# Debye Huckel Equation

## What is a Debye Huckel Equation?

The Debye Huckel equation is a mathematical expression developed to explain certain properties of electrolyte solutions, or substances found in solutions in the form of charged particles (ions). The Debye Huckel equation accounts for the interactions between the different ions, which are the primary cause of differences between the properties of dilute electrolyte solutions and those of so-called ideal solutions.

### Introduction

The entropy, rather than the enthalpy, drives the mixing of the solutions. By definition, while an ideal gas does not have the interactions between particles, an ideal solution assumes that there are interactions. Without interactions, the solution would not be in the liquid phase. Rather, the ideal solutions can be defined as having an enthalpy of either mixing or enthalpy of the solution, which is equal to zero (ΔHmixing or ΔHsolution = 0).

Since the interactions between the two liquids, A-B, are calculated as the sum of the A-A and B-B interactions, this is the case. The average A-A and B-B interactions are similar in the ideal solution, so there is no distinction between the average A-B and the A-A/B-B interactions.

Since in chemistry and biology, the average interactions between A and B are not always equivalent to the interactions of A or B alone, the enthalpy of mixing is not zero. As a result, a new definition for the concentration of molecules in solution has emerged. The effective concentration, a1, is calculated by taking into account the deviation from ideal action, with the operation of the ideal solution equal to one.

To convert from the mole fraction of the solute, x1 (as the unit of concentration, mole fraction can be determined from other concentration units like molality, molarity, or percent by weight) to activity, a1, an activity coefficient, 1, is used.

a₁ = γ₁x₁

### Debye Huckel Limiting Law

See Debye–Hückel theory for the concepts that were used to derive this equation.

To measure the activity a$_{C}$ of an ion C in a solution, the concentration and activity coefficient must be known:

a$_{C}$ = γ $\frac{[C]}{[C^{\Theta}]}$,

This is also called the debye huckel limiting law equation.

Where,

γ is given as the activity coefficient of C,

[C] is the measure of concentration of C,

[C$^{\Theta}$] is given as the concentration of chosen standard state, for example, 1 mol/kg if molality is used.

Dividing [C] with [C$^{\Theta}$] gives the dimensionless quantity.

The Debye–Hückel limiting law can be used to calculate an ion's activity coefficient in a dilute solution with a known ionic power. The following is the equation:

ln(γ₁) = $\frac{Z_{i}^{2}q^{2}k}{8 \prod \epsilon_{r} \epsilon_{0} k_{b} T}$ = - $\frac{Z_{i}^{2}q^{3}N_{A}^{1/2}}{4\prod (\epsilon_{r} \epsilon_{0} k_{B}T)^{3/2}}$ $\sqrt{10^{3} \frac{1}{2}}$ = - AZ$_{i}^{2}$$\sqrt{I}$

where

Z$_{i}$ is given as the charge number of ion species i,

q is given as the elementary charge,

k is given as the  inverse of the Debye screening length,

$\epsilon_{0}$ is the permittivity of free space,

$\epsilon_{r}$ is given as the relative permittivity of the solvent,

k$_{B}$ is given as the Boltzmann constant,

T is given as the temperature of the solution,

I is the ionic strength of the solution,

N$_{A}$ is given as the Avogadro constant,

And A is the constant that is completely based on the temperature.

The scientists have determined that it is not that simple because the things such as the sizes of the ions including the amount of charge that they contain may affect properties like conductivity. This equation is their attempt to account for certain variables when assessing an ionic behaviour of the compound.

### Experimental Verification of the Theory

Several experimental methods for calculating activity coefficients have been tried to check the validity of Debye–Hückel theory: the main problem is that we need extremely high dilutions. Measurements of the freezing point, vapour pressure, osmotic pressure (which is an indirect method), and electric potential in cells are just a few examples (which is a direct method).

Using liquid membrane cells, it was possible to examine the aqueous media 104 M at high dilutions and obtain good results and it also has been found that for the ratio 1:1 electrolytes (as either KCl or NaCl) the Debye–Hückel equation is completely correct, but for the ratio 2:2 or 3:2 electrolytes it can be possible to find the negative deviation from Debye–Hückel limit law: this strange behavior may be noticed only in the very dilute area, and in many concentrate regions the deviation becomes positive.

It is also possible that Debye–Hückel equation is unable to foresee this particular behavior because of the linearization of Poisson–Boltzmann equation, or may be not: about this, studies have been started only during the last years of the 20th-century because prior to it, it was not possible to investigate the region of 10−4 M, so it can be possible that during the next years new theories will be come up.

1. Give an Intuitive Explanation of the Debye Huckel Theory?

Answer: When the ionic salts are dissolved in water, they will dissociate into their anion and cation components. This allows them theoretically to conduct the electricity by providing the charged path via solution.

2. Give the Significance of the Debye Onsager Equation?

Answer: This equation shows how the conductivity, the parameter, can be used either to study the rate of reaction of the electrolyte solutions or to determine the dissociation constant for the weak electrolytes (debye huckel theory of strong electrolytes), depending on the electrolytes interactions including their concentration in a solution. Specifically, this theory is applied for the non-ideality cases.

3. What is the Hjulstrom Curve?

Answer: The Hjulström curve is named after Filip Hjulström, a geologist and hydrologist who used a graph to decide whether a river can transport, erode, or deposit sediment.

4. What is the Nernst Equation?

Answer: Nernst equation is the equation, which relates the reduction potential of an electrochemical reaction (which is either half-cell or the full cell reaction) to the standard electrode potential, temperature, and the activities of chemical species undergoing both oxidation and reduction.