Question

A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of adenosine triphosphate, ATP, to adenosine diphosphate, ADP, as described by

ATP(aq) +H2O (l) --->ADP(aq) +HPO4 (negative two overall charge) (aq).
for which ΔG°rxn = –30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of ΔGrxn in a biological cell in which [ATP] = 5.0 mM, [ADP] = 0.30 mM, and [HPO4^2–] = 5.0 mM.

a. What is the delta G rxn in kJ/mol?
b. Is the hydrolysis of ATP spontaneous under these conditions?

Answer 1

(a) The value of
`\Delta G_(rxn)` is -51.4 kJ/mol

(b) Yes, the hydrolysis of ATP spontaneous under these conditions.

Explanation :

First we have to calculate the reaction quotient.

Reaction quotient (Q) : It is defined as the measurement of the relative amounts of products and reactants present during a reaction at a particular time.

The given balanced chemical reaction is,

`ATP(aq)+H_2O(l)\rightarrow ADP(aq)+HPO_4^(2-)(aq)`

The expression for reaction quotient will be :

`Q=([ADP][HPO_4^(2-)])/([ATP])`

In this expression, only gaseous or aqueous states are includes and pure liquid or solid states are omitted.

Given:

`[ATP]` = 5.0 mM

`[ADP]` = 0.30 mM

`[HPO_4^(2-)]` = 5.0 mM

Now put all the given values in this expression, we get

`Q=((0.30)* (5.0))/((5.0))=0.30mM=0.30* 10^(-3)M`

Now we have to calculate the value of
`\Delta G_(rxn)`.

The formula used for
`\Delta G_(rxn)` is:

`\Delta G_(rxn)=\Delta G^o+RT\ln Q` ............(1)

where,

`\Delta G_(rxn)` = Gibbs free energy for the reaction = ?

`\Delta G_^o` = standard Gibbs free energy = -30.5 kJ/mol

R = gas constant =
`8.314* 10^(-3)kJ/mole.K`

T = temperature =
`37.0^oC=273+37.0=310K`

Q = reaction quotient =
`0.30* 10^(-3)`

Now put all the given values in the above formula 1, we get:

`\Delta G_(rxn)=(-30.5kJ/mol)+[(8.314* 10^(-3)kJ/mole.K)* (310K)* \ln (0.30* 10^(-3))`

`\Delta G_(rxn)=-51.4kJ/mol`

Therefore, the value of
`\Delta G_(rxn)` is -51.4 kJ/mol

Gibbs free energy : It is defined as the amount of energy that is available to do useful work.

A reaction to be spontaneous when
`\Delta G<0`

A reaction to be non-spontaneous when
`\Delta G>0`

As the value of
`\Delta G_(rxn)` is less than 0. So, the reaction will be spontaneous.

Yes, the hydrolysis of ATP spontaneous under these conditions.