Question

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] = 0.50 mM, and [HPO42–] = 5.0 mM.

Answer 1

-32.28 kJ/mol

Step-by-step explanation:

The expression for the calculation of the Gibbs energy is shown below as:

`\Delta{G} =\Delta{G^0}+RT \ln Q`

`\Delta{G^0}` standard Gibbs energy

R is Gas constant having value = 0.008314 kJ / K mol

Given temperature, T = 37.0 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15

So,

T₁ = (37.0 + 273.15) K = 310.15 K

Q is the reaction quotient.

The reaction quotient of an equilibrium reaction measures relative amounts of the products and the reactants present during the course of the reaction at particular point in the time. It is the ratio of the concentration of the products and the reactants each raised to their stoichiometric coefficients. The concentration of the liquid and the gaseous species does not change and thus is not written in the expression.

The equation is as follows:-

`ATP_((aq)) +H_2O_((l))\rightleftharpoons ADP_((aq)) +HPO_4^(2-)_((aq))`

The expression for the reaction quotient is:-

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

Given,

`[ATP]=5.0 mM`

`[ADP]=0.50 mM`

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

So,

`Q=(0.50* 5.0)/(5.0)=0.50`

Applying in the above equation,

`\Delta{G} =-30.5 kJ/mol+0.008314* 310.15* \ln 0.50\ kJ/mol=-30.5 kJ/mol-1.78\ kJ/mol=-32.28\ kJ/mol`

ΔGrxn = -32.28 kJ/mol