# 8.1: Electrolyte Solution Nomenclature

Biological and many chemical systems are aqueous. The rates of most biochemical reactions are dependent upon the concentration of the ions in the system. Most biological systems involve the presence of electrolytes, or substances that when dissolved in a solvent (usually water) will produce a system that conducts electricity.

### Introduction

Solutions found in nature, therefore, do not behave ideally, meaning it is necessary to describe this ‘non-ideal’ behavior with a new mathematical formula.Consider an electrolyte solution:

$$\mathrm{M}_{z+}\mathrm{X}_{z-} \longrightarrow z_+\mathrm{M}^{(z_-)+}+z_-\mathrm{X}^{(z_+)-}$$

$$\mu=z_+ \mu_+ + z_- \mu_-$$
$$= z_+ \left( \mu_+^\mathrm{o} + RT \ln m_+ \right) + z_- \left( \mu_-^\mathrm{o} + RT \ln m_- \right)$$
$$= \left( z_+ \mu_+^\mathrm{o} + z_- \mu_-^\mathrm{o} \right) + RT \ln \left( m_+^{z_+} m_-^{z_-} \right)$$
$$= \left( z_+ \mu_+^\mathrm{o} + z_- \mu_-^\mathrm{o} \right) + RT \ln \left( ( \gamma_+ m_+ )^{z_+} ( \gamma_- m_- )^{z_-} \right)$$
$$= \left( z_+ \mu_+^\mathrm{o} + z_- \mu_-^\mathrm{o} \right) + RT \ln \left( a_+^{z_+} a_-^{z_-} \right)$$
$$= \left( z_+ \mu_+^\mathrm{o} + z_- \mu_-^\mathrm{o} \right) + RT \ln a$$

 $$\mu_+^\mathrm{o}$$ and $$\mu_-^\mathrm{o}$$ standard state chemical potentials for their respective electrolyte species $$\mu_+$$ and $$\mu_-$$ chemical potentials for their respective electrolyte species $$a$$ electrolyte activity $$R$$ gas constant, 8.314 J/(mol * K) $$T$$ temperature (K) of the electrolyte solution $$z_+$$ cationic charge of the electrolyte for $$\gamma_\pm$$ $$z_-$$ anionic charge of the electrolyte for $$\gamma_\pm$$ $$m$$ molality of the electrolyte solution
 where and $$a = a_\pm^z$$ $$a_\pm = \left(a_+^{z_+} a_-^{z_-}\right) ^{1/z}$$ mean ionic activity $$z = z_+ + z_-$$ $$\gamma_\pm = \left(\gamma_+^{z_+} \gamma_-^{z_-} \right) ^{1/z}$$ mean ionic activity coefficent $$a_\pm = \gamma_\pm m_\pm$$ $$m_\pm = \left(m_+^{z_+} m_-^{z_-} \right) ^{1/z}$$ mean ionic molality

### Example

$$\mathrm{Mg}\mathrm{Cl}_{2} \longrightarrow (1)\mathrm{Mg}^{(2)+} + (2) \mathrm{Cl}^{(1)-}$$

$$\mu=\left( 1 \right) \mu_\mathrm{Mg^{2+}} + \left( 2 \right) \mu_\mathrm{Cl^{1-}}$$
$$= 1 \left( \mu_\mathrm{Mg^{2+}}^\mathrm{o} + RT \ln m_\mathrm{Mg^{2+}} \right) + 2 \left( \mu_\mathrm{Cl^{1-}}^\mathrm{o} + RT \ln m_\mathrm{Cl^{1-}} \right)$$
$$= \left( 1 \mu_\mathrm{Mg^{2+}}^\mathrm{o} + 2 \mu_\mathrm{Cl^{1-}}^\mathrm{o} \right) + RT \ln \left( m_\mathrm{Mg^{2+}}^{1} m_\mathrm{Cl^{1-}}^{2} \right)$$
$$= \left( 1 \mu_\mathrm{Mg^{2+}}^\mathrm{o} + 2 \mu_\mathrm{Cl^{1-}}^\mathrm{o} \right) + RT \ln \left( ( \gamma_\mathrm{Mg^{2+}} m_\mathrm{Mg^{2+}} )^{1} ( \gamma_\mathrm{Cl^{1-}} m_\mathrm{Cl^{1-}} )^{2} \right)$$
$$= \left( 1 \mu_\mathrm{Mg^{2+}}^\mathrm{o} + 2 \mu_\mathrm{Cl^{1-}}^\mathrm{o} \right) + RT \ln \left( a_\mathrm{Mg^{2+}}^{1} a_\mathrm{Cl^{1-}}^{2} \right)$$
$$= \left( 1 \mu_\mathrm{Mg^{2+}}^\mathrm{o} + 2 \mu_\mathrm{Cl^{1-}}^\mathrm{o} \right) + RT \ln a$$