Learn the Debye-Hückel theory and activity coefficients in electrochemistry with this complete lecture. Understand how ionic interactions affect activity, ionic strength, calculation of activity coefficients, and their applications in electrochemical systems. Perfect for CSS aspirants, chemistry students, and anyone studying physical chemistry or electrochemistry. Watch the full lecture for step-by-step explanations, examples, and exam preparation tips.
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#Electrochemistry #DebyeHuckelTheory #ActivityCoefficient #IonicStrength #ElectrochemicalReactions #CSSChemistry #PhysicalChemistry #ChemistryLecture #ChemistryEducation #ScienceLearning
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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.
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