Spinach contains a lot of iron but is not a good source of dietary iron because nearly all the iron is tied up in the oxalate complex [Fe(C 2 O 4 ) 3 ] 3- . (b) Under the acidic conditions in the stomach, the Fe 3+ concentration should be greater because of the reaction [Fe(C 2 O 4 ) 3 ] 3- (aq) + 6 H 3 O + (aq) ⇌ Fe 3+ (aq) + 3 H 2 C 2 O 4 (aq) + 6 H 2 O(l) Show, however, that this reaction is nonspontaneous under standard-state conditions. (For H 2 C 2 O 4 , K a1 = 5.9 × 10 -2 and K a2 = 6.4 × 10 -5 .)

All right. Hi, everyone. So this question says that chromium three picolinate or CRP three is a supplement used to treat type two diabetes. It is a source of chromium three positive ions that are shown to increase insulin sensitivity. Even though chromium three picolinate is more efficiently absorbed in the G I tract. Its absorption is still quite low. It might be expected that the absorption of chromium three positive will be higher in the stomach because of the following reaction, explain how the low absorption of chromium three P Colin or explain the low absorption of chromium three P colate by predicting the spontaneity of the reaction under standard conditions. And here we have a few different constants which we will discuss in a moment. But for now, we have four different answer choices discussing whether or not the absorption is spontaneous or not at standard conditions. So first lets get started. Recall that the spontaneity of a reaction discusses essentially whether or not it is favorable under standard conditions, right? And spontaneity can be predicted using jibs free energy or delta G standard. Now, the delta G standard of a given reaction is equal to negative RT lnok or are is the universal gas constant. So that's 8.314 jewels per mole. Kelvin tea is the temperature unit of Kelvin. And K refers to the equilibrium constant of the reaction in question. So recall that when the delta G standard value is negative, meaning it is less than zero, then the reaction is said to be spontaneous. When the Delta G Standard value is positive, it is non spontaneous. And when it equals exactly zero, the reaction is at equilibrium. So in this case, when it comes to our calculation, right, we do have the R value or R because that is a constant. But for temperature, right, recall it here, we're talking about standard conditions which implies a room temperature at 25.0 °C. So to convert Celsius to units of Kelvin that we need for this equation, I'll take my 25.0 °C and I'm going to add 273.15 to this value. So when I add them, I get my temperature in Kelvin which is 298.15 under standard conditions. Now, the problem here and the only piece of information we are missing is the equilibrium constant of the overall reaction depicted on the screen here. So to find the equilibrium constant of the overall reaction, we have to consider the two constants that are given in the very last part of the question, we are given a case of fa 3.548 multiplied by 10 to the fourth and A K A of 0.1023. So with this in mind, I'm going to scroll down to where I already wrote the overall reaction for our reference. So here in this case, we're going to have to apply hess's law to get the overall reaction based on the two that we were given in the question, right? Because recall that the first constant RKF refers to the formation constant, right? Referring to the formation of the chromium three picolinate complex. So case of F was equal to 3.548 multiplied by 10 to the fourth. And so the formation in question was the combination of chromium three positive in aqueous solution as well as three equivalents of the picolinate ion also in aqueous solution to create the chromium three picolinate complex. Oops also in aqueous solution, but I'm just going to go ahead and open up some space here, right? So that's one reaction we'll call this reaction A. Now reaction B refers to an acid base reaction because we are given case of A which was 0.1023. So because this was the acid dissociation constant for PICO inic acid, then we'll take into account that HP I or PICO picholine acid and aqueous solution can react with of water to produce a mixture of the picolinate ion as well as hydro right, or H 30 positive. So now these two reactions, right A and B respectively have to be manipulated in some way to get the overall reaction that is on the top of the screen. And therefore we manipulate their constants accordingly, their equilibrium constants, right? So notice how in this case, if we consider reaction A for a second, the chromium three picolinate complex is depicted on the product side, whereas it is a reactant in the overall reaction. And the same is true for the picolinate ion and are chromium three positive because chromium three positive is a reactant in reaction A but it is a product in the overall reaction. So this means that reaction A has to be reversed. So ill take reaction A and I'm simply going to have reactants and products switch sides so that the complex is the react and my ions here are the product. So now to find the new equilibrium constant, which I will call K one, I have to take the inverse of case of F. So that's one divided by 3.548 multiplied by 10 to the fourth, which gives me 2.818 multiplied by 10 to the negative fifth. And I'm going to go ahead and move this once more so that you can see it better. So now with respect to the picolinate ion, what I want to point out to you here is that it's not actually present in the overall reaction. So this means that when combining reaction A and reaction B using Hess's law, they Colin must cancel out, right. So because I already reversed reaction A I have to reverse reaction B as well to make sure that picolinate or the picolinate ion is on opposite sides of the reaction arrow so that they can cancel out across both reactions. Now, in addition to this, I also have to add a stoichiometry coefficient of three, two reaction be right because here in reaction B I only have one picolinate ion. So I have to make sure that they balance out so that all picolinate ions can be canceled out right. So four reaction B I'm going to go ahead and not only reverse it but also multiply all compounds present by three. So that's three, the coate ions as well as three hydro num ions in equilibrium with three equivalents of PICO inic acid as well as three equivalents of what? And so when I find my new equilibrium constant or K two, I'm going to go ahead and take the inverse of a case of A, which is one divided by zero point 1023. But because I added a stoichiometry coefficient of three, I'm going to take the inverse of case of A and apply an exponent of three or raise it to the third power to give me an overall value of 934.11. So now that Ive modified both reactions here, I'm going to go ahead and combine them to get my overall reaction. So as discussed previously, right, the three equivalents of the picolinate ion are going to cancel out because they are present in both the reactant and the product side. And so after that is said and done, I get the overall reaction that was discussed in the beginning going to adjust this somewhat because on the left side, I almost forgot to write Hydroa. So let me just go ahead and add that. OK, looks good on the left. So now we can go ahead and find the equilibrium constant of the overall reaction. And so the K overall is equal to K one multiplied by K two. So that is going to be 2.818 multiplied by 10 to the negative fifth multiplied by 934.11 to give us an overall equilibrium constant of 0.02633. So now it is the K overall that we can go ahead and plug in to our reaction for delta G standard. So delta G standard was equal to negative RT Ln of K. So that's negative 8.314 jewels per mole. Kelvin multiplied by the temperature which was 298.15. Kelvin multiplied by the Ln of zero point 02633. So the last thing I'm going to do actually is convert my answer from units of joules per mole to units of kilojoules, right? So to do that, I'm actually going to go ahead and divide this number by 1000 because recall that 1 kg joule is equal to 1000 joules. And so when I evaluate, I get that delta G standard is equal to 9.016 kilo joules per mole. And there you have it right? Because delta G standard is a positive number, meaning that this reaction happens to be non spontaneous. So with all that being said, if I scroll up here to the very beginning, our answer is going to be option B in the multiple choice because the absorption of chromium three picolinate is low because the reaction is non spontaneous at standard conditions. So with all that being said, if you stuck around until the end to thank you so very much for watching and I hope you found this helpful.

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

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McMurry 8th Edition

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problem 21.134b

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Chapter 18, Problem 21.134b

Spinach contains a lot of iron but is not a good source of dietary iron because nearly all the iron is tied up in the oxalate complex [Fe(C₂O₄)₃]^3-.
(b) Under the acidic conditions in the stomach, the Fe³⁺ concentration should be greater because of the reaction
[Fe(C₂O₄)₃]^3-(aq) + 6 H₃O⁺(aq) ⇌ Fe³⁺(aq) + 3 H₂C₂O₄(aq) + 6 H₂O(l)
Show, however, that this reaction is nonspontaneous under standard-state conditions. (For H₂C₂O₄, K_a1 = 5.9 × 10^-2 and K_a2 = 6.4 × 10^-5.)

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Identify the reaction given: \([\text{Fe(C}_2\text{O}_4)_3]^{3-}(aq) + 6 \text{H}_3\text{O}^+(aq) \rightleftharpoons \text{Fe}^{3+}(aq) + 3 \text{H}_2\text{C}_2\text{O}_4(aq) + 6 \text{H}_2\text{O}(l)\).

Determine the equilibrium constant \(K_{eq}\) for the reaction using the given \(K_{a1}\) and \(K_{a2}\) values for oxalic acid (\(\text{H}_2\text{C}_2\text{O}_4\)).

Calculate the \(K_{eq}\) for the reverse reaction by considering the dissociation of \(\text{H}_2\text{C}_2\text{O}_4\) into \(\text{H}^+\) and \(\text{C}_2\text{O}_4^{2-}\) using \(K_{a1}\) and \(K_{a2}\).

Use the relationship \(K_{eq} = \frac{1}{K_{sp}}\) to find the \(K_{sp}\) of the complex \([\text{Fe(C}_2\text{O}_4)_3]^{3-}\).

Conclude that if \(K_{eq} < 1\), the reaction is nonspontaneous under standard-state conditions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complex Ion Formation

Complex ions are formed when metal ions bind to ligands, which are molecules or ions that can donate electron pairs. In the case of spinach, iron is complexed with oxalate ions to form [Fe(C2O4)3]3-, making the iron less bioavailable. Understanding complex ion formation is crucial for analyzing how metal ions interact with other species in biological systems.

Acid-Base Equilibria

Acid-base equilibria involve the transfer of protons (H+) between species in solution, which can affect the solubility and availability of ions. The reaction provided shows how the acidic environment in the stomach can influence the concentration of Fe3+ ions by shifting the equilibrium. Knowledge of acid-base equilibria is essential for predicting how changes in pH can impact chemical reactions.

Gibbs Free Energy and Spontaneity

Gibbs free energy (G) is a thermodynamic potential that helps predict whether a reaction will occur spontaneously. A reaction is spontaneous if the change in Gibbs free energy (ΔG) is negative. To determine the spontaneity of the given reaction, one must calculate ΔG using standard-state conditions and the equilibrium constants provided, which is fundamental in thermodynamics.