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 the reaction ATP ( aq ) + H 2 O ( l ) ⟶ ADP ( aq ) + HPO 2 − 4 ( aq ) for which Δ G ∘ rxn = − 30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of Δ G rxn in a biological cell in which [ ATP ] = 5.0 mM, [ ADP ] = 0.20 mM, and [ HPO 2 − 4 ] = 5.0 mM.

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-03-27T09:28:37+01:00

Answer:

-52.5 kJ/mol

Explanation:

Equation for the reaction is as follows:

[tex]ATP_{(aq)} + H_2O_{(l)}----->ADP_{(aq)}+HPO_{4}^{2-}_{(aq)}[/tex]

Equilibrium constant [tex]K_{eq}= \frac{[ADP][HPO_4^{2-}]}{[ATP]}[/tex]

Given that ;

[ATP] =5.0 mM = 0.005 M

[ADP] = 0.20 mM = 0.0002 M

[HPO₄²⁻] = 5.0 mM = 0.005 M

[tex]K_{eq} = \frac{(0.0002M)(0.005M)}{(0.005M)}[/tex]

[tex]K_{eq} =0.0002 M[/tex]

Also; other given parameters include:

[tex]\delta G^0_{rxn}=-30.5kJ/mol[/tex] to J/mol; we have:

= [tex]-30.5 kJ/mol*\frac{1000J}{1kJ}[/tex]

= [tex]-30.5*10^3 J/mol[/tex]

Temperature (T) = 37.0 °C

= (37.0 + 273) K

= 310 K

The Δ[tex]G_{rxn}[/tex] can be calculated as:

Δ[tex]G_{rxn}[/tex] = Δ[tex]G_{rxn}^0RTIn(K_{eq})[/tex]

Δ[tex]G_{rxn}[/tex] = ([tex]-30.5*10^3 J/mol[/tex])+(8.314 J/mol.K)(310) In(0.0002)

Δ[tex]G_{rxn}[/tex] = (-30500 J/mol) + (2577.34 J/mol) × (-8.5172)

Δ[tex]G_{rxn}[/tex] = -52451.669 J/mol

Δ[tex]G_{rxn}[/tex] = -52.5 kJ/mol

Therefore, the Δ[tex]G_{rxn}[/tex] is -52.5 kJ/mol . This implies that the hydrolysis of ATP is spontaneous.