What is the relationship between enthalpy of formation and temperature?

[joeyjo100]

I have been told that the hydrogen ion concentration of an acid in solution depends on temperature.



What exactly is this relationship?

Is there a formal equation that relates [H+] and temperature, as well as any other physical variables that may have an effect?

 

[SpectraCat]

Well, hydrogen ion concentration in water is described by a set of equilibria. Each equilibrium is characterized by an equilibrium "constant", which is defined at a set of standard conditions called the thermodynamic standard state (1 atm pressure, 25°C, 1 M concentration, etc). As you move away from those specific conditions, all of the equilibria will shift.

So, in order to write an equation for [H+] and determine it's temperature dependence, you need to specify the system you are working with. For example, if you are just considering the autoprotolysis of pure water, you have:

H₂O --> H⁺ + OH^- K_w=[H+][OH-]=10^-14 at 25°C. So we have [H+]=[OH-]=10^-1.

However at 100°C autoprotolysis equilibrium shifts toward the products, with K_w=10^-12, so [H+] and [OH-] are each an order of magnitude larger.

If you have a more complicated chemical system involving acids and/or bases, the behavior will be different, but the shift in [H+] with temperature can still often be predicted, at least qualitatively.

 

[Borek]

However at 100°C autoprotolysis equilibrium shifts toward the products, with K_w=10^-12

Full temperature/pKw table here: http://www.chembuddy.com/?left=pH-calculation&right=water-ion-product

 

[Norfonz]

ΔG = RTlnK

As you can see, there is relationship between free energy, temperature, and the equilibrium constant.

 

[ZealScience]

Yes, self-ionization constant Kw changes with temperature. Becaus Kw=10^-14 at rtp, and ΔG=-RT ln K=ΔH-TΔS. Then the relationship is written as the Van't Hoff's equation which is ln(K2/K1)=-(ΔH/R)(1/T2-1/T1). ΔH is always negative then when T2>T1 then the right side is negative K1>K2. Which means K is smaller at higher temp. then there are less ions in the solution at higher temperature. Both [H+] [OH-] would decrease.

PS I always make mistakes please check, before doing work.

 

[Borek]

Note: this is more complicated than just a Kw, as OP asked about acid solution. Ka of a particular acid doesn't have to grow with temperature, so I can imagine a solution in which Ka goes down while Kw goes up, and in effect pH stays constant in some temperature range (or grows, or goes down).

 

[SpectraCat]

Yes, self-ionization constant Kw changes with temperature. Becaus Kw=10^-14 at rtp, and ΔG=-RT ln K=ΔH-TΔS. Then the relationship is written as the Van't Hoff's equation which is ln(K2/K1)=-(ΔH/R)(1/T2-1/T1). ΔH is always negative then when T2>T1 then the right side is negative K1>K2. Which means K is smaller at higher temp. then there are less ions in the solution at higher temperature. Both [H+] [OH-] would decrease.

PS I always make mistakes please check, before doing work.

You have made a mistake again. Why would you say that ΔH is always negative? ΔH is the change in enthalpy associated with a given process. So let's assume that ΔH *is* actually negative for some chemical reaction ... what would the sign on ΔH be for the reverse reaction?

 

[joeyjo100]

Doesn't Kw change with temperature simply because the density of water changes with temperature.

As far as my knowledge stretches, the constant of Kw at room temperature arises from the equilibrium of the auto ionisation of water. Because the concentration of water is always constant, this was combined into the equilibrium constant of the process to form the new constant, Kw.

But surely this only holds at one temperature, as the assumption is that the concentration of water is constant due to its density of 1 gram per millilitre.

So when temperature increases, the density of water changes. Is not not where the variation of the value for Kw comes from?

 

[Borek]

Doesn't Kw change with temperature simply because the density of water changes with temperature.

Nice idea, but it doesn't hold water. Density changes are much smaller than Kw changes.

 

[ZealScience]

You have made a mistake again. Why would you say that ΔH is always negative? ΔH is the change in enthalpy associated with a given process. So let's assume that ΔH *is* actually negative for some chemical reaction ... what would the sign on ΔH be for the reverse reaction?

Sorry, I'm not quite sure, but I think ΔH here is the enthalpy of formation. Then the reverse reaction is no longer formation. So I mean enthalpy of formation is negative, because free energy of formation is calculated using ΔH formation. But I'm not quite sure whether using enthalpy change of formation is appropriate or not.