Tricky exam question [closed]








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The mark scheme says carbon dioxide is produced from carbonate + acid. I know hydrogen can't be produced because both the reactions are endothermic.
But where did the acid come from? Can someone give me an example of Solid B and D which produces a mixture and when added together it gives carbon dioxide




Several organic acids are endothermic when dissolved in water: citric and tartaric are two that I have experience with. They would be good candidates for experiment 4.


The difficult one is the carbonate. I think ammonium carbonate is endothermic (the chloride and nitrate are). This could be the solid in experiment 2. It would have an odor of ammonia, which was not mentioned.


We're assuming that all the compounds are colorless. Other gases could be O2 or NO/NO2, but surely other hints would have pointed this way, so CO2 is the most likely.


Sodium bicarbonate is not as soluble as 4 g in 30 mL. I'm not sure about the endothermicity of sodium carbonate (which has several hydrates). No other possibilities come to mind.


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The obvious choice for the source of carbonate is sodium bicarbonate (UPDATE: sodium bicarbonate is not soluble enough per other answer, but sodium carbonate is a possibility), which has a positive enthalpy of solution even at high concentrations, so let's call that B.


The acid is a little trickier. If you look up the standard enthalpy of solution of most acids, you'll find negative values (meaning the temp would go up when they are added to water). However, these values refer to infinite dilution in neutral water. Once you've added a little bit and the pH has dropped, the reaction $\ce{H+ + HO- -> H2O}$, which has a large negative enthalpy, essentially stops happening and the enthalpy of solution becomes positive. This is easy to tell by looking at the maximum solubility as a function of temperature. If it increases, then the enthalpy change of solution at saturation is positive. So at the high concentrations in the problem (4 g per 30 mL), many acids that are solid at room temp will cause a temperature drop when dissolved. Citric acid is one example.


A solution of citric acid is certainly acidic enough that it will cause rapidly production of carbon dioxide gas when mixed with a solution of sodium carbonate. 


 2

There are two equilibria to consider, $\ce{ 2H2O <=> H3O^+ + OH^-}$ and $\ce{ HA +H2O <=> H3O^+ + A^-}$ where HA must be a *weak acid*, and for example, NaA its sodium salt. Because of the equilibria there is no real distinction between solutions of (1) pure HA, (2) mixtures of HA and NaA and (3) pure NaA. 


In your question one solid must be a pure salt such as NaA which will dissociate to give A$^-$ and so produce some $\ce{H3O+}$. 


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I think Andrew's (see above answer) initial choice for the source of carbonate as sodium bicarbonate ($\ce{NaHCO3}$) is correct based on its enthalpy of solution, which is listed as $\pu{+18.7 kJ\:mol^{-1}}$ in literature (Ref.1). I disagree with his final choice of sodium carbonate ($\ce{Na2CO3}$) based on its solubility in water as the carbonate of choice though. My disagreement is again based on its enthalpy of solution, which is listed as $\pu{-26.6 kJ\:mol^{-1}}$ in the same literature (Ref.1), and hence, upon dissolution, the final solution should have shown temperature increment in either experiment 2 or 4, instead of decrements as shown in the diagram. Said that, the only carbonate with positive enthalpy of solution I can find in literature is $\ce{NaHCO3}$. Thus, we don't have any choice other than $\ce{NaHCO3}$ in this case, although its solubility come a little bit short than anticipated (According to [PubChem](https://pubchem.ncbi.nlm.nih.gov/compound/sodium_bicarbonate#section=Solubility), the solubility of $\ce{NaHCO3}$ in water is $\pu{10.3 g}/\pu{100 g}$ of water at $\pu{25 ^{\circ}C}$). Nonetheless, question didn't elaborate all of solids are dissolved after $\pu{2 min}$. :-)


Now, let's see what is the approximate heat changes for these experiments (assumptions: We count only the mass of water disregarding solid substance in it, and consider its heat capacity is $\pu{4.184 Jg^{-1} ^{\circ}C^{-1}}$, for convenience):
$$
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Experiment} & \Delta T, \pu{^{\circ}C} & \text{mass, }\pu{g} & \text{heat absorbed by }\pu{4 g}\text {, in } \pu{J} & \text{heat absorbed by }\pu{1 g}\text {, in } \pu{J} \\ \hline
 \text{2 for comp B} & 26-22=4 & 30 & 502.1 & 125.5 \\ \hline
\text{4 for comp D} & 29-23=6 & 30 & 753.1 & 188.3 \\ \hline
\end{array}
$$


Now, tabulate the calculated and literature values of enthalpies of perticular solutions:


$$
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Compound} & \text{molar mass} & \mathrm{\Delta H\_{sol}}, \text {if B (calculated)} & \mathrm{\Delta H\_{sol}}, \text {if D (calculated)} & \mathrm{\Delta H\_{sol}}, \text {(Lit.)} & \text{Reference} \\ \hline
 \ce{NaHCO3} & \pu{84.01 g\:mol^{-1}} & \pu{10.5 kJ\:mol^{-1}} & \pu{15.8 kJ\:mol^{-1}} & \pu{18.7 kJ\:mol^{-1}} & 1,2 \\ \hline
 \ce{C2H2O4} & \pu{90.03 g\:mol^{-1}} & \pu{11.3 kJ\:mol^{-1}} & \pu{16.9 kJ\:mol^{-1}} & \pu{8.86 kJ\:mol^{-1}} & 3 \\ \hline
 \ce{C2H2O4.2H2O} & \pu{126.07 g\:mol^{-1}} & \pu{15.8 kJ\:mol^{-1}} & \pu{23.7 kJ\:mol^{-1}} & \pu{35.2 kJ\:mol^{-1}} & 3 \\ \hline
 \ce{C6H8O7} & \pu{192.12 g\:mol^{-1}} & \pu{24.1 kJ\:mol^{-1}} & \pu{36.2 kJ\:mol^{-1}} & \pu{18.2 kJ\:mol^{-1}} & 3 \\ \hline
 \ce{C6H8O7.H2O} & \pu{210.14 g\:mol^{-1}} & \pu{26.4 kJ\:mol^{-1}} & \pu{39.6 kJ\:mol^{-1}} & \pu{29.1 kJ\:mol^{-1}} & 3 \\ \hline
\end{array}
$$


In the Table, $\ce{C2H2O4}$ represent anhydrous oxalic acid and $\ce{C6H8O7}$ is anhydrous citric acid. All four acids in the Table are higher solubility in water. Since we have questionable assumption in the calculations of $\mathrm{\Delta H\_{sol}}$, I'd expect lower calculated value than that in literature. Thus, for proximety of the values for $\ce{NaHCO3}$, we can conclude that the compound D is $\ce{NaHCO3}$ (row 1 in the Table). Similarly, based in values in row 5 of the Table, we can also conclude that the compound B is citric acid monohydrate.




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**References:**


1. J. P. Rupert, H. P. Hopkins Jr., C. A. Wulff, “The Solution Thermochemistry of Polyvalent Electrolytes. IV. Sodium Carbonate, Sodium Bicarbonate, and Trona,” *J. Phys. Chem.* **1965**, *69(9)*, 3059–3062 (DOI: 10.1021/j100893a040).
2. C. E. Vanderzee, D. A. Wigg, “The standard enthalpies of solution and formation of Wegscheider's salt: $\ce{Na2CO3·3NaHCO3(s)}$ and of trona: $\ce{Na2CO3·NaHCO3·2H2O(s)}$ at $\pu{298.15 K}$,” *The Journal of Chemical Thermodynamics* **1981**, *13(6)*, 573–583 (<https://doi.org/10.1016/0021-9614(81)90114-2>).
3. Alexander Apelblat, “Enthalpy of solution of oxalic, succinic, adipic, maleic, malic, tartaric, and citric acids, oxalic acid dihydrate, and citric acid monohydrate in water at $\pu{298.15 K}$,” *The Journal of Chemical Thermodynamics* **1986**, *18(4)*, 351–357 (<https://doi.org/10.1016/0021-9614(86)90080-7>).


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