# Concept of Absolute Thermodynamic Activity

• Dario56
In summary, the author of the textbook claims that absolute activity allows for the definition of chemical potential without reference to the standard state, as shown in equation 1. However, this concept does not align with the definition of activity in thermodynamics, which is defined as a relative quantity. This discrepancy raises questions about the derivation of equation 1 and its significance in the context of thermodynamics.
Dario56
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: $$\mu_i=RT\ln(\lambda_i)\tag1$$

where ##\lambda_i## is the absolute activity of the component ##i##. This equation is referenced to the Guggenheim: Thermodynamics textbook. I checked this textbook, but it didn't really resolve my questions.

Author claims that absolute activity allows us to define chemical potential without reference to the standard state, as it can be seen by the equation 1. This means that absolute activity is independent on the choice of the standard state.

What I know from thermodynamics is that activity is defined as a quantity which allows us to express chemical potential for real systems in the same mathematical form as for ideal systems. Chemical potential for real systems is logarithmic function of activity as it is a logarithmic function of pressure, mole fraction, concentration etc. for ideal systems.

In the most general form, activity is defined as: $$a_i = \frac {f_i}{f_i^⦵} \tag {2}$$

where ##f_i## is the fugacity of the component in the system and ##f_i^⦵## is the standard state fugacity of the component.

Definition of activity is fundamentally tied to the chemical potential and its definition equation can also be written as: $$\mu_i = \mu_i^⦵ + RTln \frac {f_i}{f_i^⦵} = \mu_i = \mu_i^⦵ + RTln(a_i) \tag {3}$$

My question is:

Concept of absolute activity doesn't make sense to me. Activity by definition expresses how much is a component thermodynamically active RELATIVE to the standard state. This is why equation 2 is written as a ratio and why in equation 3, standard state chemical potential ##\mu_i^⦵## shows up.

Given that, I don't understand equation 1 and where is it derived from as we can see a difference comparing equations 1 and 3.

Dario56 said:
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: $$\mu_i=RT\ln(\lambda_i)\tag1$$

where ##\lambda_i## is the absolute activity of the component ##i##. This equation is referenced to the Guggenheim: Thermodynamics textbook. I checked this textbook, but it didn't really resolve my questions.

Author claims that absolute activity allows us to define chemical potential without reference to the standard state, as it can be seen by the equation 1. This means that absolute activity is independent on the choice of the standard state.

What I know from thermodynamics is that activity is defined as a quantity which allows us to express chemical potential for real systems in the same mathematical form as for ideal systems. Chemical potential for real systems is logarithmic function of activity as it is a logarithmic function of pressure, mole fraction, concentration etc. for ideal systems.

In the most general form, activity is defined as: $$a_i = \frac {f_i}{f_i^⦵} \tag {2}$$

where ##f_i## is the fugacity of the component in the system and ##f_i^⦵## is the standard state fugacity of the component.

Definition of activity is fundamentally tied to the chemical potential and its definition equation can also be written as: $$\mu_i = \mu_i^⦵ + RTln \frac {f_i}{f_i^⦵} = \mu_i = \mu_i^⦵ + RTln(a_i) \tag {3}$$

My question is:

Concept of absolute activity doesn't make sense to me. Activity by definition expresses how much is a component thermodynamically active RELATIVE to the standard state. This is why equation 2 is written as a ratio and why in equation 3, standard state chemical potential ##\mu_i^⦵## shows up.

Given that, I don't understand equation 1 and where is it derived from as we can see a difference comparing equations 1 and 3.

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