Respuesta :
Answer:
For A: The free energy change of the reaction is -5339.76 J/mol
For B: The units of free energy change of the reaction are kJ/mol
For C: The forward reaction is favorable and reverse reaction is unfavorable.
Explanation:
For the given chemical reaction:
[tex]DHAP\rightleftharpoons G_3P[/tex]
- For A:
Relation between standard Gibbs free energy and equilibrium constant follows:
[tex]\Delta G^o=-RT\ln K_{eq}[/tex]
To calculate the free energy change, we use the equation:
[tex]\Delta G=\Delta G^o+RT\ln Q[/tex]
Or,
[tex]\Delta G=-RT^o\ln K_{eq}+RT\ln Q[/tex]
where,
[tex]\Delta G[/tex] = Free energy change
R = Gas constant = [tex]8.314J/K mol[/tex]
[tex]T^o[/tex] = standard temperature = [tex]25^oC=[273+25]K=298K[/tex]
T = temperature of the cell = [tex]37^oC=[273+37]K=310K[/tex]
[tex]K_[eq}[/tex] = equilibrium constant = [tex]5.4\times 10^{-2}[/tex]
Q = reaction coefficient = [tex]\frac{[G_3P]}{[DHAP]}[/tex]
[tex][G_3P][/tex] = 0.06 M
[DHAP] = 0.125 M
Putting values in above equation, we get:
[tex]\Delta G=[-(8.314J/mol.K\times 298K\times \ln (5.4\times 10^{-2}))]+[(8.314J/mol.K\times 310K\times \ln (\frac{0.06}{0.125}))]\\\\\Delta G=-[-7231.46]+[-1891.7]=-5339.76J/mol[/tex]
Hence, the free energy change of the reaction is -5339.76 J/mol
- For B:
Converting the free energy change of the reaction into kilojoules, we use the conversion factor:
1 kJ = 1000 J
So, [tex]-5339.76J/mol\times \frac{1kJ}{1000J}=-5.34kJ/mol[/tex]
Hence, the units of free energy change of the reaction are kJ/mol
- For C:
For the reaction to be spontaneous, the Gibbs free energy of the reaction must come out to be negative. But, from the above calculation, the Gibbs free energy of the reaction is positive. Thus, the reaction is non-spontaneous.
As, the free energy change of the reaction is negative.
Hence, the forward reaction is favorable and reverse reaction is unfavorable.
