Question

Part A

Consider these hypothetical chemicalreactions:

1. ${\rm A \rightleftharpoons B}, \quad\Delta G =$ 13.2
2. ${\rm B \rightleftharpoons C}, \quad\Delta G =$ -28.9
3. ${\rm C \rightleftharpoons D},\quad \Delta G =$ 5.80

What is the free energy, , for the overall reaction, $\rm A \rightleftharpoons D$ ?

Express your answer numerically inkilojoules per mole.

=-9.90 $\rm kJ/mol$

Correct

Part B

What can be said about the favorability ofthe overall reaction?

	This reaction is thermodynamicallyfavorable. This reaction is thermodynamicallyneutral. This reaction is thermodynamicallyunfavorable. There is not enough information to determinethermodynamic favorableness.
Correct

Part C

Firefly luciferase is the enzyme that allowsfireflies to illuminate their abdomens. Because this lightgeneration is an ATP-requiring reaction, firefly luciferase can beused to test for the presence of ATP. In this way, luciferase cantest for the presence of life. The coupled reactions are

$\matrix{\hfill \rm luciferin+O_2 & \rightleftharpoons & \rm oxyluciferin +light \hfill \cr \hfill \rm ATP & \rightleftharpoons & \rm AMP+PP_i \hfill}$

If the overall of the coupled reaction is -8.70 , what is the equilibrium constant, , of the first reactions at 7 $\,^\circ C$ ? The for the hydrolysis of ATP to AMP is 31.6 $\rm kJ/mol$ .

Express your answernumerically.

=

Answer 1

Concepts and reason

Generally, Gibbs free energy of overall reaction is the sum of all the individual reactions.

Thus, the overall Gibbs free energy is calculated using a sum of Gibbs free energies of all the reactions.

A reaction is said to be thermodynamically stable, the reaction is spontaneously occurring.

A reaction is said to be spontaneous or non-spontaneous we consider the Gibbs free energy. If Gibbs free energy of the reaction is negative then the reaction is spontaneous, and Gibbs free energy of the reaction is positive then the reaction is non-spontaneous.

Therefore, a reaction is said to be thermodynamically stable, Gibbs free energy of reaction is negative.

The relation between Gibbs free energy and equilibrium rate constant is as follows:

Fundamentals

Gibbs free energy for an overall reaction is determine by considering the sum of Gibbs free energies of the given individual chemical reactions.

If Gibbs free energy of the reaction is negative then the reaction is spontaneous.

The relation between Gibbs free energy and equilibrium rate constant is as follows:

Here, R is universal gas constant, T is absolute temperature, and K is equilibrium rate constant.

From this it is possible to calculate equilibrium constant of the reaction.

(A)

The given reactions are as follows:

The overall reaction is

Add all Gibbs free energies of the reactions,

Therefore, the overall Gibbs free energy is .

(B)

The overall reaction is .

The Gibbs free energy of the above reaction is -9.9 kJ/mol.

Therefore, the reaction is thermodynamically favorable.

(C)

Consider the given reactions as follows:

The overall coupled reaction is,

The Gibbs free energy of the overall reaction is,

.

So for the first reaction is,

Calculate equilibrium rate constant of the first reaction at as follows:

Therefore, equilibrium rate constant of the reaction is .

Ans: Part A

The overall Gibbs free energy is .