Lippmann capillary electrometer is used for measuring the interfacial tension as a function of potential difference. In this many solutions interface is connected to the external sources of potential difference. The height of Mercury colum'n is proportional to the surface tension.
ʋ = hρɡr
2
ʋ −surface tension
h - height of the Mercury colum'n
r - radius of the capillary
q - acceleration due to gravity
ρ - density of a Mercury.
Electrocapillary - curve :-
Plot of interfacial tension versus changes in potential difference are known as electrocapillary curves.
A typical potential difference is almost a parabola, through a maximum which is called capillary maximum.
Lippmann Equation :-
An equation which explains the shape of the electrocapillary curves and establishing a relation between interfacial tension, potential difference and the charge at the Hg solution interface was derived by Lippmann. The equation is,
( ∂ʋ ) −−qm
∂v
Constant composition.
This equation tells that slope at each point of the electrocapillary curve. The specific charge, qm on the Hg surface at a given value of potential significance.
Significance :-
Using Lippmann Equation :-
The charge at any value of potential from the experimental electrocapillary curve (epc) can be calculated.
EPC Affords a method of finding out the excess charge density on the electrode. Constant graph of the charge on the Hg surface vs potential. Since the charge is directly measurable it's possible to check the validity of Lippmann Equation.
EXPERIMENTAL RESULTS ON ELECTROCAPILLARY MEASUREMENT :-
1) The slope of the electrocapillary curve for a number of dilute solutions electrolytes (H2SO4, kOH, KNO3, Na2SO4) are elements independent of the nature of the electrolyte is almost a parabola.
2) The maximum of the curve is observed experimentally approximately same value of potential within the large from −0.19 to −0.2 voltage on the scale.
3) The maximum value of the interfacial tension for all electrolytes appear to be the same very little charge is observed.
4) The shape of electrocapillary curves of electrolyte containing organic unionized substances are not parabolic. They are less symmetrical and their maxima are situated at other values v and ʋ.
5) The figure shows that electrocapillary curves for the electrolyte of KNO3 type in the presence. For example, molecule of amyl alcohol we can present in the solution.
The presence of Br⁻,I ⁻, s²⁻ shifts the (ecm) towards more negative (-) value of potential and lowers the surface tension. The presence of Thallium, tetrabutyl ammoniam ions displace the electrocapillary maximum to the side of more the values and reduces the surface tension. This reduction being pronounced at potential more positive (+) than the potential of the (ecm)
The presence of amyl alcohol causes a change in the shape of the electrocapillary curve mainly in the region of potential adjacent to the ecm potential with distance on either side of the potential of the ecm the effect of addition of amyl alcohol dimension and the curve traced in the presence of pure solution.
The shape of electrocapillary curves vary with the composition of the electrolyte. Concentrate of the electrolyte shifts the ecm towards more negative (-) values of potential. If the electrocapillary curve is a perfect parabola then the charge density on the electrode would vary linearly with the cell potential. Electrified interphase is a region where charges are accumulated or depleted relative to the bulk of the electrolyte. It can be considered a system storing charge. But the ability to store charge is a characteristic property of an electric capacitor. Hence the capacitance of an electrified interface in way similar to that with a condenser.
The capacitance of a Condenser is the total charge required to raise the potential difference across a condenser by one voltage. This is the integral capacitance.
Cp = ( ∂qm ) constant comp.
∂v
− ( ∂²ʋ )
∂v² constant comp.
The significance is the equation in that it shows slope of the electrode charge vs cell potential yields the value of the differential capacitance of the double layer. In case of an ideal parabola ʋ vs v curve, one gets unit capacitance.
Lippmann potential of charge free electrodes :-
From qm vs v, charge on the electrode passes through a zero charge value. Also there is a charge in the sign of the electrode charge of passing through at zero charge value.
The potential difference across the cell at which charge on the electrode is zero is known as the potential of zero charge (Epzc) This is called Lippmann potential.
This is potential at which metal phase contains no excess charge and hence the electrolyte phase is electrically neutral. The Pzc is the potential at which the electrocapillary maximum (i.e) the surface tension reaches a maximum at the Lippmann potential.
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