A New Method for Determination of Molecular Weight of Compounds Soluble in Protic Solvents by Electrochemical Impedance Spectroscopy

*Subramaniam Rameshkumar, Panjaiyan Karthikeyan, Iman Danaee and Manogaran Obulichetty*

### **Abstract**

This chapter deals with a new method for determining the molecular weight of chemical substances soluble in protic solvents. One of the well-known methods for the determination of molecular weight of a substance, based on one of the colligative properties, is Ostwald and Walker's method, which depends on relative lowering of vapor pressure of solvent. In this paper we proposed a new method for determining the molecular mass of the substances that are soluble in protic solvents such as water, methanol and ethanol employing electrochemical impedance spectroscopy (EIS) technique and Raoult's law. The moisture and vapor pressure dependent proton conductivity of some organic compounds and metal-organic frame works (MOFs) can be utilized to find the molecular mass of solutes soluble in protic solvents. This property is considered as key for determination of molecular weight of chemical substances using EIS and is simpler than Ostwald and Walker's method. This method is a non-destructive and also useful to determine the molecular weight of polymers and proteins soluble in protic solvents.

**Keywords:** impedance, molecular weight, vapor pressure, Raoult's law

#### **1. Introduction**

Electrochemical impedance spectroscopy (EIS) finds a special place among the various electrochemical techniques. It is a powerful tool for analyzing the interfaces formed in the heterogeneous systems. EIS supplies a large amount of informations, though it may not provide all the answers. EIS uses tools developed in electrical engineering and describes the behavior of the systems under study in terms of an equivalent circuit consisting of the circuit elements resistors, capacitors, Warburg impedance etc. The mathematical foundations of EIS were dealt by Heariside [1], through which it is possible to solve the integrodifferential equations appearing in the solutions of electrical circuits by converting them into a system of algebraic equations. The main advantage of EIS is the fact that it is based on the linear time invariant (LTI) theory and validity of the data may be verified using Kramers-Kronig integral transforms. Nernst was the first person who described the chemical applications of impedance spectroscopy through his work [2], followed by many others including those applications to the distribution of relaxation time constants by Cole and Cole [3] and Davidson and Cole [4]. The impedance of mass transfer was explained by Warburg using so called Warburg impedance, which extended EIS to apply for redox reactions [5]. With further development in the understanding of EIS, the structure of double layer in the absence and presence of adsorbed species was studied initially at dropping mercury electrode and then at solid electrodes using AC bridge. The analysis of electrochemical reactions using the electro analog circuit was introduced by Dolin and Ershler [6] and Randles [7, 8], where the age of electrical analog began [9] and continues up till now. The fundamental aspects of EIS give the idea to validate the data and to model the processes limited by diffusion, electrode kinetics and adsorption on different types of electrode geometries. The availability of modern instrumentation to obtain impedance data as well as computer programs to interpret the results have made this technique popular. Now a days, EIS finds applications in corrosion, biosensors, battery development, fuel cell development, drug cell membrane interaction [10], paint characterization, sensor development, polymers etc.

The development of organic proton conducting materials to substitute the per fluorinated polymers such as nafion is an important area of research in the field of fuel cell technologies [11–15]. Recent research in this field emerged some coordination polymers and metal-organic frame works (MOFs) for their proton transport capabilities, though the literature on these materials in other domains such as magnetism, catalysis, inclusion phenomenon and in supramolecular chemistry are quite extensive [16–23]. Under high humidity conditions or with water channels, MOFs show high degree of proton conductivities, comparable to nafion [24–28]. The proton conducting ability of these materials primarily depend on the existence of charge carrying molecular or ionic species such as H3O+ , OH�, or NH<sup>þ</sup> <sup>4</sup> Lewis acidic moieties. These molecular or ionic species with the complex network of hydrogen bonds or their arrangements with the water molecules play a vital role for proton conductivity. These characteristics are considered to be the important structural requirements of the proton conducting polymers and MOFs [29–33]. With the above-mentioned features, several new MOFs that exhibit Nafion-like proton conducting characters, under humidified and ambient temperature conditions have been reported [34]. The proton conducting ability of these materials was evaluated using EIS [34–36] which depends on humidity levels of the surroundings.

In this chapter, through an innovative approach we would like to propose a new method for the determination of molecular weight of compounds which are soluble in water and other protic solvents, using proton conducting ability of organic compounds or MOFs by EIS technique.
