Final answer:
The question asks for the ratio of glutamate/glutamine to spontaneously drive a biochemical reaction, which cannot be answered without the equilibrium constant. However, provided exercises involve calculating K for the Haber process, where K can be found using the concentrations of reactants and products at equilibrium for the synthesis of ammonia.
Step-by-step explanation:
The reaction given (Glutamate + ammonia → glutamine + H₂O) is a biochemical reaction occurring in cells, involving amino acids and related to metabolic pathways. To answer the original question about the ratio of glutamate/glutamine required for the reaction to proceed spontaneously at 25°C, information regarding the equilibrium constant (K) and concentrations of other species at equilibrium would be needed. Without this information, the Gibb's free energy change (ΔG) cannot be computed directly, and hence, the spontaneity of the reaction cannot be assessed.
However, the related exercises you've listed, such as Example 14.5.2 and Example 16.7.2, pertain not to glutamate and glutamine, but to the Haber process for the synthesis of ammonia. These exercises require calculating the equilibrium constant (K) given the concentrations of reactants and products at equilibrium. Let's consider Exercise 14.5.2:
For a reaction involving H₂ and N₂ producing NH₃, the equilibrium constant expression based on the balanced equation N₂ + 3H₂ → 2NH₃ is: K = [NH₃]² / ([N₂][H₂]³).
Given equilibrium concentrations:
[NH₃] = 0.00272 M
[H₂] = 0.1248 M
[N₂] = 0.0416 M
The calculation of K is as follows:
K = (0.00272²) / (0.0416 × 0.1248³) = 1.12 x 10^-5
Note that this equilibrium constant reflects the product-favored nature of the reaction at this temperature, but it does not indicate the reaction rate, which may be slow at room temperature as noted in the Haber Process examples provided.