Variations Molar Conductivity: Strong and Weak Electrolyte

Molar conductivity is defined as the conductance of that electrolytic solution that is kept between electrodes which are unit length apart. They have an area of cross-section ‘A’ which is large enough to hold one mole of electrolyte. When the concentration of a solution reaches zero, its molar conductivity is known as limiting molar conductivity. The molar conductivity of solid and weak electrolytes varies with concentration in different ways.

Key Takeaways- Variations Molar Conductivity, Molar conductivity, Electrochemistry, Specific Conductivity, Strong Electrolytes, Weak electrolytes, Electrodes, Electrolytic solution, Electrolyte

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Conductivity

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Molar conductivity is the opposite of conductivity. As you increase the concentration the molar conductivity goes down or decreases. Molar conductivity is represented by 

\(\Lambda\)_m = K/c

\(\Lambda\)_m = K \({A \over l}\)............................... (1)

\(\Lambda\)_m = K   ( length  = 1 and A=V contains one mole of electrolyte) 

In molar conductivity, one mole of the solute is present in the solution. Conductivity of the solution, when it has one mole of solute and  if the solution is dilute then one mole of solute will be present in larger volume and if it is concentrated then one mole of the solute will be present in small volume. The area of the cross section is larger for the dilute solution and smaller for the concentration solution. Keeping length is equal to unity or one.  

Multiply length ‘l’ in numerator and denominator 

\(\Lambda\)_m = K Al ×ll 

As l=1 and A×l =V volume 

\(\Lambda\)_m = KV ............................................... (2)

K’ is proportional to conductivity, as increase in concentration ‘K’ increases but ‘V’ decreases and if the concentration is decreased ‘K’ also decreases but ‘V’ is increasing. The change in the value of ‘V’ is much greater than a change in the value of ‘K’.

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Specific Conductivity

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The conductance of a material is the property of a material that allows ions to flow through it and thus conducts electricity. It is commonly defined as the reciprocal of the material's resistance. S is the SI unit of conductance (Siemens). Specific conductivity (also known as conductivity) is a measure of a material's ability to conduct electricity. It is represented by the letter "K."

An electrolytic solution's specific conductivity is determined by the following factors:

• The nature of the electrolyte in the solution and its concentration.
• The size of the ions in a solution.
• The nature of the solvent and its viscosity
• The outside temperature.

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Electrolytic Conductivity

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A direct current is passed between two metallic electrodes immersed in an ionised solution. Electric charges are carried by electrons of insignificant mass in metals. The electric charges in solutions are carried by electrolytic ions, each of which has a mass several thousand times that of an electron. Positive ions flow to the cathode, while negative ions flow to the anode.

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Variation of Molar Conductivity with Concentration

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With dilution, the molar conductivity rises steadily. If EO m is the restricting Molar Conductivity (the Molar Conductivity at 0 concentration), then the standard equation for the strong electrolyte is as follows: m = Eom – Ac Where, A is the slope of the graph. It usually depends on the type of electrolyte at a given temperature for a given solvent.

For strong electrolytes, increasing concentration results in a significant increase in conductivity. Nonetheless, weak electrolytes have significantly low specific conductivity values at low concentrations, and the value increases moderately as concentration increases. This is due to an increase in the number of active ions in the solution as a result of concentration.

The Molar Conductivity, on the other hand, strikes at lower concentrations in weak electrolytes. Because of the reduced degree of dissociation, such electrolytes have lower Molar Conductivity at higher concentrations.

In the case of specific Conductivity, the concentration of the electrolyte increases as the Conductivity increases. The specific conductivity is determined by the number of ions present in a unit volume of solution. The dissociation increases with dilution, resulting in an increase in the concentration of current-containing ions in the solution. The number of ions available in a unit volume of solution decreases due to dilution. This results in a decrease in conductivity.

Strong Electrolytes

Value of ‘A’ is depends on nature of electrolyte 

And ‘C’ is the concentration

Now plot the graph between √C and limiting molar conductivity for strong electrolyte KCL

Molar conductivity for strong electrolyte

We get a straight line that intersects with intercepts; here would be the limiting molar conductivity for KCL and slope is equal to minus A (-A). Value of ‘A’ depends upon the type of solvent and charges of ions on dissociation. 

Weak Electrolytes

Weak electrolyte does not dissociate completely in solvent. So as dilution increases the degree of dissociation of weak electrolytes increases. As the degree of dissociation increases the number of ions present increases and that can affect the conductors.  Degree of dissociation represents α Degree of dissociation increases with dilution and therefore molar conductivity changes. In such cases, molar conductivity increases steeply with dilution.

At C→0  , α=1

The weak electrolyte represents in curve of CH₃COOH

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Kohlrausch Law  

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Kohlrausch examined the limiting molar conductivities of different or number of electrolytes that the difference in limiting molar conductivities of sodium halide and potassium halide for any fixed halogen is nearly constant. Potassium and sodium are same but halogens are changed 

\(\Lambda\)^o_m (KCL) - \(\Lambda\)^o_m (NaCL) = \(\Lambda\)^o_m (KBr) - \(\Lambda\)^o_m (NaBr) = \(\Lambda\)^o_m (KI) - \(\Lambda\)^o_m (NaI) ≈ 23.4 S cm² mol^-1

Also,

\(\Lambda\)^o_m (NaBr) - \(\Lambda\)^o_m (NaCL) = \(\Lambda\)^o_m (KBr) - \(\Lambda\)^o_m (KCL) = 1.8 S cm² mol^-1

Each ion is like a separate entity which has its own limiting molar conductivity. They are independent of each other. 

Kohlrausch law is the independent migration of ions. \(\Lambda\)^om of an electrolyte can be represented as sum of individual contributions of anions and cation of the electrolyte.

\(\Lambda\)^o_m(NaCl) = λ^o_Na+ + λ^o_Cl- 

If V+ and V- are the number of anions and cations produced

\(\Lambda\)^o_m = V+ λ^o+ +V- λ^o-

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Things to Remember

• The conductivity decreases with decrease in concentration and increase in increases the concentration. 
• The concentration of ionic compounds increases, the conductivity goes on increasing.
• Molar conductivity is the opposite of conductivity. Increase the concentration and the molar conductivity goes down or decreases.
• Kohlrausch law is the independent migration of ions. 
• Each ion is like a separate entity which has its own limiting molar conductivity. They are independent of each other.