# Can you make a solution under standard conditions?

1. Dec 10, 2011

### Confusus

This is coming from junior-level physical chemistry.

Lots of thermodynamic properties of reactions involving solutions are tabulated under standard conditions; I'm particularly thinking of standard half-cell voltages, but any property will do.

How do you make, say, a sodium chloride solution under those conditions?

My best understanding is that you can't. The definition of the standard state of both solute and solvent specifies (1) the pure solvent, which isn't in the sample, and (2) the solute with some hypothetical properties in the infinitely-dilute limit (as determined by the Henry's law constant).

So if my understanding here is correct, what does a standard state property involving solutions even mean? How would you make the solution(s) and measure that property?
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To be a little more concrete, think about it in terms of the equation for chemical potential: $$\mu_i = \mu_i^° + RT \ln a_i$$
to get standard conditions the solute must have activity = 1. The formula for activity breaks down to $$a_i = \gamma_i c_i/c^°$$
Its common to say "the standard concentration c° = 1 M" but you see in this equation that the nonideality plays a role in the activity coefficient, making the activity NOT unity, and the chemical potential not the standard value.

So what's going on?

Last edited: Dec 10, 2011
2. Dec 10, 2011

### Mike H

The standard state is a reference state, and is typically considered to be a hypothetical one that is arrived upon after taking the limit of a certain parameter. For example, the IUPAC definition of standard states includes that, for gases, the standard state of a gas is determined as if it is an ideal gas, which as we know is an approximation to the behavior of real gases.

So, practically speaking, you want to measure the properties of a number of solutions where one varies one of the parameters in order to extrapolate/calculate the standard state. As the aspiring comedians will note, the goal is to keep you from dividing by zero in any calculation one may ever have to do.

3. Dec 10, 2011

### Confusus

Thanks Mike H, that was a good reminder of something I knew/should have known. I get confused thinking about it each time it comes up.

Can you be a little more concrete? Let's say I wanted to measure the standard enthalpy change of dissolving sucrose in water. The standard states of pure water and pure sucrose are straight-forward. But the solution, what is its "standard state"? If I have this right, it is an imaginary sample where you have pure water in one beaker and an imaginary solution that obeys Henry's law (as if the solute were infinitely dilute) which defines its activity coefficient but at Molarity of the reciprocal of its activity coefficient, so that the solute has activity=1.

I still have a hard time wrapping my head around what series of experiments would lead to measuring the standard enthalpy of solution of sucrose, even if just in the limit of several related experiments as concentration changes.

Can anyone make that last point more clear?

Thanks again, Mike H

4. Dec 11, 2011

### Mike H

I'm not sure just how "concrete" a hypothetical state can be, given that one arrives at it by calculation, so I'm not sure if I can help out there without confusing the matter even more. As I said, it's an idealized notion which is intended to serve as a baseline of sorts when doing thermodynamic calculations. For example, the standard state quantities one sees in a standard general chemistry or physical chemistry textbook are most likely the ones at 298.15 K and 101.325 kPa (or thereabouts) - someone doing work in geochemistry is probably going to need the standard state quantities for salts at much higher temperatures & pressures.

But I can tell you how people measure these standard state thermodynamic quantities. To take your example of measuring enthalpies of solution....

There are these fairly cool calorimeters that let you place a known amount of compound in a bulb, submerse the bulb in solvent, and then trigger the bulb's breakage, and then the compound dissolves, and one measures the heat of solution from the compound dissolving in your solvent. One needs to correct for the volume change of the bulb breaking, any heat evolved from the bulb breakage, the change in vapor pressure, and so on. But once you've measured the heat of solution at your chosen concentrations, one can then calculate the enthalpy of solution.