Question

The value of ΔG°\' for the conversion of dihydroxyacetone phosphate to glyceraldehyde-3-phosphate (GAP) is 7.53 kJ/mol. If the concentration of dihydroxyacetone phosphate at equilibrium is 1.85 mM, what is the concentration of glyceraldehyde-3-phosphate? Assume a temperature of 25.0 °C. The constant R = 8.3145 J/(mol·K)

Answer 1

Answer: The concentration of glyceraldehyde-3-phosphate is 0.0886 nM.

Explanation:

The chemical equation for the conversion follows:

$\text{Dihydroxyacetone phosphate}\rightleftharpoons \text{Glyceraldehyde-3-phosphate}$

The expression for $K_{eq}$ of above equation is:

$K_{eq}=\frac{\text{[Glyceraldehyde-3-phosphate]}}{\text{[Dihydroxyacetone phosphate]}}$

Let the concentration of glyceraldehyde -3-phosphate be 'x'

Relation between standard Gibbs free energy and equilibrium constant follows:

$\Delta G^o=-RT\ln K_1$

where,

$\Delta G^o$ = standard Gibbs free energy = 7.53 kJ/mol = 7530 J/mol  (Conversion factor: 1kJ = 1000J)

R = Gas constant = $8.3145J/K mol$

T = temperature = $25^oC=[273+25]K=298K$

[Glyceraldehyde-3-phosphate] = x

[Dihydroxyacetone phosphate] = 1.85 mM

Putting values in above equation, we get:

$7530J/mol=-(8.3145J/Kmol)\times 298K\times \ln (\frac{x}{1.85})\\\\x=0.0886mM$

Hence, the concentration of glyceraldehyde-3-phosphate is 0.0886 nM.