I need your help

[popcorn]

On dilution of different amts. of H2SO4 in given volume of water, why doesn't the temp. of the resulting solution not vary linearly. Thankyou .

[CaptainPanic]

First: you have created 4 posts about this. I have put time in answering this... what happens when somebody finds the other post, and not this one? Perhaps this other nice person also puts time in it... which is a waste of time. Please post questions only once.

 

I've been searching for a formula in my thermodynamics books... but the short answer is:

 

The excess enthalpy (or heat of mixing) is described as:

[math]H^E=S^E\cdot{T}+G^E[/math]

 

The enthalpy change is also:

 

[math]\Delta{H}=C_P\cdot{\Delta{T}}[/math]

 

The values of [math]C_P, G^E, S^E [/math] are all functions of the concentration of the two compounds. The [math]C_P[/math] is linear with the concentration for the ideal case (and [ce]H2SO4[/ce] in water is most certainly not ideal!). So the non ideality is already a reason why it is not linear... But all other properties also aren't linear:

 

[math]G^E=G-\sum_i x_i G_i - RT\sum_i x_i \ln{x_i}[/math]

[math]S^E=S-\sum_i x_i S_i - R\sum_i x_i \ln{x_i}[/math]

 

The bottom line, as I understood from my thermodynamics book (Smith, Van Ness, Abbott) is: if you want to know the heat effect of mixing, measure it.

Edited September 24, 2008 by CaptainPanic
Complaining about posting a question 4 times on the forum

[John Cuthber]

Imagine that you add the acid in several lots. Say you add 1 gram of it first then another 1g and so on.

The first gram of acid is being mixed with water and reacts vigourously. The second gram is not reacting with water- it's reacting with dilute sulphuric acid. This reaction is less vigorous.

If you add enough acid then, in the end you are adding acid to something that's nearly pure acid already. That produces very little heat.

So each addition of acid gives rise to a different heat of reaction.

 

Just to complicate things further the heat from the first reaction goes into heating up nearly pure water. Water has a very high heat capacity. However all the subsequent aditions of acid are not heating water- they are heating dilute acid whic is likely to have a smaller heat capacity.

 

Confused yet?

OK not only is the second gram of acid reacting with something different and dissipating its heat into something different, but the stuff is now hot.

The heat capacity of water (or dilute acid) changes slightly with temperature.

 

So this stuff has 3 different reasons for being non linear.