The given mixture forms a basic buffer solution.
Millimoles of base NH4OH=5×0.1=0.5 mmol
Millimoles of salt NH4Cl=250×0.1=25 mmol
Using the Henderson-Hasselbalch equation for a basic buffer:
pOH=pKb+log([Base][Salt])
pOH=4.74+log(0.525)
pOH=4.74+log(50)
We know that log(50)=log(5×10)=log5+log10=0.70+1=1.70
pOH=4.74+1.70=6.44
The pH of the solution is given by:
pH=14−pOH
pH=14−6.44=7.56
pH=756×10−2
Answer: 756