What is strong electrolyte explain relation between molar conductivity and concentration of solution with strong electrolyte?

Electrochemistry is the study of chemical reactions that occur in a solution at the interface of an electron conductor (the electrode: a metal or a semiconductor) and an ionic conductor (the electrolyte). Electron transfer occurs between the electrode and the electrolyte or species in solution in these reactions.

A solution’s conductivity is defined as the conductance of a solution with a length of 1 cm and a cross-sectional area of 1 sq. cm. Conductivity, or particular conductance, is the inverse of resistivity. The letter k is used to signify it. If p stands for resistivity, we can write:

K= 1/p 

The conductivity of a solution at any given concentration is equal to the conductance (G) of one unit volume of solution held between two platinum electrodes with the same cross-sectional area and separated by the same distance.

i.e., 

G = K × a/l = K × l = K

(Since a = 1, l = 1)

For both weak and strong electrolytes, conductivity diminishes as concentration decreases. This is because as the concentration of a solution declines, the number of ions per unit volume that carry the current in the solution reduces.

Molar Conductivity

The conductance of volume V of a solution containing 1 mole of the electrolyte kept between two electrodes with the area of cross-section A and distance of unit length is the molar conductivity of a solution at a particular concentration.

Am = K × A/l

Now, l = 1 and A = V (volume containing 1 mole of the electrolyte).

Am = KV

With a decrease in concentration, molar conductivity rises. This is due to the fact that when a solution containing one mole of electrolyte is diluted, the total volume V of the solution increases.

The following graph depicts the fluctuation of Am with √c for strong and weak electrolytes:

Variation of Molar Conductivity with Concentration for Strong and Weak Electrolytes

• Variation of Molar Conductivity with Concentration for Strong Electrolytes

Molar conductivity grows slowly with dilution in strong electrolytes, and it has a tendency to approach a limiting value as the concentration approaches 0, i.e. when the dilution is infinite. Molar conductivity at infinite dilution is the molar conductivity as the concentration approaches 0 (infinite dilution).  It is denoted by Am°

Am = Am°, when C ⇢ 0 (at infinite dilution)

The expression for the change of molar conductivity with concentration might be used.

Am = Am° − AC1/2

where 

• A is constant and A° stands for molar conductivity at infinite dilution. 

This equation, known as the Debye Huckel Onsager equation, holds true at low concentrations.

• Variation of Molar Conductivity with Concentration for Weak Electrolytes

When opposed to strong electrolytes, weak electrolytes dissociate to a far smaller level. As a result, when compared to strong electrolytes, the molar conductivity is low.

However, the variation of Am with C1/2 is so enormous that the extrapolation of Am against C1/2 plots cannot yield molar conductance at infinite dilution ( Am°).

Variation of Molar Conductivity with Concentration

(A) Conductance behavior of weak electrolytes

The degree of dissociation with dilution determines the number of ions supplied by an electrolyte in a solution. The degree of dissociation rises as dilution increases, and molar conductance increases as a result. The limiting value of molar conductance (Am) corresponds to a degree of dissociation of 1, which means that the electrolyte completely dissociates.

At every concentration, the degree of dissociation may therefore be estimated.

α = Amc / Am°

where α represents the degree of dissociation, Amcrepresents the molar conductance at concentration C, and Am° represents the molar conductance at infinite dilution.

• Conductance behavior of strong electrolytes

For strong electrolytes, there is no increase in the number of ions with dilution because strong electrolytes are completely ionized in solution at all concentrations.

Interionic forces are strong forces of attraction between ions of opposing charges in concentrated solutions of strong electrolytes. In concentrated solutions, the ions’ conducting capacity is reduced due to these interionic interactions. The ions grow farther apart as a result of dilution, and interionic forces diminish. As a result, molar conductivity rises as the solution is diluted. When the solution’s concentration is exceedingly low, interionic attractions are minimal, and molar conductance approaches the limiting value known as molar conductance at infinite dilution. This number is unique to each electrolyte.

Sample Questions 

Question 1: What effect does a solution’s concentration have on its specific conductivity?

Answer:

The specific conductivity decreases as the concentration decreases. This is because the number of energized ions per unit volume  in a solution decreases with dilution. Therefore, concentration and conductivity are directly proportional to each other.

Question 2: Explain why the Cu+ ion is not stable in aqueous solutions?

Answer:

Cu2+ is more stable in aqueous media than Cu+. This is because, while removing one electron from Cu+ to Cu2+ requires energy, the high hydration energy of Cu2+ compensates for it. As a result, the Cu+ ion is unstable in an aqueous solution. Cu2+ and Cu are disproportionately produced.

2Cu+(aq) ⇢ Cu2+(aq) + Cu(s)

Question 3:  The molar conductivity of 0.025 mol L-1 methanoic acid is 46.1 S cm2 mol-1. Calculate its degree of dissociation and dissociation constant. Given λ0(H+) = 349.6 S cm2 mol-1 and  λ0(HCOO–) = 54.6 S cm2 mol.

Answer:

Given that,

C = 0.025 mol L-1

Am = 46.1 S cm2 mol-1

 λ0(H+) = 349.6 S cm2 mol-1

 λ0(HCOO−) = 54.6 S cm2 mol-1

Am°(HCOOH) =  λ0(H+) +  λ0(HCOO−) 

= 349.6 + 54.6

= 404.2 S cm2 mol-1

Now, degree of dissociation:

α = Am(HCOOH)/Am°(HCOOH)

= 46.1/404.2

= 0.114(approx.)

Thus, dissociation constant:

K = c×α2/(1−α)

= (0.025 mol L-1)(0.114)2/(1 − 0.114)

= 3.67×10-4 mol L-1

Question 4:  The conductivity of 0.20M solution of KCl at 298K is 0.0248 S/cm. Calculate its molar conductivity 

Answer:

Given:-

 K= 0.0248 S/cm

C= 0.20M

Am = K×1000/C

= (0.02481000)/0.2

= 124 S cm2 mol-1

Question 5: Prove that “Molar conductivity increases with a decrease in concentration”.

Answer:

Keeping length is equal to one.  

Multiply length ‘l’ in numerator and denominator

Am = K×A/l

Keeping length is equal to one.  

Multiply length ‘l’ in numerator and denominator

Am = K×A/l × l/l
As l=1 and A×l =V volume 

Am = KV

The concentration is low, the volume grows, and the cross-sectional area expands. As a result, both the volume and the molar conductivity rise. When the concentration is low, the volume is raised.

Because ‘K’ is related to conductivity, when concentration rises, ‘K’ rises while ‘V’ falls. When the concentration drops, ‘K’ drops as well, while ‘V’ rises. The change in the value of ‘V’ is significantly bigger than the change in the value of ‘K.’

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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.

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.

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

Kohlrausch Law  

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 

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

Also,

\(\Lambda\)om (NaBr) - \(\Lambda\)om (NaCL) = \(\Lambda\)om (KBr) - \(\Lambda\)om (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.

\(\Lambda\)om(NaCl) = λoNa+ + λoCl- 

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

\(\Lambda\)om = V+ λo+ +V- λo-

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Points 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. 

Ques  – Calculate \(\Lambda\)om  for CaCl2 (2 marks)

Ans:

Using formula,

\(\Lambda\)om = V+ λo+ +V- λo-

V+ is 1 and V- is 2

\(\Lambda\)om CaCl2 = 1 λoCa+ +2 λoCl-

= 119 + 2× 76.3

= 271.6 S cm2 mol-1

Que  - Calculate for MgSO4 from the data given in the table (2 marks)

Ans:

Using formula,

\(\Lambda\)om = V+ λo+ +V- λo-

Using formula,

\(\Lambda\)om MgSO4 =  λomg2+ + λoso4 2-

= 106 + 160

= 266 S cm2 mol-1

Que  – What is conductivity? Explain in detail (3 marks)

Ans: The conductivity decreases with decrease in concentration and increase in increases the concentration. It is applicable for both strong and weak electrolytes. The number of ions per unit volume carrying the current decreases in the solution and conductivity decreases. Fewer ions are responsible for less conductivity. The conductance is represented by ‘G’, ‘K’ is conductivity, ‘A’ is area and ‘l’ is length

G = K A/l

When area and length is equal then conductivity is equal to conductance. 

Que - What is molar conductivity? (2 marks)

Ans: Molar conductivity is the opposite of conductivity. Increase the concentration and the molar conductivity goes down or decreases. Molar conductivity is represented by ?m

\(\Lambda\)m = K \({A \over l}\)

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

Que - “Molar conductivity increases with decrease in concentration” Prove it (4 Marks)

Ans:

Keeping length is equal to one.  

Multiply length ‘l’ in numerator and denominator 

\(\Lambda\)m = K \({A \over l}\)

Keeping length is equal to one.  

Multiply length ‘l’ in numerator and denominator 

\(\Lambda\)m = K \({A \over l}\) x \({l \over l}\) 

As l=1 and A×l =V volume 

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

The concentration is low, the volume increases and the area of cross-section is more. So volume increases and the molar conductivity increases. And volume is increased when the concentration is low. 

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

Que - Explain the effect of strong and weak electrolyte in molar conductivity (4 Marks)

Ans:

Strong electrolyte

As increase slowly with dilution

\(\Lambda\)m = \(\Lambda\)om - A√C

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

We get a straight line that has an intersection 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 electrolyte does not dissociate completely  solvent. 

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

Que  – Explain Kohlrausch law in detail (3 Marks)

Ans:  

• 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 fix halogen is nearly constant.Potassium and sodium are same but halogens are changed 
• \(\Lambda\)om (KCL) - \(\Lambda\)om (NaCL) = \(\Lambda\)om (KBr) - \(\Lambda\)om (NaBr) = \(\Lambda\)om (KI) - \(\Lambda\)om (NaI) ≈ 23.4 S cm2 mol-1
• Also,
• \(\Lambda\)om (NaBr) - \(\Lambda\)om (NaCL) = \(\Lambda\)om (KBr) - \(\Lambda\)om (KCL) = 1.8 S cm2 mol
• 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.

Ques - The conductivity of 0.20M solution of KCl at 298K is 0.0248 S/cm. Calculate its molar conductivity (2 Marks)

Ans:   Given- Conductivity K= 0.0248 S/cm

Concentration C= 0.20M

Molar conductivity = \(\Lambda\)m = \({K \times 1000 \over C}\)

\(\Lambda\)m= (0.02481000)/0.2

\(\Lambda\)m = 124 S cm2 mol-1

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