2. A chemical reaction between maleic acid H2C4H2O4(aq) and sodium bicarbonate NaHCO3(s) occurs in t — Stoichiometry, Kinetics, Thermodynamics, Acid-Base Equilibria Chemistry Question
Problem Context
2. A chemical reaction between maleic acid H2C4H2O4(aq) and sodium bicarbonate NaHCO3(s) occurs in the presence of water to produce carbon dioxide and sodium maleate Na2C4H2O4(aq), as represented by the following equation.
H2C4H2O4(aq) + 2 NaHCO3(s) → 2 CO2(g) + 2 H2O(l) + Na2C4H2O4(aq)
(a) A student combines equal masses of H2C4H2O4(s) chunks and NaHCO3(s) chunks with sufficient water at 20.0°C. The student determines that 0.0114 mol of CO2(g) is produced after the reaction goes to completion.
(i) Calculate the number of grams of CO2(g) produced.
Model Answer
0.0114 mol CO2 × (44.01 g / 1 mol) = 0.502 g CO2 [1, 2].
(ii) The CO2(g) produced from the reaction at 20.0°C was collected and found to have a pressure of 1.25 atm. Calculate the volume of CO2(g), in liters.
Model Answer
PV = nRT; V = nRT / P = ((0.0114 mol)(0.08206 L·atm/(mol·K))(293 K))
/ 1.25 atm = 0.219 L [2, 3].
(b) The student performs a second experiment that is identical to the first except that the student grinds the chunks of H2C4H2O4(s) and NaHCO3(s) into powder before combining the powder with water.
(i) What happens to the surface area of the reactants when the student grinds the chunks into powder?
Model Answer
The surface area of the solid reactants increases [2, 3].
(ii) The rate-determining step for the overall reaction is the dissolving of the solids. Would the time required for the dissolving of the solids in the second experiment be longer than, shorter than, or the same as the time required in the first experiment? Justify your answer based on the collisions between particles.
Model Answer
Shorter than [2, 3]. The powdered solids have a larger surface area
than the solid chunks, thus collisions between water and the surface particles
occur more frequently, resulting in a faster rate of dissolution and a shorter
amount of time to dissolve the solids [2, 3].
(iii) When the reaction is complete, will the volume of CO2(g) at the end of the second experiment be greater than, less than, or equal to the volume at the end of the first experiment? Justify your answer.
Model Answer
Equal to [2, 4]. Both experiments begin with the same amount of
reactants, so they will produce the same number of moles of CO2(g) under the
same conditions of pressure and temperature; therefore, the final volume will be
the same [2, 4].
The student conducts additional trials of the experiment and produces the following data table.
(c) Based on the student’s data, identify the limiting reactant in trial 3. Justify your answer.
Model Answer
Accept one of the following: NaHCO3 is the limiting reactant because
changing the mass of NaHCO3 alters the amount of CO2 produced, OR NaHCO3 is the
limiting reactant because the amount present has a smaller theoretical yield of
the CO2 product [2, 4]. Calculations: 1.543 g H2C4H2O4 × (1 mol H2C4H2O4 /
116.07 g) × (2 mol CO2 / 1 mol H2C4H2O4) = 0.02659 mol CO2; 1.251 g NaHCO3 × (1
mol NaHCO3 / 84.01 g) × (2 mol CO2 / 2 mol NaHCO3) = 0.01489 mol CO2 [2, 5].
(d) The reaction has a value of ΔS° greater than zero. Using particle-level reasoning, explain why the entropy increases as the reaction progresses.
Model Answer
The entropy change is positive because the aqueous reactants produce 2
moles of gas particles, according to the balanced chemical equation [2, 5].
Gases are far more dispersed (occupy a greater number of microstates) than
condensed phases, so the entropy of the products is greater than that of the
reactants [2, 5].
The student notices that the temperature of the reaction mixture decreases as the reaction takes place and correctly determines that the reaction is endothermic.
(e) The student claims that the reaction is thermodynamically favorable at all temperatures because ΔS°rxn > 0 and the reaction is endothermic. Do you agree or disagree with the student’s claim? Justify your answer.
Model Answer
Accept one of the following: Disagree, the reaction is endothermic and
has a positive entropy change [2, 6]. Thus, the reaction is only
thermodynamically favorable at a high enough temperature such that the magnitude
of -TΔS is greater than that of ΔH [2, 6]. OR Disagree, for the reaction to be
thermodynamically favorable (ΔG < 0) at all temperatures, the reaction must be
exothermic (ΔH < 0) and have a positive entropy change (ΔS > 0) [2, 6].
Next, the student investigates the acid-base behavior of maleic acid. The student notes that maleic acid is a diprotic acid. The two acid dissociation processes that occur are represented by the following equations.
H2C4H2O4 + H2O ⇌ HC4H2O4- + H3O+ Ka1 = 1.5 × 10^-2
HC4H2O4- + H2O ⇌ C4H2O4^2- + H3O+ Ka2 = 8.5 × 10^-7
(f) Calculate the pKa2 value for the HC4H2O4- ion.
Model Answer
pKa2 = -log(8.5 × 10^-7) = 6.07 [6].
(g) A buffer solution with a pH of 7.00 is prepared using C4H2O4^2- and HC4H2O4-. Calculate the ratio [C4H2O4^2-] / [HC4H2O4-] in this solution.
Model Answer
pH = pKa2 + log([C4H2O4^2-] / [HC4H2O4^-]) [6]. [C4H2O4^2-] /
[HC4H2O4^-] = 10^(pH - pKa2) = 10^(7.00 - 6.07) = 8.5 [6].
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