All of which depend on the electrochemical gradients.
11:06So, next we will talk about the analytical chemistry.
11:10In analytical settings, this equation helps to calculate the concentration of ions in a solution.
11:18For instance, in acid based titration, we can use it to determine the concentration of hydrogen ions.
11:25Making it a valuable tool in the pH measurements and the sensor calibrations.
11:31Such as in glass electrodes.
11:34Okay.
11:35So, moving next, we will talk about the further applications.
11:42We will talk about the gel winding cells or the batteries.
11:46This equation is essential for calculating the voltage of a gel winding cell.
11:52When the ionic concentration is derived from the standard molar solution, which is the one molar solution.
11:59This is actually critical in real life applications like battery design and the performance analysis.
12:07Where electrolyte concentrations often vary due to usage or environmental factors.
12:14Using the non-fat equation, we can determine how the cell voltage changes as the battery changes, giving insight into the efficiency and the shelf life.
12:27Next, we will study about the electrode potential under non-standard conditions.
12:32This equation also helps us to calculate electrode potential under non-standard conditions.
12:38Which means that the concentration of the reactants and the products is not one molar.
12:43The situation is very common in practical electrochemistry.
12:46Where in industrial processes, research or biological systems, the concentration deviates from the one molar solution.
12:55It ensures that our calculations match real world conditions.
13:00Which make our predictions about the cell behavior much more accurate.
13:04Let us continue exploring how the non-set equation proves valuable in the practical electrochemistry.
13:16Especially when working with the real world devices and the reaction.
13:21So first of all, we see that the non-set equation is widely used to calculate the actual cell potential.
13:28For electrochemical reactions and devices such as batteries, fuel cells and electrolysis systems.
13:35It factors in the concentration of ions and the temperature.
13:39Giving us a precise value from the cell voltage under non-standard conditions.
13:43This is crucial and very valuable for evaluating performance, predicting the energy output and troubleshooting issues in the electrochemical system.
13:54Also, it can predict the direction of the reaction.
13:59By using this equation, we can examine the electrode potential and ion concentration.
14:04And determines whether the reaction is spontaneous or not.
14:08If the cell potential is positive, the reaction will proceed spontaneously.
14:13Indicating it is thermodynamically favorable.
14:16On the other hand, a negative cell potential suggests that the reaction is non-spontaneous under the current conditions.
14:23This insight is actually extremely valuable for reaction planning and electrochemical process designs.
14:30Let us now discuss the limitations of non-set equation, which are important to understand when applying it in the real scenarios.
14:44So we see that the non-set equation assumes ideal conditions, constant temperature and pressure.
14:50But in reality, these conditions often fluctuate, especially in industrial or biological systems.
14:57This deviation can lead to inaccuracies in calculated electrode potential, especially in fieldwork or lab environments, where exact conditions cannot always be maintained.
15:09Also, it assumes that the electrode potential stays constant, which is not always valid.
15:17In practical applications, effects like electrode polarization, where the potential at the electrode surface shifts due to the current flow,
15:25it can alter the expected readings.
15:29This is particularly noticeable in systems operating over long durations or at high currents like electrolytic cells or matter plating units.
15:39Also, another significant limitation is its restricted applicability.
15:47The equation works well only for the simple reactions involving a few winds.
15:53It does not work as accurately for reactions with complex science, biochemical reactions or processes involving multiple electron transfer, such as in the redoxy cascades or complex biological pathways.
16:07For such reactions, modified or empirical models are needed for more accurate results.
16:13These limitations don't render the non-set equation useless.
16:17Rather, they remind us of the context and boundaries within which it remains reliable and insightful.
16:27Next, we will study about an example and we see that how the non-set equation can be applied in the real time.
16:37So, we see that we see a reaction in which lead and silver react with one another at 25 degrees centigrade in an electrochemical cell.
16:48So, the overall thing that is happening in the cell is that lead loses its two electrons and convert it to PB2 plus ions and silver ions gain two electrons and they convert it into solid silver metals.
17:02So, if we know that the concentration for the silver ions is 0.75 for example,
17:09and the concentration of lead is equal to 0.1 molar and also the standard cell potential is 0.95 volts.
17:18So, using these two values, we can actually calculate the cell potential.
17:24So, we know that the original equation is this where E of the cell is equal to E0 minus RT divided by NF multiplied by LNQ.
17:33We have already put the values for the R, T and F and by putting these values and using log instead of natural logarithm,
17:43we get the value of 0.592 volts divided by N.
17:48So, the two unknowns are the quotient variables which are the PB2 plus signs and the AG2 plus signs.
17:56So, by putting their concentration, we have the PB2 plus signs concentration 0.1 and the lead concentrations are or the silver concentrations are 0.5 molar.
18:06Okay.
18:07So, by putting these values and solving for the reaction, we get the value of 0.95 volts.
18:13And there is one mistake that the unit value, this is the unit value, it is 0.93 instead of 0.95.
18:24So, we see that the overall value for the cell comes out to be 0.95 but the standard potential value is 0.93.
18:33So, here in the simple example, we showed that how you can calculate the value of the cell potential using the value of the ionic concentrations and the standard electrode potential.
18:48So, that was all for today's lecture.
18:54Thank you very much.