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# Molar Conductivity

Last updated date: 11th Aug 2024
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## Define Molar Conductivity

Electrochemistry is quite an important topic in JEE and other competitive engineering exams. Molar Conductivity is a very significant topic under electrochemistry which you need to learn about in order to score well. Molar Conductivity is defined as the Conductivity of the solution of an electrolyte divided by the Molar concentration of the electrolyte, and so gauges the efficiency with which an allotted electrolyte conducts electricity in solution. This is to say that Molar Conductivity is the conducting power of all the ions that are developed by dissolving a mole of electrolyte in a solution.

### Molar Conductivity Formula

The below-given expression is used to mathematically denote Molar Conductivity.

Λm = K / C

Where

K = specific Conductivity

C = concentration in mole per liter.

The si unit of Molar Conductivity is S⋅m²⋅mol⁻¹.

### Molar Conductance

The Molar conductance is described as the conductance of all ions produced by one mole of an electrolyte present in a fixed volume of the solution.

It is given as:

Molar conductance μ = k ×V

where,

V = volume in (mL) having 1 g mole of the electrolyte. If c is the solution in g mole/litre, then μ = k × 1000/c

Units of Molar conductance:  Omega- cm-² mol²

Equivalent conductance = (Molar conductance)/n

Where

n = (Molecular mass) / (Equivalent mass)

### Variation of Molar Conductivity with Concentration

It is important to note that Molar Conductivity of both strong and weak electrolytes increases with the depletion in dilution. You must be aware already that the Molar Conductivity is the Conductivity provided by one mole of ions. Even after dilution, we are taking into account the same unit mole of ions. However, the increased dilution causes dissociation of more electrolytes into ions and optimally increasing the number of active ions in the concentration. These active ions set forth more Conductivity.

The visual representation explains that for strong electrolytes, the Molar Conductivity is increasing steadily with the dilution. If EO m is the restricting Molar Conductivity (the Molar Conductivity at 0 concentration), then the standard equation for the strong electrolyte can be delineated using the Kohlrausch’s law as below;

Λm = Eom – A√c

Where,

A = slope of the graph. It typically depends on the kind of the electrolyte at a given temperature for an assigned solvent.

For strong electrolytes, the increase in concentration yields a striking increment in Conductivity. Nevertheless, weak electrolytes carry significantly low values of specific Conductivity at lower concentration and the value moderately shows an increase as the concentration is increased. This is because of an increase in the number of active ions present in the solution due to concentration.

However, for weak electrolytes, the Molar Conductivity strikes at lower concentrations. On the contrary, such electrolytes are contained in lower Molar Conductivity at higher concentrations because of the reduced degree of dissociation.

In an instance of specific Conductivity, it is observed that the concentration of the electrolyte increases with the increase in Conductivity. The specific Conductivity relies upon the number of ions that exists in the unit volume of the solution. On dilution, the dissociation increases, leading to current-containing ions to increase in the solution. Due to the dilution, the number of ions available in a unit volume of the solution decreases. This gives rise to a reduction in Conductivity.

### Solved Examples on Molar Conductivity

Problem1: Find out the Molar Conductivity of the KCl solution?

Solution:

Given:

Molarity (M) = 0.60M

Conductivity at 298 K (k) = 0.047 S cm–

Now, Using the Molar Conductivity formula = (1000 × k) / M

= (1000 × 0.047) / 0.60

= 78.33 cm² mol⁻¹

Therefore, Molar Conductivity of the KCl solution is 78.33 cm² mol⁻¹

Problem 2: The Molar conductance measures at infinite dilution of Na+ and Cl- ions are 32.54 × 10⁻² Sm²mol⁻¹ and 67.12 × 10⁻² Sm²mol⁻¹ respectively. Find out the total Molar conductance of NaCl?

Solution:

Calculating the Molar conductance at infinite dilution, given is

λ+Na = 32.54 × 10⁻² Sm²mol⁻¹

λ+Cl = 67.12 × 10⁻² Sm²mol⁻¹

Molar conductance of NaCl = λ+Na + λ+Cl

= 32.54 × 10⁻² + 67.12 × 10⁻²

= 99.66 ×10⁻² Sm²mol⁻¹

Therefore, Molar conductance of NaCl is 99.66 ×10⁻² Sm²mol⁻¹

## FAQs on Molar Conductivity

1. What Happens to Molar Conductance Equivalent and Molar Equivalent Conductivity on Dilution?

Understand this by considering an example. Consider taking 1cc of the solution having 1 g eq. of the electrolyte taken in a jar. Now, the conductance of this solution will become the specific Conductivity. Also according to the definition of equivalent Conductivity is the conductance of 1g eq. of electrolyte solvated in V cc of the solution when the space between the electrodes is 1cm and area of the electrodes are so sizeable that the entire solution is held between them (P.S - area may or may not be equal to 1cm² and duly then eq. Conductivity will be the same as specific Conductivity). Therefore, when considering 1cc of the solution having 1 gm equivalent of the electrolyte, the equivalent Conductivity will be equal to its specific Conductivity.

2. Is there any Difference Between Molar Conductance and Molar Conductivity?If yes, What is the Difference Between Molar Conductance and Molar Conductivity?

While Conductance refers to the degree to which the solution conducts electricity, Conductivity, on the other hand, is the conductance per unit volume of the solution. Conductivity can also be regarded as the assemblage of ions per unit volume of solution. While the Molar Conductivity is the conductance of the whole solution containing 1 mole of electrolyte dissolved in it. Further, as per the Ostwald's Dilution Law, higher the dilution, higher the dissociation of the electrolyte in solution. For dilution of an electrolyte solution, as dilution increases, Conductivity decreases. Thus, as dilution increases, Molar Conductivity (conductance of 1 mole of electrolyte in total solution) should INCREASE in compliance with Ostwald's Law.

3. What is Molar conductance?

At the point when one mole of an electrolyte is broken up in a solution, the particles delivered in the arrangement are fit for directing power. Molar conductance is characterized as the directing force of the disintegrated particles created in the arrangement.

When the point where a solution is weakened, it's Molar Conductivity increases. Notwithstanding, the Molar Conductivity of solid electrolytes and feeble electrolytes shows various sorts of conduct when weakened.

In solid electrolytes, on weakening, there is finished separation of particles and the power between the particles diminishes. This assists the particles with moving quicker which prompts an increment in Molar conductance of the solution.

In feeble electrolytes, the particles don't separate totally. They go through fractional ionization and subsequently on weakening, there is a progressive expansion initially. As the solution is more weakened there is a sharp expansion in the Molar Conductivity of the solution.

4. What is specific conductance?

Specific conductance is characterized as the property of a metal which permits particles to move through it and lead power. It is typically the proportionality of Resistance and is addressed by 'k'.

5. Who discovered Molar Conductivity?

Friedrich Kohlrausch in 1875–1879 established that to a high accuracy in dilute solutions, Molar Conductivity can be decomposed into contributions of the individual ions. This is known as Kohlrausch's law of independent ionic migration.[7] For any electrolyte AxBy, the limiting Molar Conductivity is expressed as x times the limiting Molar Conductivity of Ay+ and y times the limiting Molar Conductivity of Bx−.

The limiting Molar Conductivity of a weak electrolyte cannot be determined reliably by extrapolation. Instead it can be expressed as a sum of ionic contributions, which can be evaluated from the limiting Molar conductivities of strong electrolytes containing the same ions.

Electrolytes conduct Energy because of the presence of loose ions contained in it. It is just like the case of metal Conductors, wherein free Electrons favor the conduction of Energy. The electrolytic conduction is defined based on the Arrhenius equation or concept.

We realize that electrolytic solutions can be created from the dissolution of a few salts. The salts now no longer want to be continually ionic in nature. The simplest standards are that the compound should be composed of oppositely charged ions.

Arrhenius theory explains that once a neutral electrolyte is dissolved in water, the electrolyte molecules are broken up into  in a different way charged ions. The positively charged one is known as the cation and the negatively charged one is known as an anion. The idea assumes that ions are already there in the electrolyte, but however, bound collectively via means of electrostatic pressure and as a result, they may be neutral. But once dissolved, the ions dissociate from their bound form.

AB → A⁻ + B⁻

However, there may be a recombination of ions additionally taking place. Hence, the real response taking place withinside the electrolytic answer is a reversible response. It is represented below.

AB ⇄ A⁺ + B⁻

The charged particles are capable of flowing freely via the solution. The positive ions or cations are capable of flow toward a negative electrode or cathode to get itself reduced. At an equal time, the negative ions or anions are capable of flowing toward the positive electrode or anode to get itself oxidized. This motion of charged particles known as migration imparts electric-powered conduction.

Eleсtriсity:  The  term  eleсtriс it  refers  to a  form  оf  Energy  оr  vаriety  оf  рhenоmenоn  resulting  frоm  the  ассumulаtiоn  оf  stаtiс  сhаrges  оr  flоw  оf  сhаrged  раrtiсles.

Eleсtriс  сhаrge:  The  eleсtriс  сhаrge  is  the  fundаmentаl  аnd  соnserved  рrорerty  оf  sоme  subаtоmiс  раrtiсles  whiсh  determines  their  eleсtrоmаgnetiс  interасtiоns.  It  exhibits  twо  stаtes  i.e.,  positive  аnd  negаtive.

In  SI  units,  the  eleсtriс  сhаrge  is  meаsured  in  Соulоmbs  (С).

The  smаllest  vаlue  оf  “free”  сhаrge  knоwn  in  nаture  is  the  сhаrge  оf  аn  eleсtrоn  оr  а  рrоtоn,  whiсh  hаs  а  mаgnitude  оf  1.602  x  10-19  Соulоmb

.

The  сhаrge  оn  оne  eleсtrоn  is:  -1.602  x  10-19  С.

Where the  charge on a  рrоtоn  is  equаl  tо:  +1.602  x  10-19  С.

Eleсtriс  field:  It  is  аn  influenсe  рrоduсed  by  аn  eleсtriс  charge  оn  оther  сhаrges  in  its  viсinity.

А  сhаrged  раrtiсle  exрerienсes  fоrсe  when  рlасed  in  аn  eleсtriс  field.  The  electric  field  exerts  а  fоrсe  оn  сhаrged  раrtiсles,  ассelerаting  them  in  the  direction of  the  fоrсe,  in  either  the  same or  the  орроsite  direсtiоn  of the  electric  field.

Hence  some  amount  оf  wоrk  has to  be  done  аgаinst  this  fоrсe  tо  bring  the  сhаrged  раrtiсle  tо  а  сertаin  роint  in  аn  eleсtriс  field.

Eleсtriс  роtentiаl:  The  eleсtriс  роtentiаl  аt  аny  роint  in  аn  eleсtriс  field  is  defined  аs  the  Energy  required  to bring  a unit  charge  frоm  аn  infinite  distаnсe  tо  thаt  роint.

It  is  usuаlly  meаsured  in  vоlts  (V).  Vоlt  can  be  fоrmаlly  defined  аs  the  rаtiо  of Energy  in  joules to  the  сhаrge  in  соulоmbs.

The  absolute  eleсtriс  potential  саnnоt  be  meаsured.  Hоwever,  the  difference  in  electric  potential  between  two  роints  саn  be  meаsured  аnd  hаs  mоre  рrасtiсаl  usаge.