Question

What is the [OH-] of a solution which is 0.18 M in ammonium ion and 0.10 M in ammonia?

The answer should be 1.0 x 10^-3. Please show al the work. Thanks!

Answer 1

Let α be the dissociation of the weak base,NH₄OH
                        NH₄OH <---> NH₄⁺ + OH^-

initial conc.            c               0         0

change               -cα            +cα      +cα

Equb. conc.         c(1-α)        cα      cα

Dissociation constant, K_b = (cα x cα) / ( c(1-α)               

                                          = c α² / (1-α)

In the case of weak bases α is very small so 1-α is taken as 1

So K_b = cα²

==> α = √ ( K_b / c )

Given K_b = 1.8x10^-5

[NH₄OH] = 0.10 M & [NH₄+] = 0.18 M

      c(1-α) = 0.10 M     &   cα = 0.18 M

So [OH-] = cα = 0.18 M