# Conductivity of Electrolyte Solutions

**Topics:**Electrochemistry, Electrolyte, Concentration

**Pages:**14 (4087 words)

**Published:**February 19, 2012

(Dated: October 29, 2009)

I.

INTRODUCTION

Pure water does not conduct electricity, but any solvated ionic species would contribute to conduction of electricity. An ionically conducting solution is called an electrolyte solution and the compound, which produces the ions as it dissolves, is called an electrolyte. A strong electrolyte is a compound that will completely dissociate into ions in water. Correspondingly, a weak electrolyte dissolves only partially. The conductivity of an electrolyte solution depends on concentration of the ionic species and behaves diﬀerently for strong and weak electrolytes. In this work the electric conductivity of water containing various electrolytes will be studied. The data will be extrapolated to inﬁnitely dilute solutions and the acidity constant for a given weak electrolyte will also be determined. Additional theoretical background for electrolyte solutions can be found from Refs. [1–3]. II. THEORY

Movement of ions in water can be studied by installing a pair of electrodes into the liquid and by introducing a potential diﬀerence between the electrodes. Like metallic conducting materials, electrolyte solutions follow Ohm’s law: R= U I (1)

where R is the resistance (Ω, “ohms”), U is the potential diﬀerence (V, “Volts”), and I is the current (A, “Amperes”). Conductance G (S, Siemens or Ω−1 ) is then deﬁned as reciprocal of the resistance: G= 1 R (2)

Conductance of a given liquid sample decreases when the distance between the electrodes increases and increases when the eﬀective area of the electrodes increases. This is shown in the following relation: G=κ A l (3)

where κ is the conductivity (S m−1 ), A is the cross-sectional area of the electrodes (m2 ; e.g. the eﬀective area available for conducting electrons through the liquid), and l is the distance between the electrodes (m). Molar conductivity Λm (S m2 mol−1 ) is deﬁned as: Λm = κ c (4)

where c is the molar concentration of the added electrolyte. A “typical” value for molar conductivity is 10 mS m2 mol−1 . The molar conductivity of an electrolyte would be independent of concentration if κ were proportional to the concentration of the electrolyte. In practice, however, the molar conductivity is found to vary with the concentration (see Fig. 1). One reason for this variation is that the number of ions in the solution might not be proportional to the concentration of the electrolyte. For example, the concentration of ions in a solution of a weak acid depends on the concentration of the acid in a complicated way, and doubling the concentration of the acid does not double the number of ions. Another issue is that ions interact with each other and tend to slow down each other leading reduced conductivity. In this limit, the molar conductivity depends on square root of electrolyte molar concentration. In the 19th century Friedrich Kohlrausch discovered the following empirical relation between the molar concentration of a strong electrolyte and the molar conductivity (Kohlrausch’s law) at low concentrations: √ Λm = Λ0 − K c m Typeset by REVTEX (5)

FIG. 1: Variation of molar conductivity as a function of molar concentration. a) Strong electrolute and b) weak electrolyte.

where K is a non-negative constant depending on the electrolyte and Λ0 is the limiting molar conductivity (e.g. the m molar conductivity in the limit of zero concentration of the electrolyte). Furthermore, Kohlrausch was able to show that Λ0 can be expressed as a sum of contributions from its individual ions. If the limiting molar conductivity for m the cations is λ+ and for the anions λ− , the “law of the independent migration of ions” states: 0 Λ m = v+ λ + + v− λ −

(6)

where v+ is the number of cations per formula unit, v is the corresponding number of anions, and λ+ and λ− are the limiting molar conductivities for cations and anions, respectively. For example, for HCl v+ = 1 and v− = 1...

References: [1] P. W. Atkins and J. de Paula, Physical Chemistry (7th ed.) (Oxford University Press, Oxford, UK, 2002). [2] R. J. Silbey, R. A. Alberty, and M. G. Bawendi, Physical Chemistry (4th ed.) (Wiley, New York, 2004). [3] R. Chang, Physical chemistry for the chemical and biological sciences (University Science Books, Sausalito, California, 2000).

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