Thermodynamics - Heat of Reaction

[Prathamesh]

Calculate the difference between heat of reaction at constant pressure and at constant volume for following reaction at 298 K.
N₂(g)+3H₂(g)→2NH₃(g)

My attempt ~
At constant pressure
ΔH_p=ΔU_p+PΔV

At constant volume
ΔH_v=ΔU_v

∴ΔH_p-ΔH_v
=ΔU_p-ΔU_v+ PΔV
And PΔV = ΔnRT
But what to do of ΔU_p-ΔU_v?
In solution,
For both , at constant pressure and volume
ΔU is mentioned and
ΔU-ΔU =0 is given..
But how is it possible that
ΔU_p=ΔU_v ?

 

[CrazyNinja]

Well, if you move from one state to another, it doesen't matter how you move. ΔU is zero anyway. So yes, ΔU_p = ΔU_v.

 

[Prathamesh]

Well, if you move from one state to another, it doesen't matter how you move. ΔU is zero anyway. So yes, ΔU_p = ΔU_v.

so, ΔH_p should also be equal to ΔH_v since it is a state function like internal energy U , why it is not so?

 

[TSny]

What thermodynamic state variables determine the internal energy of an ideal gas?

If you know this, then you should be able to compare the final internal energy for the constant pressure process with the final internal energy for the constant volume process.

 

[CrazyNinja]

so, ΔH_p should also be equal to ΔH_v since it is a state function like internal energy U , why it is not so?

ΔH is defined as the enthalpy change of a reaction at constant pressure and is a state function.. There is no such thing as ΔH_p and ΔH_v. What you must mean is Q_p and Q_v.

 

[TSny]

ΔH is defined as the enthalpy change of a reaction at constant pressure and is a state function.. There is no such thing as ΔH_p and ΔH_v. What you must mean is Q_p and Q_v.

ΔH is defined for any process between any two equilibrium states. As you say, H is a state variable. The process need not be at constant pressure in order to calculate ΔH.

 

[CrazyNinja]

ΔH is defined for any process between any two equilibrium states. As you say, H is a state variable. The process need not be at constant pressure in order to calculate ΔH.

To directly calculate ΔH, I agree the process need not be done at constant pressure. But ΔH is defined as such.

 

[Ygggdrasil]

To directly calculate ΔH, I agree the process need not be done at constant pressure. But ΔH is defined as such.

ΔH is not defined as the heat produced at constant pressure and temperature, though it is true that ΔH = q for such a process. H is most rigorously defined as H = U + PV.

Also a helpful note. Performing the reaction at constant temperature does not lead to the same final state as performing the reaction at constant volume. In one case, the final volume will be different and in the other case the final pressure will be different.

 

[TSny]

At constant volume
ΔH_v=ΔU_v

Is this true?

ΔH = Δ(U + PV) = ΔU + Δ(PV).

Does Δ(PV) equal 0 for the reaction at constant volume?

 

[CrazyNinja]

ΔH is not defined as the heat produced at constant pressure and temperature

Constant pressure and temprature @Ygggdrasil ?

 

[Chestermiller]

Constant pressure and temprature @Ygggdrasil ?

Yes. For tabulated heats of reaction, both the temperature and the pressure are specified to not change between the initial state of pure reactants and for the final state of pure products.

 

[CrazyNinja]

Yes. For tabulated heats of reaction, both the temperature and the pressure are specified to not change between the initial state of pure reactants and for the final state of pure products.

So basically we start at some T,P... do the reaction with reactant A... get product B... bring product B to the same state T,P... measure the heat exchanged... and label this as the heat of the reaction? OK, that actually makes sense.

 

[Chestermiller]

So basically we start at some T,P... do the reaction with reactant A... get product B... bring product B to the same state T,P... measure the heat exchanged... and label this as the heat of the reaction? OK, that actually makes sense.

Yes. That's basically right.