How many moles of NaOH must be added to a buffer to change its pH by 1 unit?

A buffer solution is 1.50 M in NH3 and 1.30 M in NH4Cl. How many moles of NaOH must be added to 1.00 L of the buffer to change its pH by 1.00 unit? Assume the volume remains constant. Kb of NH3 = 1.8 10-5.How many moles of NaOH must be added to a buffer to change its pH by 1 unit?
The buffer counters the effect of OH- addition by the reaction:

NH4+ + OH- -%26gt; NH4OH (or NH3).



So we first find the pOH of the initial buffer. The H-H eqtn is:

[NH4+][OH-]/[NH3]= Kb. Then [OH-]= 1.5Kb/1.3. To change it one pH unit (which, for a base will be upwards), the [OH-] is increased tenfold. Then [OH-]=15Kb/1.3. Also, the total amount of ammonia/ammonium is unchanged, so [NH3]+[NH4+]=2.8M Substituting, the [OH-] relation to Kb into the H-H eqtn, we get

15[NH4+]/1.3[NH3]=1, or 15[NH4+]=1.3[NH3]. Sub that back into the mass balance, 16.3/15[NH3]=2.8 or [NH3]=42/16.3. The difference between that and 1.5 M is the NaOH moles added (about 1.1).