Answer:
Δ [tex]G_{rxn}[/tex] = −51. 4 kJ/mol
However, since Δ [tex]G_{rxn}[/tex] is negative. The hydrolysis of ATP for this reaction is said to be spontaneous
Explanation:
From the question; The equation for this reaction can be represented as :
[tex]ATP_{(aq)} + H_2O_{(l)} \to ADP_{(aq)}+ HPO_4^{2-}} _{(aq)}[/tex]
where:
[tex]\Delta G ^0 _{rxn} =[/tex]-30.5 kJ/mol
= -30.5 kJ/mol × 1000 J/ 1 kJ
= -30.5 × 10 ⁻³ J/mol
Temperature T = 37 ° C
= (37+273)
= 310 K
pH = 7.0
[ATP] = 5.0 mM
= 5.0mM × 1M/1000mM
= 0.005 M
[ADP] = 0.30 mM
= 0.30 mM × 1M/1000mM
= 0.0003 M
[tex][HPO_4^{2-}}][/tex] = 5.0 mM
= 5.0mM × 1M/1000mM
= 0.005 M
The objective is to calculate the value for Δ [tex]G_{rxn}[/tex] in the biological cell and to determine if the hydrolysis of ATP is spontaneous under these conditions.
Now;
From the equation given; the equilibrium constant [tex]K_{eq}[/tex] can be expressed as:
[tex]K_{eq} = \dfrac{[ADP][ HPO_4^{2-}]} {[ATP]}[/tex]
[tex]K_{eq} = \dfrac{(0.0003 \ M)(0.005 \ M)} {(0.005 \ M)}[/tex]
[tex]K_{eq} = 3*10^{-4}[/tex]
The Δ [tex]G_{rxn}[/tex] in the biological cell can now be calculated as:
Δ [tex]G_{rxn}[/tex] = [tex](-30.5 * 10 ^3 \ J/mol) + (8.314 \ J/mol.K)(310 K ) In ( 3*10^{-4})[/tex]
Δ [tex]G_{rxn}[/tex] = [tex](-30.5 * 10 ^3 \ J/mol) + (-20906.68126)[/tex]
Δ [tex]G_{rxn}[/tex] = −51406.68 J/mol
Δ [tex]G_{rxn}[/tex] = −51. 4 × 10³ J/mol
Δ [tex]G_{rxn}[/tex] = −51. 4 kJ/mol
Thus since Δ [tex]G_{rxn}[/tex] is negative. The hydrolysis for this reaction is said to be spontaneous
