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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 95b
Chapter 19, Problem 95b

Living organisms use energy from the metabolism of food to create an energy-rich molecule called adenosine triphosphate (ATP). The ATP acts as an energy source for a variety of reactions that the living organism must carry out to survive. ATP provides energy through its hydrolysis, which can be symbolized as follows: ATP(aq) + H2O(l) → ADP(aq) + Pi(aq) ΔG°rxn = -30.5 kJ where ADP represents adenosine diphosphate and Pi represents an inorganic phosphate group (such as HPO42-). b. The free energy obtained from the oxidation (reaction with oxygen) of glucose (C6H12O6) to form carbon dioxide and water can be used to re-form ATP by driving the given reaction in reverse. Calculate the standard free energy change for the oxidation of glucose and estimate the maximum number of moles of ATP that can be formed by the oxidation of one mole of glucose.

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1. The first step is to write down the balanced chemical equation for the oxidation of glucose. This reaction is: C6H12O6(s) + 6O2(g) → 6CO2(g) + 6H2O(l).
2. The standard free energy change (ΔG°) for this reaction is given by the equation ΔG° = ΔH° - TΔS°, where ΔH° is the standard enthalpy change, T is the temperature in Kelvin, and ΔS° is the standard entropy change. You can find the values for ΔH° and ΔS° for this reaction in a thermodynamic data table.
3. Once you have calculated ΔG° for the oxidation of glucose, you can compare it with the ΔG° for the hydrolysis of ATP, which is given as -30.5 kJ. The ratio of these two values will give you the maximum number of moles of ATP that can be formed by the oxidation of one mole of glucose.
4. The ratio is calculated as follows: (ΔG° for the oxidation of glucose) / (-30.5 kJ). The negative sign in the denominator is because the hydrolysis of ATP releases energy, so ΔG° is negative.
5. The result of this calculation is the maximum number of moles of ATP that can be formed by the oxidation of one mole of glucose. Remember that this is a theoretical maximum, and the actual number may be less due to inefficiencies in the process.

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Key Concepts

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

Adenosine Triphosphate (ATP)

ATP is a nucleotide that serves as the primary energy carrier in cells. It consists of adenine, ribose, and three phosphate groups. The energy stored in ATP is released when one of the phosphate bonds is hydrolyzed, converting ATP to ADP and inorganic phosphate (Pi). This process is crucial for powering various cellular processes, including muscle contraction and biochemical reactions.
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Free Energy Change (ΔG)

The free energy change (ΔG) of a reaction indicates the spontaneity and energy dynamics of that reaction. A negative ΔG value, such as -30.5 kJ for ATP hydrolysis, signifies that the reaction releases energy and can occur spontaneously. Understanding ΔG is essential for predicting whether a reaction can proceed and how much energy can be harnessed for cellular work.
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Oxidation of Glucose

The oxidation of glucose is a metabolic process where glucose (C6H12O6) is broken down in the presence of oxygen to produce carbon dioxide (CO2) and water (H2O), releasing energy. This process is central to cellular respiration and is coupled with ATP synthesis. The standard free energy change for this reaction can be calculated to determine how many moles of ATP can be generated from one mole of glucose, illustrating the efficiency of energy conversion in biological systems.
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Related Practice
Textbook Question

Consider this reaction occurring at 298 K: BaCO3(s) ⇌ BaO(s) + CO2( g) b. If BaCO3 is placed in an evacuated flask, what is the partial pressure of CO2 when the reaction reaches equilibrium?

Textbook Question

Consider this reaction occurring at 298 K: BaCO3(s) ⇌ BaO(s) + CO2(g) c. Can the reaction be made more spontaneous by an increase or decrease in temperature? If so, at what temperature is the partial pressure of carbon dioxide 1.0 atm?

Textbook Question

Living organisms use energy from the metabolism of food to create an energy-rich molecule called adenosine triphosphate (ATP). The ATP acts as an energy source for a variety of reactions that the living organism must carry out to survive. ATP provides energy through its hydrolysis, which can be symbolized as follows: ATP(aq) + H2O(l) → ADP(aq) + Pi(aq) ΔGrxn ° = -30.5 kJ where ADP represents adenosine diphosphate and Pi represents an inorganic phosphate group (such as HPO42-). a. Calculate the equilibrium constant, K, for the given reaction at 298 K.

Textbook Question

These reactions are important in catalytic converters in automobiles. Calculate ΔG° for each at 298 K. Predict the effect of increasing temperature on the magnitude of ΔG°.

a. 2 CO(g) + 2 NO(g) → N2(g) + 2 CO2(g)

b. 5 H2(g) + 2 NO(g) → 2 NH3(g) + 2 H2O(g)

c. 2 H2(g) + 2 NO(g) → N2(g) + 2 H2O(g)

d. 2 NH3(g) + 2 O2(g) → N2O(g) + 3 H2O(g)

Textbook Question

Calculate ΔG° at 298 K for these reactions and predict the effect on ΔG° of lowering the temperature.

a. NH3(g) + HBr(g) → NH4Br(s)

b. CaCO3(s) → CaO(s) + CO2(g)

c. CH4(g) + 3 Cl2(g) → CHCl3(g) + 3 HCl(g) (ΔG°f for CHCl3(g) is -70.4 kJ/mol.)

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