# Variations Of Molar Conductivity With Concentration

Specific conductivity or conductivity of an electrolytic solution at any given concentration is the conductance of unit volume of solution kept between two platinum electrodes with unit area of cross section and at a distance of unit length. Conductivity decreases with decrease in concentration as the number of ions per unit volume that carry the current in a solution decrease on dilution. Molar conductivity of a solution at a given concentration is the conductance of the volume $V$ of solution containing one mole of electrolyte kept between two electrodes with area of cross section $A$ and distance of unit length.

$Ʌ_m$ = $\frac{К}{c}$

Here,

$c$ = concentration in moles per volume
$К$ = specific conductivity
$Ʌ_m$ = molar conductivity.

As the solution contains only one mole of electrolyte, the above equation can be modified as:

$Ʌ_m$ = $К V$

Molar conductivity increases with decrease in concentration as the total volume, $V$, of solution containing one mole of electrolyte also increases. Upon dilution the concentration decreases. When the concentration approaches zero, molar conductivity of the solution is known as limiting molar conductivity, $Ë°m$. Variation of molar conductivity with concentration is different for strong and weak electrolytes.

Variation of molar conductivity with concentration for strong electrolytes: For strong electrolytes the molar conductivity increases slowly with the dilution. The plot between the molar conductivity and $\frac{c_1}{2}$ is a straight line having y-intercept equal to $Ë°m$. The value of limiting molar conductivity, $Ë°m$ can be determined from the graph or with the help of Kohlrausch law. The general equation for the plot is given as:

For strong electrolytes the molar conductivity increases slowly with the dilution. The plot between the molar conductivity and $\frac{c_1}{2}$ is a straight line having y-intercept equal to $Ë°m$. The value of limiting molar conductivity, $Ë°m$ can be determined from the graph or with the help of Kohlrausch law. The general equation for the plot is given as:

$Ʌ_m$ = $Ë°m ~-~ \frac{Ac_1}{2}$

Where, $-A$ is a constant equal to the slope of the line. For a given solvent, the value of “$A$” depends on type of electrolyte at a particular temperature.

Variation of molar conductivity with concentration for weak electrolyte:

For weak electrolytes, the graph plotted between molar conductivity and $\frac{c_1}{2}$ (where $c$ is the concentration) is not a straight line. Weak electrolytes have lower molar conductivities and lower degree of dissociation at higher concentrations which increases steeply at lower concentrations. Therefore, limiting molar conductivity, $Ëm°$ cannot be obtained by extrapolation of molar conductivity to zero concentration. Hence, we use Kohlrausch law of independent migration of ions for determining limiting molar conductivity, $Ëm°$ of weak electrolytes.

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#### Practise This Question

An aqueous solution of X is is added slowly to an aqueous solution of Y as shown in Column I. The variation in conductivity of these reactions is given in Column II. Match Column I with Column II and select the correct answer using the codes given below the Columns.
Column IColumn IIP.(C2H5)3XN+CH3COOHY1.Conductivity decreases and then increasesQ.KI(0.1M)X+AgNO3Y(0.01M)2.Conductivity decreases and then does not change muchR.CH3COOHX+KOHY3.Conductivity increases and then does not change muchS.NaOHX + HIY4.Conductivity does not change much and then increases