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00:00Hello everyone, welcome to this exciting lecture series on electrochemistry.
00:07Today, we are diving into one of the most important breakthroughs in the physical chemistry
00:16that is the modern theory of strong electrolytes.
00:20So here is the deal.
00:22Older theories worked fine for the weak electrolytes,
00:25but they could not explain why strong electrolytes, such as HCl or NCl, behave weirdly at higher concentrations.
00:35That is where the Debye Huckel and Onsgaard stepped in.
00:43Let us explore the modern theory of strong electrolytes, which was developed in the early 20th century.
00:50In 1923, Debye and Huckel introduced their groundbreaking theory,
00:55and later in 1926, Onsgaard expanded it to give a modern and more complete explanation.
01:05Unlike the earlier theories, this modern theory or approach takes into account the electrostatic forces
01:14that exist between ions in the solution, which earlier models had ignored.
01:21The Debye Huckel theory explains how strong electrolytes, which completely dissociate into the ions,
01:28still don't follow their ideal behavior.
01:31This is due to the interaction between the charged ions.
01:35It introduces the concept of an ionic atmosphere,
01:41which means that any given ion is surrounded by a cloud of oppositely charged ions.
01:48This affects how freely it can move and interact.
01:53So there are two main concepts, ions in the solution,
01:57and their mobility or behavior in the ions, which is the ionic atmosphere.
02:03The electrostatic interaction influences the mobility of the ions,
02:10that is how easily they can move through the solution,
02:14and this in turn impacts the overall conductivity of the electrolyte.
02:19The theory also explains how ion concentrations play a major role
02:23as concentration increases, the interaction becomes stronger,
02:28and conductivity does not increase as much as we have expected.
02:35Now, let us go over the main assumptions of the Debye Huckel theory,
02:40which help us understand how it models a strong electrolyte.
02:44First, the theory assumes that the solute or electrolyte is completely dissociated in the solution.
02:52That means it is only applicable to strong electrolyte,
02:57which fully break up into the ions when dissolved.
02:59It is not applicable to partial dissociation like in the weak electrolytes.
03:05Second, it assumes that ions are spherical in shape,
03:09which is a simplification to make calculations easier.
03:13Also, solvation of ions is ignored.
03:17So, the theory does not take into account how water molecules or solvent particles surround
03:23and interact with the ions.
03:25In reality, solvation can impact ion behavior,
03:31but this theory leaves that out.
03:34Thirdly, and very importantly,
03:37the solvent plays no direct role in this theory.
03:40It is only seen as a passive medium that allows ions to interact and move around.
03:47So, while the solvents dielectric constant may influence the interactions,
03:52it does not participate chemically or structurally.
03:57Finally, the theory makes a statistical assumption
04:01that the individual ions that surround a center line are not looked at one by one.
04:07Instead, they are represented as an average cloud of continuous charge density.
04:13This ionic atmosphere helps describe how a center line fails the net factors rounding ions,
04:20not their individual positions.
04:22These simplifications helped Debye and Haeckel build a model
04:28that could still explain the behavior of strong electrolytes with surprising accuracy,
04:34especially how conductivity drops with increasing concentration,
04:38which earlier theories could not explain.
04:43Let us now talk about one of the key ideas in the Debye Haeckel theory,
04:48which is the concept of ionic atmosphere.
04:52Imagine a center line floating in a solution.
04:55Around it, there forms a kind of spherical haze made up of other ions.
05:01This haze has a net charge that is equal in magnitude,
05:07but opposite in sign to that of the central ion.
05:10This surrounding cloud is basically called ionic atmosphere.
05:15Because of these opposite charges,
05:18the center line interacts electrostatically with the ionic atmosphere.
05:22This interaction has an important effect that is it actually lowers the energy
05:29and chemical potential of the center line.
05:32So you can think of the ionic atmosphere as a kind of cushion
05:36that stabilizes the ion and reduces its free energy.
05:41According to Debye Haeckel model,
05:44at very low concentrations where ions are far apart and behave more ideally,
05:49we can quantitatively calculate the activity coefficient of an ion
05:53using what is called the Debye Haeckel limiting law.
05:56This tells us how much the behavior of an ion
05:59deviates from idle behavior due to these ionic interactions.
06:03So the ionic atmosphere is a key part of understanding why ion activity,
06:09not just the concentration, matters in real solutions,
06:12especially when dealing with the strong electrolytes.
06:16here we can see visually the ionic atmosphere.
06:21If there is one charge, for example positive charge,
06:24it will be surrounded by some opposite charge,
06:27for example negative charge.
06:29We can see there that the number of charges will be equal,
06:33but they are opposite in their sign.
06:37Negative charge is surrounded by the positive charge,
06:41and the positive charge is being surrounded by the negative charge.
06:44So this is basically the ionic atmosphere.
06:47Let us now go over with the main ideas of the Debye Haeckel theory,
06:56which help us understand the behavior of strong electrolytes in the solution.
07:00First one is the complete ionization or almost complete ionization.
07:07The theory explains that if a strong electrolyte is completely ionized at all dilutions,
07:14that means when it dissolves in water, it breaks apart fully into the ions,
07:20or no neutral molecules remain.
07:23However, modern studies have shown that this is not entirely true.
07:28There is usually a very small amount of unionized substances still present,
07:35even in the strong electrolytes.
07:37So instead of saying completely ionized,
07:41a better way to describe it would be almost completely ionized.
07:45This correction reflects a more accurate picture based on the experimental evidence.
07:51The second one is the non-uniform ionic distribution.
07:57The theory also highlights that the ions in the solution are not randomly scattered.
08:02Because oppositely charged ions attract,
08:05there is a new natural tendency for cations to be surrounded by anions,
08:09and for the anions to be surrounded by the cations.
08:12This means the distribution of ions is not uniform in the solution.
08:17Instead, we see a kind of organized clustering
08:21where positive and negative ions tend to be near each other.
08:25This behavior plays a crucial role in creating the ionic atmosphere
08:29that we have just discussed in the previous slide.
08:32And it affects the things like the mobility and activity of ions in the solution.
08:38These two points set the foundation for understanding
08:41how electrostatic interactions affect the properties of the electrolytic solutions.
08:47And they explain why conductivity does not always behave the way as it should,
08:53based on just the concentration.
09:01Continuing with the main ideas of the double vehicle theory,
09:04here are few more important points that help to explain the behavior of strong electrolyte in the solution.
09:11Third one is the decrease in the conductance with the concentration.
09:16As the concentration of an electrolyte increases,
09:20we observe a decrease in its equivalent conductance.
09:24So why does this happen?
09:26It is due to a fall in the mobility of the ions.
09:29Basically, the ions cannot move as freely when they are crowded together,
09:34as they are when they are not crowded together.
09:38This crowding causes stronger interionic effects or electrostatic interaction between neighboring ions,
09:44which actually slows them down.
09:47And the reverse is also true.
09:49At lower concentrations, ions are more spread out and face less interaction.
09:54So eventually, the conductance of the solution will increase.
09:59Fourth one is the degree of dissociation and the conductance ratio.
10:06Traditionally, for wake electrolytes, we can find the degree of dissociation,
10:11which is the lambda V over lambda infinity.
10:14Lambda V is the molar conductivity at a given concentration,
10:19and the lambda infinity is the molar conductivity at infinite dilution.
10:24But for the strong electrolytes, the same ratio does not give us the true value of the degree of dissociation.
10:34Because the strong electrolytes are almost fully ionized dissociated.
10:39They are not 100% dissociated, but they are almost fully dissociated.
10:44Instead, this ratio gives us something called the conductance coefficient,
10:49which relates more to how well the ions conduct electricity at a particular concentration,
10:56not just how they are dissociated.
11:00Okay.
11:01So the question is why lambda V is less than lambda infinity.
11:08Even though strong electrolytes are almost completely ionized,
11:12the value of lambda V, which is the molar conductivity at a normal concentration,
11:17is still very much less than the lambda infinity,
11:21which is the molar conductivity at infinite dilution.
11:24That is because, again, in a more concentrated solution,
11:29ions interact more and this hinders their mobility.
11:33So even with fully ionization, the increased electrostatic effects cause a noticeable drop in the overall conductivity,
11:42which is again basically due to the ionic atmosphere.
11:46Now, let us talk about the W. Hickel and Onsagar conductance equation.
11:55This equation was a major step forward because it takes into account the key factors that affect the conductance of the strong electrolyte in the solution,
12:06especially the intra-ionic interactions and the influence of the ionic atmosphere.
12:12For a univalent electrolyte that is an electrolyte with a single positive and negative charges and one that is assumed to be completely dissociated,
12:22the conductance equation is written in a specific mathematical form.
12:26The equation is given as this.
12:28Lambda V is equal to lambda infinity minus which is multiplied with the a plus b lambda infinity and the concentration term,
12:38which is in the under root form.
12:41We have seen that the lambda V is the conductance at a specific concentration
12:46and the lambda infinity is the conductance at infinite dilution.
12:51In this equation, we see two important constants a and b and a concentration term c.
13:00This concentration term c is measured in the gram equivalent per liter.
13:05Now, here is the important part.
13:07The constant a and b are not just a random parameters.
13:11They depend only on the nature of the solvent like water or alcohol and on the temperature of the solvent.
13:18So, if you change the solvent or adjust the temperature,
13:23the values of a and b will be changed accordingly.
13:27Here are the values equations for the a and b.
13:33We can see that a is equal to 82.4 divided by dt which is in the under root form multiplied by eta
13:45and b is also equal to 8.2 multiplied by 10 to the power 5 which is a and it is divided by dt under root 3 by 2.
13:55Here d and eta are the dielectric constants and the coefficient of viscosity of the medium respectively.
14:02Eta is the coefficient of viscosity of the medium and d is the dielectric constant.
14:08So, in this equation, we can see that a depends only on the two factors which is basically temperature and the solvent
14:17and b also depends on the temperature and the sum of the properties of the solvent.
14:22These values are obtained at an absolute temperature which is in the Kelvin scale.
14:29The constant a is actually a measure of the electrophoretic effect while b is that of the asymmetric effect.
14:38For water, for example, d will be equal to 78.5 and eta will be equal to 8.95 multiplied by 10 to the power minus 3.
14:48And the value of a comes out to be 60.20 and that of b we can also calculate.
14:56These equations help us understand how and why the equivalent conductance of an electrolyte decreases with increasing concentration
15:05and it provides a much more accurate picture than the older models.
15:11Now, let us move on to the concept of activity in the solution.
15:21The activity of a solution is basically a measure of the effective concentration of an anion or an electrolyte.
15:28It is not just how much it is present but how much is actually active in terms of chemical behavior.
15:36It is denoted by the symbol A. Mathematically, it can be defined as A is equal to C multiplied by F.
15:45Here, C is the actual concentration of the solution which is made in the molality and F is the activity coefficient.
15:57Now, when we are dealing with very dilute solutions, the ions that don't interfere with each other in the very dilution.
16:10So, in this case, the activity coefficient F will be nearly equal to 1.
16:16That means, in such cases, the activity becomes equal to the actual concentration.
16:22But, in more concentrated solutions, the value of F which is the activity coefficient drops below 1 due to the interaction below the ions.
16:37So, the activity is less than the concentration of the ions.
16:41We can also rearrange the equations to get F is equal to A divided by C.
16:46So, the activity coefficient is defined as the ratio of the activity to the actual concentration of the solution.
16:57The ratio of activity to the actual concentration of the solution will be the activity coefficient.
17:03This concept is super important when we deal with real-world solutions that are not ideally dilute, like in industrial or biological systems,
17:14where the effective behavior of ions can be very different from what their concentration suggests.
17:20Now, let us move further and talk about the activity and activity coefficient of the electrolyte.
17:35For an electrolyte, the overall activity is not just a single value.
17:40It is actually the product of individual activities of its cations and anions.
17:46So, we can write that A is equal to A plus multiplied by A minus.
17:51Here, A plus is the activity of cation and A minus is the activity of anions.
17:57It means that the total activity depends on how active both type of ions are in the solution.
18:04Similarly, the activity coefficient of the entire electrolyte, which tells us how closely these solutions behave to ideal,
18:13is given by the product of the activity coefficient of the cations and the anions.
18:19F will be equal to F plus multiplied by F minus, where F plus is the activity coefficient of the cation and F minus is the activity coefficient of the anions.
18:31These relationships help us understand the real behavior of ions in a solution,
18:36especially when interaction between ions start to matter, like in concentrated solutions or when working with strong electrolytes.
18:46Now, here is something important.
18:52The individual activity and activity coefficient of ions in an electrolyte cannot be measured directly through some of the experiment.
19:00This is because we cannot isolate a single ion to measure its behavior independently.
19:06So, ions are always exist in the pairs or groups to maintain the electrical neutrality.
19:13However, what we can measure is their mean value and that is extremely useful in the practice.
19:20The mean value of the electrolyte, which can be shown by the Ax or By, can be determined by the following relation.
19:29So, if you assume that stychometrically this is the equation, Ax, By, they are nice in the solution, giving these signs.
19:37Then we can find the mean value by this equation.
19:41A positive or negative activity can be found by V under root A plus X dot A minus Y.
19:49Here we can see that X and Y are basically the exponents or the coefficients for the stychometric values.
19:59And V is the total number of ions present in the solution, which appears in this equation.
20:04So, finally, that is the end of our discussion.
20:14I hope you have learned something new and benefited from this lecture.
20:19Thank you very much.