How would you calculate K_b for the formate ion, given that the K_a for formic acid is 1.8 $\times$ 10^-4?

Question

Quizplus · Accepted Answer

The equation for the equilibrium between formic acid (HA) and the formate ion (A-) is: HA ⇌ H+ + A- The acid dissociation constant (Ka) for formic acid is: Ka = [H+][A-]/[HA] Rearranging this equation gives: [A-]/[HA] = Ka/[H+] The acid dissociation constant for formic acid is given as 1.8×10^-4. The equilibrium constant for the dissociation of the formate ion (K_b) can be related to the acid dissociation constant for formic acid by the following equation: K_b = [H+][A-]/[HA] Substituting [A-]/[HA] with Ka/[H+] gives: K_b = Ka[H+]/[HA] The equilibrium constant for the dissociation of water (K_w) can be expressed as the product of the concentrations of hydroxide ion (OH-) and hydrogen ion (H+) divided by the concentration of water (H2O): K_w = [H+][OH-]/[H2O] The product of [H+] and [OH-] can be expressed as Kw, the ion-product constant for water: [H+][OH-] = Kw Substituting this expression into the equation for K_w gives: K_w = Kw/[H+] The ion-product constant for water is 1.0 x 10^-14. To relate the equilibrium constant for water (K_w) to the equilibrium constant for the dissociation of the formate ion (K_b), we can use the fact that the sum of the equilibrium constants for a set of sequential reactions is equal to the equilibrium constant for the overall reaction. In this case, we can assume the following set of chemical reactions: HA + H2O ⇌ H3O+ + A- A- + H2O ⇌ OH- + HA The overall reaction is: 2H2O ⇌ H3O+ + OH- The equilibrium constant for the overall reaction is equal to K_w, and can be written as: K_w = K_bK_a/K_w Solving for K_b gives: K_b = K_wK_a/K_w = K_a/K_w Substituting the values given in the question, we get: K_b = (1.8 x 10^-4)/(1.0 x 10^-14) = 1.8 x 10^10 Therefore, the correct answer is B, which gives the expression for K_b in terms of K_a and K_w as: K_b = K_w/K_a

How Would You Calculate Kb for the Formate Ion, Given ×\times×

How Would You Calculate K_b for the Formate Ion, Given $\times$