[quantum-mechanic]

In the thermodynamics of solutions you learn that the standard reference state of a solute is an imaginary sample, one where the solution has a certain concentration yet has a vapor-pressure property referred to as satisfying Henry's Law which only actually holds in the limit of infinite dilution.

I'm trying to understand what this standard state is.  I'm getting hung up on the typical formula for chemical potential: (mu)

mu = mu^o + RT ln a

mu^o is the chemical potential in the standard state, and the activity (a) is in terms of the activity coefficient (gamma) , the concentration (c), and the standard concentration (c^o):

a = gamma * c/c^o

Usually c^o = 1M is by definition, and the activity must be a=1 to make the chemical potential hold its standard state value (as per above equation).   

But is a c = 1M solution actually the "standard state concentration"?  Can you even specify any one concentration as the standard state value for all solutions?  Obviously if  c = 1, then gamma = 1 must hold too to make the activity a = 1.  But gamma can't = 1 for all solutions at 1 M, because gamma = 1 implies perfect ideality.

So there is some contradiction here I can't solve.   Can any one help?

[juanrga]

In the thermodynamics of solutions you learn that the standard reference state of a solute is an imaginary sample, one where the solution has a certain concentration yet has a vapor-pressure property referred to as satisfying Henry's Law which only actually holds in the limit of infinite dilution.

I'm trying to understand what this standard state is.  I'm getting hung up on the typical formula for chemical potential: (mu)

mu = mu^o + RT ln a

mu^o is the chemical potential in the standard state, and the activity (a) is in terms of the activity coefficient (gamma) , the concentration (c), and the standard concentration (c^o):

a = gamma * c/c^o

Usually c^o = 1M is by definition, and the activity must be a=1 to make the chemical potential hold its standard state value (as per above equation).  

But is a c = 1M solution actually the "standard state concentration"?  Can you even specify any one concentration as the standard state value for all solutions?  Obviously if  c = 1, then gamma = 1 must hold too to make the activity a = 1.  But gamma can't = 1 for all solutions at 1 M, because gamma = 1 implies perfect ideality.

So there is some contradiction here I can't solve.   Can any one help?

I do not understand well what you are asking.

a = 1 implies (gamma * c/c^o) = 1; that is, any solution for which c = (c^o/gamma) is in a standard state and has a chemical potential equal to the standard.

Only for an ideal solution gamma = 1. The standard state of a dilute solution is a hypothetical solution of concentration c^o = 1M which shows ideal behavior (also referred to as "infinite-dilution" behavior).

[quantum-mechanic]

a = 1 implies (gamma * c/c^o) = 1; that is, any solution for which c = (c^o/gamma) is in a standard state and has a chemical potential equal to the standard.

Only for an ideal solution gamma = 1. The standard state of a dilute solution is a hypothetical solution of concentration c^o = 1M which shows ideal behavior (also referred to as "infinite-dilution" behavior).

Thanks for the reply, juanrga.

I think my confusion might be that people "overload" the symbol for standard state.  It is common to say " the standard state molarity is 1 M" by which they mean c^o=1 M by definition.   But an actual solution you might make as c = 1 M can't possibly be in the standard state (unless it was ideal) because you need c = 1/gamma [M] to provide activity=1.    Do you think this observation is correct?

[juanrga]

a = 1 implies (gamma * c/c^o) = 1; that is, any solution for which c = (c^o/gamma) is in a standard state and has a chemical potential equal to the standard.

Only for an ideal solution gamma = 1. The standard state of a dilute solution is a hypothetical solution of concentration c^o = 1M which shows ideal behavior (also referred to as "infinite-dilution" behavior).

Thanks for the reply, juanrga.

I think my confusion might be that people "overload" the symbol for standard state.  It is common to say " the standard state molarity is 1 M" by which they mean c^o=1 M by definition.   But an actual solution you might make as c = 1 M can't possibly be in the standard state (unless it was ideal) because you need c = 1/gamma [M] to provide activity=1.    Do you think this observation is correct?

Good point, a concentration c = c^o = 1M does not implies that the actual solution is standard unless gamma = 1.

Maybe it would be better to substitute the above definition of the chemical potential by

mu = mu^o + RT ln (gamma * c/1M)

for avoiding that "overload" of the symbol for standard state. In this way a standard solution is defined as one for the which a = a^o = 1, which reduces to c = c^o = 1 M only for an ideal solution.

Thank you for this interesting discussion. I will think more about .

[quantum-mechanic]

Thanks for replying again.  I'm glad this makes "sense" to someone else too.  I haven't seen any p-chem books that make this clear. 

[bumperstickers]

Elements in their standard states are considered to have chemical potentials and enthalpies of 0, or

The standard state of an element is its natural state at 1 atom pressure, 25oC.

By defining the free energy of the elements in this way, we can regard any compound as having a chemical potential (partial free energy), or an enthalpy of formation, composed of the sum of all changes in chemical potential (or of enthalpy) for the reactions leading to its formation, by any convenient path. Since free energy and enthalpy are variables of state, the value is a unique function of the state, so this approach can be used to define the the relative energy content of any chemical system by reference to the work needed to get there starting from the elements.