[eyenir]

Given the reaction between ${CH_{3}COOH_{(l)}}$ and ${NaHCO_{3_{(s)}}}$ which happens in same pressure but in different temperatures, is there any way to mathematically compare between the rate of reactions?

I thought using the rate equations of order 2 (as described in http://en.wikipedia.org/wiki/Rate_equation) but I use the same concentration of materials. Suppose I could have find the connection between temperature of material and its concentration, I would be able to find my requested rate-indicators.

Do anybody have any ideas how to find the connection between temp. and concentration in acid-base reactions or how to describe the rate of the reaction more exactly? (Every PDE/ODE are accepted).

[Borek]

Suppose I could have find the connection between temperature of material and its concentration

No such connection.

The only viable approach is to measure the reaction rate experimentally.

In general acid/base reactions are quite fast, my bet is that its the gas evolution that is a limiting factor here.

[eyenir]

So the only way to measure the rate of reaction is to measure the gas emission per minute ?

I found out in wikipedia that I can use Arrhenius equation (http://en.wikipedia.org/wiki/Arrhenius_equation) but I wonder how can I find E_a and A for CH₃COOH_(l) ?

[Borek]

how can I find E_a and A for CH₃COOH_(l) ?

Measuring reaction rate at different temperatures and fitting parameters to the experimental data.

[Corribus]

Both rate laws and the Arrhenius equation are semi-empirical. I.e., they are not formulated from first principles considerations and require experimental data for parameters to be determined. The Arrhenius equation has, since it was first devised, been derived from first principles but even so it's still considered an empirical relation. Chemical kinetics in general is mostly an empirical science because so much of it depends on the reaction mechanism. In principle if you know the mechanism you can predict kinetics theoretically, but this is not the order in which things are usually done... experimental kinetic data are used to determine the mechanism, not the other way around. So in general: no, just writing a reaction equation down is not sufficient to determine the kinetics using any rate expression.