A solution is prepared by mixing 16ml. of 2.5M HCl and 40ml. of 2M NH_4OH. What will be the pH of the solution if pK_b is 4.75? Thank you:)

1 Answer
Oct 4, 2017

sf(pH=9.25)

Explanation:

Ammonium hydroxide is not a discrete substance and is better referred to as "aqueous ammonia" sf(NH_(3(aq)).

sf(HCl_((aq))+NH_(3(aq))rarrNH_(4)Cl_((aq)))

sf(c=n/v)

:.sf(n=cxxv)

:.sf(n_(HCl)=2.5xx16/1000=0.04)

sf(n_(NH_3)=2xx40/1000=0.08)

The sf(NH_3) is INXS. This means that sf(n_(NH_4^+)=0.04)

and the no. moles sf(NH_3) remaining is given by:

sf(n_(NH_3)=0.08-0.04=0.04)

sf(NH_4^+) ions undergo hydrolysis:

sf(NH_4^+rightleftharpoonsNH_3+H^+)

For which:

sf(K_a=([NH_3][H^+])/([NH_4^+]))

These are equilibrium concentrations which, because sf(K_a) is small, we will approximate to initial concentrations.

Rearranging:

sf([H^+]=K_axx([NH_4^+])/([NH_3])

We have a buffer solution here.

Because the total volume is common we can put the no. moles straight into this:

sf([H^+]=K_axxcancel(0.04)/cancel(0.04))

sf([H^+]=K_a)

:.sf(pH=pK_a)

We know that sf(pK_a+pK_b=14)

:.sf(pK_a=14-pK_b=14-4.75=9.25)

:.sf(pH=9.25)