Why Do Hess's Law Calculations Show Discrepancies in Enthalpy Values?

[mrxtothaz]

Homework Statement

I have been provided with the results of a lab:

Reaction 1:
NaOH(s) --> Na⁺(aq) + OH^-(aq)
Reaction 2:
Na⁺(aq) + OH^-(aq) + H⁺(aq) + Cl^-(aq) --> H2O(l) + Na⁺(aq) + Cl^-(aq)
OH^-(aq) + H⁺(aq) --> H2O(l)
Reaction 3:
NaOH(s) + H⁺(aq) + Cl^-(aq) --> H2O(l) + Na⁺(aq) + Cl^-(aq)
NaOH(s) + H⁺(aq) --> H2O(l) + Na⁺(aq)

The enthalpies for each reaction:
∆H°r: -5.80 kJ (Reaction 1)
∆H°r: -5.06 kJ (Reaction 2)
∆H°r: -16.7 kJ (Reaction 3)

I have been asked to add the equations of 1 and 2 (Hess's Law), and to compare the sum with equation 3.

Homework Equations

Hess's Law.

The Attempt at a Solution

NaOH(s) --> Na⁺(aq) + OH^-(aq) ∆H°r: -5.80 kJ (Reaction 1)
OH^-(aq) + H⁺(aq) --> H2O(l) ∆H°r: -5.06 kJ (Reaction 2)

NaOH(s) + H⁺(aq) + OH^-(aq) --> Na⁺(aq) + H2O(l) + OH^-(aq) ∆H°r: -10.9 kJ (Reaction 1+2 intermediate)

NaOH(s) + H⁺(aq) --> Na⁺(aq) + H2O(l) ∆H°r: -10.9 kJ (Reaction 1+2)

NaOH(s) + H⁺(aq) --> Na⁺(aq) + H2O(l) ∆H°r: -16.7 kJ (Reaction 3)

So, as can be seen, the equations for reactions 1&2 are added and are identical to that of reaction 3. However, the enthalpies of reaction are way different. I do not know how I can account for this steep a difference, as all the lab results were provided with the question. The only difference is that, in the addition of reactions 1&2, there was a hydroxide ion on both sides of the equation that was canceled out (since I was asked for the net ionic equations for each reaction). Could this account for the difference, or does it have no role in the enthalpy of reaction, given that it is a spectator ion?

If I did nothing wrong, I suspect I am supposed to identify this discrepancy between reaction 1+2 with reaction 3.

 

[mrxtothaz]

I'm looking into possible sources of error; the only thing I can think of is that the experimenters assumed the specific heat capacity of each solution to be same as that of water? As with density.

Could this account for the discrepancy?

 

[chemisttree]

Homework Statement

I have been provided with the results of a lab:

Reaction 1:
NaOH(s) --> Na⁺(aq) + OH^-(aq)
Reaction 2:
Na⁺(aq) + OH^-(aq) + H⁺(aq) + Cl^-(aq) --> H2O(l) + Na⁺(aq) + Cl^-(aq)
OH^-(aq) + H⁺(aq) --> H2O(l)
Reaction 3:
NaOH(s) + H⁺(aq) + Cl^-(aq) --> H2O(l) + Na⁺(aq) + Cl^-(aq)
NaOH(s) + H⁺(aq) --> H2O(l) + Na⁺(aq)

The enthalpies for each reaction:
∆H°r: -5.80 kJ (Reaction 1)
∆H°r: -5.06 kJ (Reaction 2)
∆H°r: -16.7 kJ (Reaction 3)

I have been asked to add the equations of 1 and 2 (Hess's Law), and to compare the sum with equation 3.

Homework Equations

Hess's Law.

The Attempt at a Solution

NaOH(s) --> Na⁺(aq) + OH^-(aq) ∆H°r: -5.80 kJ (Reaction 1)
OH^-(aq) + H⁺(aq) --> H2O(l) ∆H°r: -5.06 kJ (Reaction 2)

NaOH(s) + H⁺(aq) + OH^-(aq) --> Na⁺(aq) + H2O(l) + OH^-(aq) ∆H°r: -10.9 kJ (Reaction 1+2 intermediate)

NaOH(s) + H⁺(aq) --> Na⁺(aq) + H2O(l) ∆H°r: -10.9 kJ (Reaction 1+2)

NaOH(s) + H⁺(aq) --> Na⁺(aq) + H2O(l) ∆H°r: -16.7 kJ (Reaction 3)

So, as can be seen, the equations for reactions 1&2 are added and are identical to that of reaction 3. However, the enthalpies of reaction are way different. I do not know how I can account for this steep a difference, as all the lab results were provided with the question. The only difference is that, in the addition of reactions 1&2, there was a hydroxide ion on both sides of the equation that was canceled out (since I was asked for the net ionic equations for each reaction). Could this account for the difference, or does it have no role in the enthalpy of reaction, given that it is a spectator ion?

If I did nothing wrong, I suspect I am supposed to identify this discrepancy between reaction 1+2 with reaction 3.

How did you get H⁺_aq? From HA_aq?

 

[mrxtothaz]

How did you get H⁺_aq? From HA_aq?

Not sure what you mean by HA_aq, but the hydrogen ions arise from the dissolution of hydrochloric acid.

 

[chemisttree]

Then shouldn't there be an enthalpy of HClaq -----> H⁺aq + Cl^-aq?

 

[mrxtothaz]

I'm sure a solution can be found by those means, but the three reactions should be enough for this kind of exercise.

The first two equations combined yield the third equation, so there is no need for additional equations. The only issue is that the enthalpies are quite a bit off.

Do you believe that this difference can be accounted for by the fact that density & heat capacity of water was assumed for each solution? Or is there an error in any of my work?

Note that no experimental error can be attributed to my doing, since the data itself was provided with the question.