Concept of Absolute Thermodynamic Activity

AI Thread Summary
The concept of absolute thermodynamic activity, as presented in Newman's "Electrochemical Systems," defines chemical potential as a function of absolute activity, which is independent of the standard state. This contrasts with traditional definitions of activity that express how a component's thermodynamic activity relates to the standard state, as shown in equations involving fugacity ratios. The discussion highlights confusion over the derivation and implications of the absolute activity equation, particularly its departure from standard state references. The relationship between chemical potential and activity remains logarithmic, but the introduction of absolute activity raises questions about its practical application. Overall, the distinction between absolute and relative activity needs further clarification to reconcile these concepts in thermodynamics.
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: $$\mu_i=RT\ln(\lambda_i)\tag1$$

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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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.
I agree with your assessment.
 
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