Standard Activity in Electrochemistry

In summary, the textbook Electrochemical Systems by Newman and Alyea chapter 14 has a definition of chemical potential as a function of absolute activity. It is important to note that this chemical potential is relative to a state of pure component at the temperature and pressure of the system, and can be expressed in a familiar way as a function of activity. Next, it is explained that standard activity is a proportionality constant that is independent of composition and electrical state, but dependent on temperature, pressure and solute type. However, by definition, this value always remains equal to 1. Finally, equation 5 can be written in terms of molarity by adding RTln(M(solvent)) to the previous value of standard activity.
  • #1
Dario56
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In the textbook Electrochemical Systems by Newman and Alyea, chapter 14: The definition of some thermodynamic functions, chemical potential of component (ionic or neutral) is written as a function of absolute activity: $$ \mu_i = RTln(\lambda_i) \tag {1} $$

where ##\lambda_i## is the absolute activity of the component ##i##.

What I know from thermodynamics is the following: $$ \mu_i = \mu_i ^⦵ + RTln \frac { f_i}{f_i ^⦵} = \mu_i ^⦵ + RT ln\frac {a_i}{a_i ^⦵} \tag{2}$$

where ##f_i## and ##f_i^⦵$## are partial and standard fugacities of component, respectively. It is important to note that ##a_i = \frac {f_i}{f_i^⦵}## and ##a_i ^⦵ = 1##.

Since we don't know the values of chemical potential, we can express them relatively to the standard state if we take that chemical potential at standard state is equal to zero: $$ \mu_i = RTln(a_i) = RTln(\lambda_i)\tag {3} $$

This is all well and good.

For mixtures in general (solutions of electrolytes are mixtures), standard state of the component is usually taken as a state of pure component at the temperature and pressure of the system (pure liquid for solvent or pure solid for solute). Choice of such standard state allows us to express chemical potential of the component in a mixture as a function of activity in a familiar way: $$ \mu_i = \mu_i ^⦵ + RT ln (x_i \gamma_i) \tag {4}$$

where ##\gamma_i## is the activity coefficient of the component ##i##. It is also evident that ##a_i = x_i \gamma_i##.

If solution is diluted than mole fractions are directly proportional to the molarity of the component ##m_i## (##m_i = \frac {x_i}{M(Solvent)})##

This allows us to express equation 5 in terms of molarity: $$\mu_i = \mu_i ^⦵ + RTln(m_i\gamma_i M(solvent)) \tag{5} $$

Standard state chemical potential is now redefined as we add ##RTln(M(solvent))## to its previous value and refers to the state of ideal solution with unit molarity: $$ \mu_i = \mu_i^{⦵'} + RTln(m_i \gamma_i) \tag{6} $$

Comparing with equation 2 we can write: $$ \frac {a_i}{a_i ^⦵} = \frac {\lambda_i}{\lambda_i ^⦵} = m_i \gamma_i \tag{7} $$

Next equation is written: $$ \lambda_i = m_i\gamma_i \lambda_i ^⦵ \tag {8} $$

In the textbook, it is explained that standard activity ##\lambda_i ^⦵## is a proportionality constant independent of composition and electrical state, but dependent on temperature, pressure and solute type. However, by definition of activity this value should always be equal to 1 and thus independent on any variable. Standard fugacity doesn't need to be equal to 1, but activity must be since ##\lambda_i ^⦵ = \frac {f_i^⦵}{f_i ^⦵}##, as far as my knowledge of thermodynamics goes.
 
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  • #2
mi as you define it is molality, not molarity.
 
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  • #3
mjc123 said:
mi as you define it is molality, not molarity.
Yep, that's a mistake. It is clear what is meant, though.
 

FAQ: Standard Activity in Electrochemistry

What is standard activity in electrochemistry?

Standard activity in electrochemistry refers to the reference state of a substance in a given phase, typically set to a value of 1. This standard state is used as a baseline to measure and compare the activities of substances under different conditions. For example, the standard activity of a pure solid or liquid is 1, and for ions in solution, it is often based on a 1 molar concentration.

Why is standard activity important in electrochemistry?

Standard activity is crucial because it allows for the comparison of electrochemical potentials under consistent conditions. This standardization is essential for accurately predicting and comparing the behavior of electrochemical cells, reactions, and processes. It provides a common reference point, making it easier to understand and communicate experimental results.

How is standard activity related to the Nernst equation?

The Nernst equation uses standard activity to calculate the actual cell potential under non-standard conditions. By incorporating the activities of the reactants and products, the Nernst equation adjusts the standard electrode potential to account for real-world concentrations and pressures, providing a more accurate prediction of cell behavior.

What is the standard state for gases in electrochemistry?

The standard state for gases in electrochemistry is typically defined as 1 bar of pressure. This standard state is used to establish the standard activity of gases, which is set to 1 when the gas is at 1 bar pressure. This helps in simplifying calculations and comparisons of electrochemical reactions involving gases.

How do you determine the standard activity of ions in solution?

The standard activity of ions in solution is usually based on a 1 molar concentration. In practice, activity coefficients are used to account for deviations from ideal behavior at different concentrations. For dilute solutions, the activity of an ion can be approximated by its concentration, but for more concentrated solutions, the activity coefficient must be considered to accurately determine the ion's activity.

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