Reaction enthelpy at non-standard conditions

[giokara]

Hi

I am tutoring a pupil in high-school out of necessity (no other teachers avail), while I am not so acquainted anymore with chemistry. The pupil showed me a question concerning the calculation of the reaction enthalpy which looked somewhat as follows:

1. Problem statement, all variables and given/known data

Calculate the reaction-enthalpy for the reaction:

$C_3H_8 (g) + 5O_2 (g) \rightarrow 3CO_2 (g) + 4H_2O (g)$

at 30$^\mathrm{o}$C and 1.08 atm.
The formation enthalpies at standard conditions and the heat capacities at constant pressure were known.

Homework Equations

The Attempt at a Solution

NOTE: I am not sure anymore about the exact reaction or the exact temperature and pressure, the above is meant as a generic example of the exercise that the pupil showed me.

As I remember, first the formation enthalpies at the non-standard conditions should be computed. This should be done in two steps:

1) Take into account the increase in temperature assuming constant pressure: use $\Delta H = C_p\Delta T$.
2) Take into account the increase in pressure assuming constant temperature.

I cannot remember how the second step should be computed, neither did I find some appropriate formula during a quick search.
Is the current approach the correct one? Could it be possible to give me some more information about how to proceed?

Thanks in advance
Giorgos

 

[Chestermiller]

Hi

I am tutoring a pupil in high-school out of necessity (no other teachers avail), while I am not so acquainted anymore with chemistry. The pupil showed me a question concerning the calculation of the reaction enthalpy which looked somewhat as follows:

1. Problem statement, all variables and given/known data

Calculate the reaction-enthalpy for the reaction:

$C_3H_8 (g) + 5O_2 (g) \rightarrow 3CO_2 (g) + 4H_2O (g)$

at 30$^\mathrm{o}$C and 1.08 atm.
The formation enthalpies at standard conditions and the heat capacities at constant pressure were known.

Homework Equations

The Attempt at a Solution

NOTE: I am not sure anymore about the exact reaction or the exact temperature and pressure, the above is meant as a generic example of the exercise that the pupil showed me.

As I remember, first the formation enthalpies at the non-standard conditions should be computed. This should be done in two steps:

1) Take into account the increase in temperature assuming constant pressure: use $\Delta H = C_p\Delta T$.
2) Take into account the increase in pressure assuming constant temperature.

I cannot remember how the second step should be computed, neither did I find some appropriate formula during a quick search.
Is the current approach the correct one? Could it be possible to give me some more information about how to proceed?

Thanks in advance
Giorgos

Yes. Your methodology is correct. As far as the pressure effect is concerned, it is hard to imagine how the pressure correction could be significant at that pressure and with that pressure change.

If you still want to get the pressure correction, you calculate the molar enthalpy change for each of the species individually (as a pure species) using:
$$\frac{∂H}{∂P}=(V-T\frac{∂V}{∂T})dP$$
To do this calculation, you need to know the PVT behavior of each pure species slightly beyond the ideal gas range (with an equation of state). Probably, Van Der Waals would be adequate, but you need to know the Van Der Waals parameters for each species). In my judgement, it's not worth the effort.

Chet

 

[giokara]

Hi Chet,

Thanks for your answer.
The pressure change is indeed minimal, and I had difficulties understanding how this is relevant at high-school level.
But I'm glad I understand how it should be taken into account.

Giorgos