Question

In: Chemistry

Part F: The phosphorylation of ADP3− is given by: ADP3−+H++HPO2−4→ATP4−+H2O(l) . At T=310K the molar Gibbs...

Part F: The phosphorylation of ADP3− is given by: ADP3−+H++HPO2−4→ATP4−+H2O(l) . At T=310K the molar Gibbs energy change for the phosphorylation of ADP is ΔGrxn=32.0kJ/mol . In the cell the phosphorylation of ADP3− is coupled to the oxidation of glucose by the reaction C6H12O6+38ADP3−+38H++38HPO2−4+6O2→38ATP4−+44H2O+6CO2. We define the efficiency of this coupling as the fraction of the molar Gibbs energy change from oxidation of glucose that is diverted into ADP phosphorylation. Calculate the efficiency ϵ of this coupling.

Part G: Instead of the mechanism described in Part F, suppose an organism produced work after the fashion of a Carnot engine, i.e. by exploiting the thermal gradient between the interior of the organism at T=310K and the temperature of the exterior at T=298K. Calculate the efficiency of work production by this approach.

I found the the Gibb energy change ΔGrxn for the oxidation of glucose at T=310K in part D. ΔGrxn = −2.88×106 J/mol

This problem had several parts where I found the values that might be relevant:

Calculate the standard molar enthalpy change ΔH∘rxn for the oxidation of glucose, ΔH∘rxn = -2800 kJ/mol

Calculate the molar heat of reaction ΔHrxn at T=310K. ΔHrxn = −2.80×106 J/mol

Calculate the standard molar entropy change ΔS∘rxn for the oxidation of glucose. ΔS∘rxn = 261 J/K⋅mol

Calculate the molar entropy change ΔSrxn at T=310K. ΔSrxn = 272 J/K⋅mol

Please help me solve for part F and G

Expert Solution

F. The given reaction,

is a biological coupling reaction for two other reactions, given below with their respective values

1.

2.

(as calculated by you in the previous parts)

It is worth noting that the first reaction has a positive and the second reaction has negative .

Now for the coupled reaction to be spontaneous, the should be negative. So a part of the will be 'spent' or compensated by the

The ratio of these two is defined as the efficiency(as defined in the question).

So efficiency

G. This step says the organism does work by using the temperature difference between the environment and the organism, hypothetically by the Carnot Engine mechanism.

The efficiency of Carnot engine is given by the following expression:

Efficiency

where T_H is the higher temperature of the organism and T_C is the lower temperature of the surroundings.

queen_honey_blossom answered 2 years ago

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