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00:00Hello everyone, welcome to this exciting lecture series on electrochemistry.
00:07In this video, we will learn about Kohlraub's law, which is one of the key principles in the electrochemistry.
00:16This law is especially useful when we are working with the dilute solutions of the electrolytes.
00:23We will explore how this law helps to us understand the behavior of electrolytes at infinite dilutions
00:30and how it allows us to calculate the molar conductivities of weak electrolytes,
00:36even though when they are not fully dissociated in the solutions.
00:41Then, we will also talk about where the law comes from and how it is represented mathematically,
00:48and most importantly, how we apply it in the real solutions.
00:52So, we will also look into the applications in detail.
01:02So, what does Kohlraub's law actually state?
01:06It states that the equivalent conductance of an electrolyte at infinite dilution
01:12is equal to the sum of equivalent conductance of its individual ions,
01:18that is the cation and the ions, each measured at infinite dilution as well.
01:25In other words, at infinite dilution, the ions are so far apart that they don't interfere with each other's movement,
01:34and each ion contributes independently to the total conductance of the solution.
01:39Mathematically, we can say that the equivalent conductance of an electrolyte, which is shown by the lambda infinity,
01:49is equal to the lambda A plus lambda C.
01:52Here, lambda shows the equivalent conductance of the anion,
01:56and lambda C shows the equivalent conductance of cations.
02:01So, mathematically, it is a very simple equation.
02:06For example, the equivalent conductance of sodium chloride at 25 degrees centigrade is 126.45 per ohm cm3 of equivalent conductance.
02:23If we look into the individual conductance, then we can have the values of sodium ion as 50.11 ohm per ohm cm3,
02:35and equivalent conductance of calorie 9 comes out to be 76.34 respectively.
02:42So, according to this equation, if we add these two values, it should be equal to the equivalent conductance of the electrolyte.
02:54So, mathematically, we can see that both of these values are equal.
02:58Lambda infinity, which is calculated experimentally, is basically equal to the theoretical values of the sum of its ions.
03:07This law, or this equation, confirms the Kohlrast law.
03:13This law actually helps us calculate unknown values too.
03:18For example, if we know the values for certain ions,
03:22we can use Kohlrast law to find the values of an electrolyte or some of the missing ions.
03:30It is also super useful when we study weak electrolytes,
03:36which don't fully dissociate because we can still predict their behavior at infinite dilution using this principle.
03:43After studying this simple definition and mathematically proving the equation,
03:51let us move toward the most important application of this law.
03:56Also, its use in calculating the lambda infinity will also be discussed especially for the weak electrolytes.
04:03So, first of all, the first major application is that it is used to calculate lambda infinity for the weak electrolytes.
04:13As we know that weak electrolytes like acetic acid or ammonium hydroxide, they do not ionize completely in the solution.
04:23Even when we try very high dilution, they still don't ionize fully.
04:29Because of this, it is practically impossible to directly measure the lambda infinity or the equivalent conductance.
04:39We can't just keep diluting and hope to reach a fully ionized state.
04:44It does not happen.
04:45Because there is a maximum capacity at which vehicle electrolytes can ionize.
04:50After that, they do not ionize.
04:53No matter what type of dilution or how much extent of dilution is there.
04:58But, here is where correlates law comes to the rescue.
05:05It allows us to calculate the equivalent conductance of the solution of a weak electrolyte indirectly
05:13by using the unknown values of lambda infinity for strong electrolytes that share some common ions.
05:19Here is the equation.
05:24We can see that lambda A over lambda C, which shows the equivalent conductance of anion over cation,
05:33is equal to the transport number of cation divided by 1 minus transport number of cation.
05:40Here is just the rearrangement of the equations.
05:47And we can calculate lambda for the equivalent conductance of any ion using this relationship.
05:57Or we can add these two values, lambda A plus lambda C, which corresponds to the lambda infinity.
06:04So, if we know the transport number, which is shown by the T minus and the lambda infinity,
06:11we can actually calculate the equivalent conductance of any ion.
06:15This gives us an accurate value for the lambda infinity of the weak electrolytes,
06:21even though the weak could not measure it directly.
06:24This method is very simple, smart and powerful.
06:28Just one of the reasons why Kohlraaf's law is such a valuable tool in the electrochemistry,
06:33because of its simple application and its accuracy.
06:37Now, let us move on to how we can use transport number to determine ionic conductance,
06:49which is another very useful application in electrochemistry.
06:52First, what is ionic conductance?
06:55It refers to how much current a particular ion can carry through a solution.
07:03The ionic conductance of an ion is obtained by multiplying the equivalent conductance at infinite dilution of any strong electrolyte containing that ion by its transport number.
07:15So, here is the simple equation that we have studied before.
07:19If we simply multiply the transport number by the equivalent conductance at infinite dilution,
07:25then we can get the ionic conductance of a specific kind.
07:29So, we use these two values to obtain the value of ionic conductance.
07:35Transport number actually simply tells us what fraction of the total current is carried by a particular ion in the solution.
07:46In this manner, the ionic mobilities of the two ions present in the vehicle electrolyte can be calculated.
07:53We have seen in the previous slide that if we want to get the conductance at the infinite dilution,
08:03we can just add up the values of its anions and the cations.
08:09This method is especially useful for weak electrolytes where direct measurement of lambda infinity is not practical.
08:15It combines experimental data with theoretical understanding to give us a complete picture of
08:21how ions behave in a solution and that is why ionic conductances are used in the laws.
08:33Now, let us move on to the second major application of the Kodrast law
08:37and that is the calculation of absolute ionic mobilities.
08:41So, what do we mean by the ionic mobilities?
08:45It is the velocity of an ion in centimeters per second.
08:50When it moves through a solution under a potential gradient of one volt per centimeter.
08:56Think of it like this.
08:58If you apply a certain voltage across a solution,
09:01how fast does an ion move under that electric push?
09:05So, that is the ionic mobilities.
09:09Here is the simple formula.
09:12The potential gradient is equal to the applied EMF across the electrodes divided by the distance between the electrodes.
09:20So, this is for the potential gradient.
09:23The unit for the ionic mobilities is centimeter per second.
09:28Now, we will understand it by an example.
09:34For example, if we have a voltage of 100 and the distance between the electrodes is 20 centimeters.
09:43Then, the potential gradient comes out to be 5, which we can simply obtain by dividing the voltage with the distance between the electrodes.
09:54100 divided by 20 comes out to be 5 volts per centimeter.
09:58And the ionic mobility is the 5 centimeter per second.
10:02This value is really useful because it helps us understand how efficiently different ions move in a solution under an electric current.
10:12So, it is very crucial in designing batteries, fuel cells, and other electrochemical devices.
10:20So, again, Kohlraaf's law is not just a theoretical concept.
10:25It provides us the tool to make real measurement and prediction in the lab and in the field of electrochemistry.
10:32Now, we will look into the calculation of solubility of sparingly soluble salts.
10:46Substances like silver chloride or lead sulfate, which are typically labeled as insoluble, actually dissolves to a very small extent in water.
10:57This means that even when they don't dissolve much, they do have a measurable and definite solubility.
11:06The solubility of these salts can be determined by measuring the conductance of their standard solutions.
11:13A saturated solution means the maximum amount of the salt which has been dissolved in water at a given temperature and no more can be dissolved in that solution.
11:26Because the concentration of dissolved salt is extremely low, we can assume that all of the dissolved salt is fully ionized into its constituent ions.
11:39So, even though the total amount is small, it behaves as if it is completely dissociated.
11:46As a result of this complete dissociation, the equivalent conductance of the supersaturated solution, which is the KV, is taken to be equal to the equivalent conductance at infinite dilutions.
12:03Because there is so little solute that further dilution would not change its ionization state.
12:14According to the KV, the equivalent conductance at infinite dilutions can be calculated by adding the individual ionic conductances or mobilities of the cations and anions of the salt.
12:28This sum represents the total contribution to the conductance from both ions.
12:35Knowing the values of K and lambda infinity, we can actually find the V, which is the volume in the milliliter, which contains the 1 gram equivalent of electrolyte.
12:57So, next, we will look into the calculation of degree of dissociation or conductance ratio.
13:13The degree of dissociation, often denoted by the symbol alpha, tells us how much of a weak electrolyte has broken into its sign in the solution.
13:25It is a measure of how far the ionization process has proceeded.
13:31We calculate this by taking the ratio of equivalent conductance at a given concentration to the equivalent conductance at infinite dilution.
13:41The idea is that at infinite dilution, the electrolyte is assumed to be fully dissociated.
13:47So, this ratio, which is given here, directly gives us the degree of dissociation, which is the alpha.
13:57A lower ratio indicates that only a small fraction of the electrolyte has ionized, while a ratio closer to 1 means most of it has been ionized or dissociated.
14:09This method is especially useful for weak acids and weak bases, for the calculation of degree of dissociation.
14:21Because weak acids are weak bases, do not dissociate completely in the water, and whose dissociation levels vary with the concentration.
14:30Next, next application of Kohlraff's law is the calculation of ionic product of water.
14:38The ionic product of water is the product of concentration of hydrogen ions, which are H plus ions, and the hydroxide ion, which is O minus ions in pure water.
14:50This value can be calculated by measuring the conductance of pure water very precisely.
14:56Since pure water slightly ionizes into H plus and O minus ions, its value can be obtained from the Kohlraff's law.
15:05Once the specific conductance is known, and the molar conductance at infinite dilution is calculated using the ionic mobilities of H plus and O minus,
15:15the concentration of ions can easily be found.
15:18Here we can see that the conductance for the water comes out to be 5.54 multiplied by 10 to power minus C.
15:28And we multiply this by 1000 to make the unit consistent.
15:33At same temperature, the conductance of the individual ions are H plus comes out to be 349.8 Mohs, which is the unit for the conductance.
15:52And the conductance for the O minus ions comes out to be 198.5 Mohs.
16:04According to Kohlraff's law, lambda H2O should be equal to lambda H plus plus lambda OH minus.
16:13These are the ions for the dissociation of H2O.
16:18The values for the H plus sign was seen to be 349.8.
16:22And the value for the OH minus sign comes out to be 198.5.
16:27And the sum of these values comes out to be 548.3.
16:32One molecule of water gives one H plus sign and one OH minus sign, which is evident from the psychometry.
16:43Assuming that the ionic concentration is proportional to the conductance, then we can have H plus should be equal to OH minus signs.
16:51Because their ionic concentration is equal, here one H plus sign is formed and one OH minus sign is formed.
16:58So their concentration should be equal.
17:02We have the values for the water, which we have seen in the previous slide.
17:08For water, the value comes out to be 5.5 multiplied by 10 raised to the power minus 5.
17:13And for the individual ions, we have the value for the 548.3.
17:17By dividing these two values, we get the values as 1.01 multiplied by 10 to the power minus 7 gram ion per litre.
17:27So these are the concentration of the hydrogen ion at 25 degree centigrade.
17:32The ionic product of water will be then.
17:37It is shown by the H plus multiplied by OH minus sign.
17:42And when we multiply these values, 1.01 multiplied by 10 to the power minus 7, this value for H plus sign.
17:51And the same value for OH minus sign.
17:54When we multiply these values two times, we get the value 1.02 10 to the power minus 14 at 25 degree centigrade.
18:03So this is the ionic product of water.
18:06For most purposes, we actually take the value of KW as 10 to the power minus 14.
18:13We ignore the small fractions as 0.02.
18:16So, that is all for today's lecture.
18:19We have seen the simple mathematical equations for the Kulrastala.
18:26And we have focused mainly on its example to understand the Kulrastala and also to the applications of the Kulrastala.
18:34We have seen that how practically important is the Kulrastala in calculating the ionic mobilities of the vehicle electrolytes of the water and predicting some other parameters.
18:46I hope you have learned something new.
18:48Thank you very much.