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Chapter 21: Problem 87

Carbon monoxide is toxic because it binds more strongly to iron in hemoglobin \((\mathrm{Hb})\) than does \(\mathrm{O}_{2} .\) Consider the following reactions and approximate standard free energy changes: $$\begin{aligned} \mathrm{Hb}+\mathrm{O}_{2} \longrightarrow \mathrm{HbO}_{2} & \Delta G^{\circ}=-70 \mathrm{kJ} \\ \mathrm{Hb}+\mathrm{CO} \longrightarrow \mathrm{HbCO} & \Delta G^{\circ}=-80 \mathrm{kJ} \end{aligned}$$ Using these data, estimate the equilibrium constant value at $25^{\circ} \mathrm{C}$ for the following reaction: $$\mathrm{HbO}_{2}(a q)+\mathrm{CO}(g) \rightleftharpoons \mathrm{HbCO}(a q)+\mathrm{O}_{2}(g)$$

Short Answer

Expert verified
The equilibrium constant at 25°C for the reaction HbO₂(aq) + CO(g) ⟷ HbCO(aq) + O₂(g) is approximately: K ≈ 56.23

Step by step solution

01

Determine the final reaction by combining the given reactions

First, we will obtain the reaction of interest by combining the given reactions. This can be done by: 1. Reversing the first reaction 2. Adding the reversed first reaction to the second reaction The reversed first reaction is: HbO₂(aq) ⟶ Hb + O₂(g), ΔG° = +70 kJ Now, let's add the reversed first reaction and the second reaction together: HbO₂(aq) ⟶ Hb + O₂(g) Hb + CO(g) ⟶ HbCO(aq) The final reaction is: HbO₂(aq) + CO(g) ⟷ HbCO(aq) + O₂(g)
02

Determine the standard free energy change of the combined reaction

Since we added the reversed first reaction and the second reaction, we must add their standard free energy changes as well. So, the standard free energy change for the desired reaction, ΔG°, would be: ΔG° = (+70 kJ) + (-80 kJ) = -10 kJ/mol
03

Convert standard free energy change to equilibrium constant

We will use the relation between standard free energy change and equilibrium constant K, which is given by the formula: ΔG° = -RT ln(K) where R is the gas constant (8.314 J/mol∙K), T is the temperature in Kelvin, and K is the equilibrium constant. We are given the temperature in Celsius, so we need to convert it to Kelvin. At 25°C, the temperature in Kelvin is: T = 25 + 273.15 = 298.15 K Now, let's solve for the equilibrium constant, K: -10,000 J/mol = -(8.314 J/mol∙K) × (298.15 K) × ln(K) Rearrange to isolate ln(K): ln(K) = -10,000 J/mol / (-8.314 J/mol∙K × 298.15 K) ≈ 4.030 Now, take the exponent on both sides to solve for K: K = e^(4.030) ≈ 56.23
04

Write the final answer for the equilibrium constant

The equilibrium constant at 25°C for the given reaction HbO₂(aq) + CO(g) ⟷ HbCO(aq) + O₂(g) is approximately: K ≈ 56.23

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Most popular questions from this chapter

What is the electron configuration for the transition metal ion(s) in each of the following compounds? a. $\left(\mathrm{NH}_{4}\right)_{2}\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{4}\right]$ b. $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)_{2}\right] \mathrm{I}_{2}$ c. \(\mathrm{Na}_{2}\left[\mathrm{TaF}_{7}\right]\) d. $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{I}_{2}\right]\left[\mathrm{PtI}_{4}\right]$ Pt forms \(+2\) and \(+4\) oxidation states in compounds.

The complex ion NiCl \(_{4}^{2-}\) has two unpaired electrons, whereas \(\mathrm{Ni}(\mathrm{CN})_{4}^{2-}\) is diamagnetic. Propose structures for these two complex ions.

Name the following coordination compounds. a. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{2}\) b. $\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{I}_{3}$ c. \(\mathrm{K}_{2}\left[\mathrm{PtC}_{4}\right]\) d. \(\mathrm{K}_{4}\left[\mathrm{Pt} \mathrm{C}_{6}\right]\) e. $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2}$ f. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{NO}_{2}\right)_{3}\right]\)

Draw the \(d\) -orbital splitting diagrams for the octahedral complex ions of each of the following. a. \(\mathrm{Zn}^{2+}\) b. \(\mathrm{Co}^{2+}\) (high and low spin) c. \(\mathrm{Ti}^{3+}\)

Which of the following statement(s) is(are) true? a. The coordination number of a metal ion in an octahedral complex ion is 8. b. All tetrahedral complex ions are low-spin. c. The formula for triaquatriamminechromium(III) sulfate is $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]_{2}\left(\mathrm{SO}_{4}\right)_{3}$ d. The electron configuration of \(\mathrm{Hf}^{2+}\) is $[\mathrm{Xe}] 4 f^{12} 6 s^{2}$ e. Hemoglobin contains \(\mathrm{Fe}^{3+}\)
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