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Molar conductivity of a solution is the conductance of a volume of solution containing one mole of electrolyte kept between two electrodes with the same unit area of cross-section and same distance between them at a given concentration. When the concentration of a solution is decreased, the molar conductivity of the solution increases. The increase in molar conductivity is due to the increase in the total volume containing one mole of the electrolyte as a result of the increase in total volume. It is known as limiting molar conductivity (m°) when the concentration of the electrolyte approaches zero and the molar conductivity becomes insignificant.
What is Kohlrausch’s Law? Explain
When comparing the values of limiting molar conductivities of some strong electrolytes, Kohlrausch noticed some patterns that were consistent with his observations. Kohlrausch proposed that the “limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anions and cations of the electrolyte” based on his observations. This law is referred to as the Kohlrausch law of independent migration of ions in the scientific community. In the case of sodium chloride, for example, the knowledge of the limiting molar conductivities of sodium ion and chloride ion allows the determination of the limiting molar conductivity of sodium chloride. The following are some examples of important applications of Kohlrausch’s law of independent migration of ions:
- Kohlrausch’s law is useful in determining the limiting molar conductivities of any electrolyte, regardless of its composition. Molecular conductivities of weak electrolytes are lower at higher concentrations, as is the degree of dissociation exhibited by the electrolyte. For weak electrolytes, the graph plotting the relationship between molar conductivity and c1/2 (where c is the concentration) does not show a straight line. The molar conductivity of a weak electrolyte increases rapidly as the concentration of the electrolyte decreases.
- We can also use Kohlrausch law to figure out how to calculate the value of dissociation constant from the value of molar conductivity, as well as how to determine the limit of molar conductivity for a weak electrolyte at a given concentration.
α = Λ /Ëm°
Where, α = dissociation constant
Λ = molar conductivity
Ëm° = limiting molar conductivity
The fraction of the total number of electrolyte molecules that are dissociated that ionises at equilibrium is referred to as the degree of ionisation or the degree of dissociation, respectively.
For this, various concepts are provided to help you classify electrolytes as acids or bases.
1. The concept of acids and bases developed by Arrhenius
According to the Arrhenius concept, an acid is a substance that can either supply or produce hydrogen ions (H+) in its aqueous solution, depending on the situation.
A base is a substance that produces hydroxyl ions in its aqueous solution when dissolved.
Strong acids are acids that have almost completely lost their ionisation, such as HCl, HNO3, and H2SO4, among others.
Weak acids are acids that have only a weak ionisation, such as CH3COOH and H2CO3, and are found in small amounts in nature.
2. Strong bases are bases that are completely ionised in an aqueous solution, in a similar way to weak bases. For example, NaOH, KOH, and so on.
Weak bases, such as NH4OH, are bases that have only a slight ionisation when compared to other bases.
As shown in the equation, H3O + + H + + H2O is considered to contain the H+ ion, which is present in hydrated form in combination with the water molecular form. The ion H3O + is referred to as the Hydronium ion.
Application
Kohlrausch’s law has a variety of applications.
- Formula for determining the degree of dissociation
- Calculation of the solubility of a salt that is only sparingly solubleCalculation of the Dissociation Constant for Electrolytes with Low Dissociation Constant
- Formula for calculating the molar conductivity of weak electrolytes under conditions of infinite dilution
- It is employed in the calculation of the dissociation constant of an electrolyte in solution. When dealing with a weak electrolyte
- It is necessary to compute the limiting molar conductivity.
- With the help of this law, we may also determine the degrees of dissociation of weak electrolytes.
- In addition, this law can be used to compute the solubility constants of various salts. As well as this, it is employed in many electrochemical cells to calculate the cell potential.
Solubility of a sparingly soluble salt
Conductance measurements can be used to determine the solubility of slightly soluble substances such as BaSO4, PbSO4, AgCl, and other similar substances.. As soon as a sparingly soluble salt is added to water, only a very small amount of the salt dissolves in the water, resulting in the formation of a solution. In order to achieve this, a saturated solution of the salt in conductivity water is prepared and allowed to stand until almost all of the insoluble fraction has settled down completely. The conductance of the clear solution from the top is measured in a conductance cell using the clear solution from the top. The cell is thoroughly cleaned and then filled with the same conductivity water, with the conductance of the water being measured in the same cell as the conductivity water. The observed conductance is then converted to specific conductance using a mathematical formula.
The solubility of such salts can be calculated through the use of Kholrausch’s law and conductance measurements, among other methods. According to equation-, the molar conductance (m) of a saturated solution is
m = (x 1000)/c = (x 1000)/c
where ‘c’ is the concentration of the solution in mol L-1 and ” is the specific conductance of the solution. The concentration of the salt in eq/l, and thus the solubility of the salt, is represented by the letter ‘c’. Considering that the salt is only sparingly soluble in water, the solution is extremely dilute, and m may be taken to be equal to 0, which is the molar conductance at infinite dilution. The value of 0m tor AgCl can be determined by applying Kohlrausch’s law of independent ionic migration to the solution. According to this law, Λm(AgCl) = Λag + ΛCl is equal to 0. It is possible to calculate the value of c by substituting Λm in the above equation if the value of c is known. This will give the value of ‘c’ in mol L-1, from which the solubility in gL-1 can be calculated using the equation above. Because the salt dissolves so slowly, the solutions are extremely dilute, and because the salts are strong electrolytes, the solutions are extremely dilute.
Conclusion
As a result, at infinite dilution, when dissociation is complete, each ion contributes significantly to the equivalent conductance of the electrolyte, irrespective of its association with another ion. The value of equivalent conductance at infinite dilution for any electrolyte is equal to the sum of contributions made by its constituent ions at infinite dilution (cations and anions). In other words, it states that the ‘conductivity of ions in an electrolyte at infinite dilution is constant and does not depend on the nature of the co-ions.’
Λ∞eq = λ∞c + λ∞a
