In the fifth reaction of Glycolosis, G3P dehydrogenase converts glyceraldehydes-3-phosphate into glycerate-1,3-bisphosphate. In order to make the reaction spontaneous at biological conditions it must be coupled to the reduction of NAD+.


a) DG° for the reaction of just G-3-P, which is shown below, is -3.4 kJ/mol at 298K. Calculate the values of DG°¢, K, and K¢ for the reaction, where DG°¢ = -RTlnK¢.
H5C3O6P + HPO4 Þ H4C3O10P2 + 2H+
b) Calculate the Gibbs energy change (DGrxn ) using both the physical chemical standard state and biochemical standard state for the reaction when [G-1,3-P2] = 30mM and [G-3-P] = 15 mM.

To calculate the values of DG°¢, K, and K¢ for the reaction in question, we need to use the Gibbs free energy equation and the relationship between DG°¢ and K¢. Here's how you can do it:

a) To calculate DG°¢:

1. Start with the given value of DG° for the reaction involving just G-3-P, which is -3.4 kJ/mol at 298K.

2. Convert the temperature from Kelvin to Celsius: 298K - 273 = 25°C.

3. Use the equation DG°¢ = -RTlnK¢, where R is the gas constant (8.314 J/mol*K) and T is the temperature in Kelvin.

DG°¢ = - (8.314 J/mol*K) * (298 K) * ln(K¢)

4. Use the conversion factor 1 kJ = 1000 J to convert the result to kJ/mol.

DG°¢ = - (8.314 J/mol*K) * (298 K) * ln(K¢) / 1000

b) To calculate K and K¢:

1. Use the relationship between DG°¢ and K¢:

DG°¢ = -RTlnK¢

Rearrange the equation to solve for K¢:

K¢ = e^(-DG°¢/RT)

Where e is the base of the natural logarithm (approximately 2.71828).

2. Calculate K¢ using the value of DG°¢ obtained in part a) and the temperature in Kelvin (298K).

3. To calculate K, use the equation K = (K¢ * [H+]) / ([HPO4] * [H5C3O6P]) based on the balanced chemical equation for the reaction.

Now let's move on to part b) and calculate the Gibbs energy change (DGrxn):

1. Determine the concentration of G-1,3-P2 and G-3-P based on the given values: [G-1,3-P2] = 30 mM and [G-3-P] = 15 mM.

2. Use the equation DGrxn = DG° + RTlnQ, where Q is the reaction quotient.

3. Calculate the reaction quotient Q using the concentrations of G-1,3-P2 and G-3-P in the equation.

Remember to use consistent units throughout the calculations.