[SirMoses]

Ok, lets say we have a NaCl and water solution at a certain temperature (somewhere around room temp) and we know that it is saturated. How can I find the molarity or molality of the solution? I thought this would be simple and straight forward, but I can't recall any equation to do this. Any help is appreciated

[billnotgatez]

The WIKI has 2 tables on
http://en.wikipedia.org/wiki/Sodium_chloride

They compare reasonably with each other


portion of table on right
=====================================
Properties
Molecular formula    NaCl
Molar mass    58.44 g mol−1
Appearance    Colorless crystals
Odor    Odorless
Density    2.165 g cm−3
Melting point    

801 °C, 1074 K, 1474 °F
Boiling point    

1413 °C, 1686 K, 2575 °F
Solubility in water    359 g L−1
Solubility in ammonia    21.5 g L−1
Solubility in methanol    14.9 g L−1
Refractive index (nD)    1.5442 (at 589 nm)

Except where noted otherwise, data are given for materials in their standard state (at 25 °C, 100 kPa)
=====================================

Table within text
=====================================
Solubility of NaCl in various solvents
(g NaCl / 1 kg of solvent at 25 °C)[3]
H2O    360
Formamide    94
Glycerin    83
Propylene glycol    71
Formic acid    52
Liquid ammonia    30.2
Methanol    14
Ethanol    0.65
Dimethylformamide    0.4
1-Propanol    0.124
Sulfolane    0.05
1-Butanol    0.05
2-Propanol    0.03
1-Pentanol    0.018
Acetonitrile    0.003
Acetone    0.00042
=====================================

[SirMoses]

Yes, but is there a way to write the solubility as a function of temperature and such and theory to back it up? Of course I can look up tables, but lets say the temperature is farther off and I want to reduce error, what can I do? Oh yea, I didn't mention it, but assume standard pressure.

[Big-Daddy]

Yes, but is there a way to write the solubility as a function of temperature and such and theory to back it up? Of course I can look up tables, but lets say the temperature is farther off and I want to reduce error, what can I do? Oh yea, I didn't mention it, but assume standard pressure.

The solubility at saturation is given by the equilibrium constant K_sp, the solubility product, which you can easily look up. This governs the equilibrium:

NaCl (s)  Na⁺ (aq) + Cl^- (aq)

K_sp=[Na⁺ (aq)]·[Cl^- (aq)] (we neglect solids in any equilibria that involve solutions, so [NaCl (s)] becomes unity - it =1 and we needn't write it in) so as you can see, the greater the K_sp, the more NaCl would be fitted into the solution at the point of saturation. Molar solubility of NaCl in this solution = [Na⁺] or [Cl^-], take your pick, they will be the same, in which case you can write Molar Solubility[NaCl]²=K_sp and readily solve for Molar Solubility[NaCl].

K_sp is like any other equilibrium constant and we can model it in terms of the Gibbs' energy of the reaction, entropy and enthalpy. Find the entropy and enthalpy changes of your reactions, and the K_sp, and it will be easy to model changing Ksp (and, by extension, changing solubility) with temperature.

[Borek]

No way of solving the problem without tables of some kind. And the best table in this case is a table of NaCl solubilities vs temperature.

[Big-Daddy]

No way of solving the problem without tables of some kind. And the best table in this case is a table of NaCl solubilities vs temperature.

Why? Does K_sp, when the solution is saturated, not have the same temperature variance as any other equilibrium constant? i.e. ΔG^O=-R*T*log_e(K). And if we get K_sp at a certain temperature then the square root should just be the molar solubility ...

[Borek]

Where do you take Ksp from? Thin air, or tables?

[Big-Daddy]

Where do you take Ksp from? Thin air, or tables?

The dependence of most equilibria on temperature can be shown by log_e(K₂/K₁)=-(ΔH^O/R)*(1/T₂-1/T₁). This is ΔH^O so measured under standard conditions of 298.15 K and 1 bar pressure etc., so it does not have temperature variance. Therefore, why would you need a table? If you can find one value of the K_sp and the corresponding temperature, as well as the standard enthalpy change of solution for NaCl, then you should be able to calculate K_sp at any other temperature?

[Borek]

If you can find one value of the K_sp

Find where?

the standard enthalpy change of solution for NaCl

Find where?

[Big-Daddy]

If you can find one value of the K_sp

Find where?

the standard enthalpy change of solution for NaCl

Find where?

Yes you need 2 values but that's it, not a table. Doesn't matter which temperature your K_sp value that you found corresponds to, you can convert it by calculation to the K_sp at any other temperature that you like (only thing you need is the standard enthalpy and the universal gas constant). As for the standard enthalpy change of solution of NaCl, it is by definition of being "standard", constant.

[Corribus]

@BigDaddy

I think he's suggesting that you still need to look up a base value on a table in order to perform the temperature transformation you are referring to.

I would also like to point out that while you can predict the Ksp at any temperature in the way you are suggesting, it is only that: an estimate.  Theoretical projection is never better than a good experiment.  In the case of solubility, there are many things that could cause deviations from the "perfect" relationship between Ksp and temperature.  The particle size of the solute, for example, can affect the thermodynamics of dissolution, as can the crystal phase - which in turn is temperature dependent - and the properties of the solvent, which may change as a function of temperature.  Some solvents can have a significant change in polarity, density and so forth as temperature is changed, and these will all impact the solubility thermodynamics, which could cause significant deviations between predicts Ksp values and real ones.

The best way is to measure, and then use theory to understand, but measuring Ksp values is itself very difficult.  Best to look up data in a table if possible.

[Big-Daddy]

@BigDaddy

I think he's suggesting that you still need to look up a base value on a table in order to perform the temperature transformation you are referring to.

I would also like to point out that while you can predict the Ksp at any temperature in the way you are suggesting, it is only that: an estimate.  Theoretical projection is never better than a good experiment.  In the case of solubility, there are many things that could cause deviations from the "perfect" relationship between Ksp and temperature.  The particle size of the solute, for example, can affect the thermodynamics of dissolution, as can the crystal phase - which in turn is temperature dependent - and the properties of the solvent, which may change as a function of temperature.  Some solvents can have a significant change in polarity, density and so forth as temperature is changed, and these will all impact the solubility thermodynamics, which could cause significant deviations between predicts Ksp values and real ones.

The best way is to measure, and then use theory to understand, but measuring Ksp values is itself very difficult.  Best to look up data in a table if possible.

Fair enough, then it makes sense why you might use a table instead. I've been practising too much with calculations to keep a practical head

[billnotgatez]

http://users.stlcc.edu/gkrishnan/ksptable.html
@Big-Daddy
Is the above a table
It does not have Sodium chloride in it though

here is an interesting link as well
http://ph.answers.yahoo.com/question/index?qid=20100301012443AANqI90
Why are compounds such as sodium chloride not given ksp values

And here is another interesting link
http://www.funqa.com/chemistry/1892-2-chemistry-2.html

[Big-Daddy]

here is an interesting link as well
http://ph.answers.yahoo.com/question/index?qid=20100301012443AANqI90
Why are compounds such as sodium chloride not given ksp values

I don't understand why they aren't given K_sp values. Kf formation constants range from 10^-10 to 10⁵⁰, what's the issue with Ksp ranging from 10^-25 to 10¹⁰, for instance? And NaCl is not nearly 10¹⁰ mol²dm^-6 (nothing will be anywhere near that - in case of NaCl K_sp=10¹⁰ would suggest you could dissolve 5.8 tonnes of NaCl in a dm³ of water) but rather well under 10² mol²dm^-6. I don't see what the problem is, frankly. It seems to me that anyone who says 37.7, order of magnitude of less than 10², is "approaching infinity" is misinformed.

I suggest you can easily use Ksp values for this kind of calculation. They are experimental sums, they cannot be wrong (only your calculation or measurement of them might be wrong!).