Proton affinity via. Born Haber cycle

[jbowers9]

I'm baaaaack...
Is this the correct way to procede
1. The problem statement, all variables and given/known d

The Born Haber cycle for the process was given as follows:
........U
......NH4Cl(s) → NH4+ + Cl-
......↑......↓.....P(NH3)
......↑......NH3 + H+ + Cl-
......↑......↓.....-IH + ECl
1/2N2(g) + 2H2(g) + 1/2Cl2(g) → NH3 + H + Cl
where;
lattice energy/mole NH4CL U = 640kj/mol, ionization energy/mole hydrogen atoms IH = 1305kj/mol, electron affinity/mole ECL = 387kj/mol, heat of formation for NH3 = -45.6kj/mol, heat of formation for NH4Cl = -314.2

Homework Equations

-U......NH4+ + Cl- → NH4Cl(s)
-∆ƒHºmNH4Cl...NH4Cl(s) → 1/2N2(g) + 2H2(g) + 1/2Cl2(g)
∆ƒHºmNH3...2N2(g) + 3/2H2(g) → NH3(g)
∆ƒHºmH......1/2H2(g) → H(g)
∆ƒHºmCl......1/2Cl2(g) → Cl(g)
IH - ECl...NH3(g) + H(g) + Cl(g) → NH3(g) + H+ + Cl-
- P(NH3)...NH3(g) + H+ + Cl- → NH4+ + Cl-

The Attempt at a Solution

All added entities should sum to zero if the cyclical process is reversible, no?
You're ending where you began.

U - ∆ƒHºmNH4Cl + ∆ƒHºmNH3 + ∆ƒHºmH + ∆ƒHºmCl + IH - ECl =

P(NH3) = 2761 kJ/mol

 

[jbowers9]

The original question wanted proton affinities @ 0*C.
The values for U, I, & E and the heats of formation for ammonium chloride and ammonia are from the statement of the problem and presumably are for 0*C. But the only reference to temperature is in the beginning of the problem statement where it says the proton affinity can be calculated @ 0*C.
How do Imust I correct the heats of formation for H and Cl? There's a table in this chapter containing coefficients for heat capacity. But the coefficients list H2 and Cl2 only. Wher would I get H and Cl coefficients. I would need them to correct for 0*C. (Cppro. - Cpreac.)dT

 

[Gokul43201]

Can you write down the (text part of the) original question exactly as it was given to you? The diagram above is fine. Your general logic (using Hess' Law) seems fine, but I haven't looked at the numbers.

Nevertheless, I've got several problems with this problem:

1. The proton affinity is defined as the standard enthalpy per mole of the protonation reaction, and is hence defined at T=298K. So the instruction about using T=273 is very important. Please write it down exactly as you have it.

2. All other standard enthalpies are also defined at T=298K, so if the values given to you are meant to be for 273K, they are no longer "standard". This means you shouldn't be writing $\Delta H^0$, when in fact you mean $\Delta H(T=273K)$. I, on the other hand, suspect that the values given to you are indeed standard values. But this would make the (alleged) statement about proton affinity at T=273K quite idiotic.

3. Since the question provides all data except for the formation enthalpies of H and Cl (or the H-H and Cl-Cl bond energies), one would imagine you are expected to solve the problem without requiring this data (though I don't see how that's possible). Else, it's quite tasteless of the source to provide a partial list of data.

4. If everything is indeed as you've interpreted and you need to find the formation enthalpies of H and Cl at T=273, then as you say, you need Cp values for H and Cl if you want to get an exact answer. A quick estimate tells you that the correction is going to be small (<1kJ), and not worth the trouble. If you still want to do this, simply use the value of Cp for a monoatomic ideal gas (Cp=2.5R) and this approximation should cut the error down to no worse than a few tens of Joules..

 

[jbowers9]

Ex Libris: verbatim
The "proton affinity," P, of a substance such as NH3, is defined as the change in energy for the reaction

NH4(+)g = NH3g + H(+)g

P(NH3) at 0 K can be computed from other thermal data through consideration of an appropriate Born-Haber cycle (all substances except NH4Cl being gases):

.......U
......NH4Cl(s) → NH4+ + Cl-
......↑......↓...P(NH3)
......↑......NH3 + H+ + Cl-
......↑......↓...-IH + ECl
1/2N2(g) + 2H2(g) + 1/2Cl2(g) ← NH3 + H + Cl

in which U represents the lattice energy per mole of crystalline NH4Cl, IH the ionization energy of a mole of hydrogen atoms, and ECL the electron affinity of a mole of chlorine atoms. The values of these quantities are (in kJ mol-1) 640, 1305, and 387.0, respectively. Using -314.2 kJ mol-1 as the enthalpy of formation of NH4Cls and -45.6 kJ mol-1 as the enthalpy of formation of NH3g, and finding any other quantities you need from tables in this chapter, calculate P(NH3).