Electrochemistry

A = R k ( . ) Once the cell constant is determined, we can use it for measuring the resistance or conductivity of any solution. The set up for the measurement of the resistance is shown in Fig. . . It consists of two resistances R and R , a variable resistance R and the conductivity cell having the unknown resistance R . The Wheatstone bridge is fed by an oscillator O (a source of a.c. power in the audio frequency range to cycles per second). P is a suitable detector (a headphone or other electronic device) and the bridge is balanced when no current passes through the detector. Under these conditions: Unknown resistance R = R R R ( . ) These days, inexpensive conductivity meters are available which can directly read the conductance or resistance of the solution in the conductivity cell. Once the cell constant and the resistance of the solution in the cell is determined, the conductivity of the solution is given by the equation: cell constant G* R R    ( . ) The conductivity of solutions of different electrolytes in the same solvent and at a given temperature differs due to charge and size of the Fig. . : Arrangement for measurement of resistance of a solution of an electrolyte. ions in which they dissociate, the concentration of ions or ease with which the ions move under a potential gradient. It, therefore, becomes necessary to define a physically more meaningful quantity called molar conductivity denoted by the symbol L m (Greek, lambda). It is related to the conductivity of the solution by the equation: Molar conductivity = L m = c  ( . ) In the above equation, if k is expressed in S m – and the concentration, c in mol m – then the units of L m are in S m mol – . It may be noted that: mol m – = (L/m ) × molarity (mol/L), and hence L m (S cm mol – ) =  (S cm L m × molarity (mol L ) If we use S cm – as the units for k and mol cm – , the units of concentration, then the units for L m are S cm mol – . It can be calculated by using the equation: L m (S cm mol – ) = (S cm ) × (cm /L) molarity (mol/L)  Both type of units are used in literature and are related to each other by the equations: S m mol – = S cm mol – or S cm mol – = – S m mol – . Resistance of a conductivity cell filled with . mol L – KCl solution is W . If the resistance of the same cell when filled with . mol L – KCl solution is W , calculate the conductivity and molar conductivity of . mol L – KCl solution. The conductivity of . mol L – KCl solution is . S/m. The cell constant is given by the equation: Cell constant = G* = conductivity × resistance = . S/m × W = m – = . cm – Conductivity of . mol L – KCl solution = cell constant / resistance * G R = – m  = . S m – Concentration = . mol L – = × . mol m – = mol m – Molar conductivity  c  – – – × S m mol m = × – S m mol – Alternatively, k = – . cm  = . × – S cm –