Final answer:
To calculate Kb for NH2 with a given pOH of 2.57, convert pOH to hydroxide ion concentration, then use the formula Kb = [OH-]^2 / [NHz], assuming a 1:1 ratio from the dissociation reaction.
Step-by-step explanation:
To calculate the base dissociation constant (Kb) for the base NH2, we need to first convert the pOH to the hydroxide ion concentration [OH-]. The pOH is given as 2.57, so the concentration of OH- is calculated using the following formula:
[OH-] = 10-pOH = 10-2.57
After calculating the hydroxide ion concentration, we can use the formula Kb = [OH-]2 / [NHz], where we must assume that the concentration of the hydroxide ion is squared because in the reaction NH2 + H2O => NH3+ + OH-, the [OH-] produced is equal to the [NH3+] produced, so we have a 1:1 ratio.
Using the provided concentration of NH2, which is 0.4 M, we get:
Kb = [OH-]2 / [NHz] = (10-2.57)2 / 0.4 M
Note that we must carry out the actual calculations for [OH-] and thus for Kb to determine their numerical values.