# Computational heat of reation vs. using literature values

My question is I don't understand how to explain why or what I did wrong to have such large differences between my computational heat of reaction and heat of reaction using enthalpies of formation from literature, and my experimental heat of reaction.

I performed a lab in which three methods were used to compute the heat of reaction for the reaction:

$$\ce{Na2CO3 (s) + 2 HCl (aq) -> 2 NaCl (aq) + H2O (l) + CO2 (g)}$$

First method I used was using experimental data from solution calorimetry and from my results I got that the average heat of reaction was $\textbf{-89.835 kJ/mol}$.

For my second method I found the heat of reaction computationally with Orca. I was instructed to use this equation instead of the original equation to calculate heat of reaction for the above reaction.

$$\Delta U = U \left[ \ce{CO2 (g)} \right] + 3U \left[ \ce{H2O (l)} \right] - 2U \left[ \ce{H3O+ (aq)} \right] - U \left[ \ce{CO3^{2-} (aq)} \right]$$

So basically I used Orca to find the energy for each of the molecules, and I plugged those values into their proper U(molecule) in the above formula and I calculated delta U and then I used the approximation of $\Delta H = \Delta U + R \Delta T$ to transform it into heat. My overall answer ended up being $\textbf{-378 kJ/mol}$. My work (data from Orca optimization is listed first):

\begin{align*} \ce{CO3^{2-} (aq)} &= -264.0667 \, \text{Ha} \\ \ce{H3O+ (aq)} &= -76.8491 \, \text{Ha} \\ \ce{H2O (l)} &= -76.4409 \, \text{Ha} \\ \ce{CO2 (g)} &= -188.5873 \, \text{Ha} \\ 1 \, \text{Ha} &= 627.503 \, \text{kcal/mol} \\ \Delta H &= \Delta U + R \Delta T \\ \Delta U &= \left[ -188.5873 + (3*-76.4409) \right] - \left[ (2*-76.8491) + -264.0667 \right] = -0.1451 \, \text{Ha} \\ -0.1451 \, \text{Ha} &\rightarrow 627.503 \, \frac{\text{kcal/mol}}{\text{Ha}} * -0.1451 \, \text{Ha} = -91.0507 \, \frac{\text{kcal}}{\text{mol}} \\ -91.0507 \, \frac{\text{kcal}}{\text{mol}} &* 1000 \, \frac{\text{cal}}{\text{kcal}} * 4.184 \, \frac{\text{J}}{\text{cal}} * \frac{1}{1000} \frac{\text{kJ}}{\text{J}} = -380.956 \, \frac{\text{kcal}}{\text{mol}} \\ \Delta H_{\text{rxn}} &= -380.956 \frac{\text{kJ}}{\text{mol}} + \left[ 8.314 \frac{\text{J}}{\text{mol K}} * (273.15 + 25.27) \, \text{K} * \frac{1}{1000} \frac{\text{kJ}}{\text{J}} \right] = -378.475 \, \text{kJ/mol} \end{align*}

My third method I used enthalpies of formation (values for looked up from various sources) and my work is shown below.

\begin{align*} \ce{Na2CO3 (s)} &= -1130.7 \, \text{kJ/mol} \\ \ce{HCl (aq)} &= -167.2 \, \text{kJ/mol} \\ \ce{NaCl (aq)} &= -407.27 \, \text{kJ/mol} \\ \ce{H2O (l)} &= -285.8 \, \text{kJ/mol} \\ \ce{CO2 (g)} &= -393.5 \, \text{kJ/mol} \\ \Delta H_{\text{rxn}} &= \left[ (2*-407.27) + (-285.8) + (-393.5) \right] - \left[ (2*-167.2) + (-1130.7) \right] = \mathbf{-28.74 \, \textbf{kJ/mol}} \end{align*}

I'm not really sure how to say why the computational method did so poorly, I would have thought the computer would have done a decent job. Please let me know if something looks wrong in my calculations! Thanks for all the help! Even just a little advice will help this non-chemistry nerd!

• Can you give more details about how you performed the ORCA calculation? The settings line (everything after ! near the top) should suffice. – pentavalentcarbon Sep 28 '16 at 22:45
• For the molecules that were in aqueous state I used ! B3LYP def2-TZVPP COSMO(Water) !OPT For molecules that were not in water I used ! B3LYP def2-TZVPP ! OPT – bbbeenn32 Sep 29 '16 at 3:34
• I don't understand your approximation $\Delta H = \Delta U + R \Delta T$. It would seem to make sense only for an ideal gas. Also you plug in ~300 K as a temperature; was there really a temperature change of 300 K during your experiment or simulation? – Curt F. Sep 29 '16 at 13:58
• It's also unclear why in the second method you assume the carbonate is dissolved (you speak of $\ce{CO3^2-}$ ions) while in the other examples you assume it is a solid. – Curt F. Sep 29 '16 at 14:00
• I was told to use the delta H = U +Rt equation from my professor. The t in the equation is not a delta t, it is just t, and since everything is in kJ/mol whatever t is used doesn't make much of a difference, so I just used the temp. That my reactions took place in which was about 25C. Before the reaction took place sodium carbonate was in solid form and it was reacted with .1M HCl. I was given the second equation with all the U(molecules) from my professor and was told that finding the energy of this equation and converting it to heat would somehow relate to the original reaction. – bbbeenn32 Sep 29 '16 at 14:21