Final answer:
To calculate the actual delta G for the reaction dihydroxyacetone phosphate → glyceraldehyde-3-phosphate at 298 K when given the initial concentrations of the reactants and products, we can use the formula delta G = delta G° + RT ln(Q). The calculation involves determining the reaction quotient (Q) using the concentrations of the reactants and products, and plugging the values into the formula to find the actual delta G.
Step-by-step explanation:
The reaction you are asking about, dihydroxyacetone phosphate → glyceraldehyde-3-phosphate, has a standard change in Gibbs free energy (delta G) of 7.53 kJ/mol at 298 K. To calculate delta G for this reaction at 298 K when [dihydroxyacetone phosphate] = 0.100 M and [glyceraldehyde-3-phosphate] = 0.00400 M, we can use the formula: delta G = delta G° + RT ln(Q), where delta G is the actual change in Gibbs free energy, delta G° is the standard change in Gibbs free energy, R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin (298 K), and Q is the reaction quotient.
To calculate Q, we need to multiply the concentrations of the products raised to their stoichiometric coefficients, and divide by the concentrations of the reactants raised to their stoichiometric coefficients. In this case, Q = ([glyceraldehyde-3-phosphate]^1) / ([dihydroxyacetone phosphate]^1). Since the stoichiometric coefficients are both 1, Q simplifies to [glyceraldehyde-3-phosphate] / [dihydroxyacetone phosphate].
Now we can plug the values into the formula: delta G = 7.53 kJ/mol + (8.314 J/(mol·K))(298 K) ln(0.00400 M / 0.100 M). By performing the calculation, we can find the actual value of delta G for this reaction at 298 K when [dihydroxyacetone phosphate] = 0.100 M and [glyceraldehyde-3-phosphate] = 0.00400 M.