For this, we can use the Henderson-Hasselbalch Equation, which states that:
pH = pKa + log([base]/[acid])
We can find the pKa of the solution by finding Ka from Kb
Kb*Ka = 10^-14
Ka = (10^-14)/(1.8*10^-5)
Ka = 5.56*10^-10
pKa = -logKa
pKa = 9.2553
Now, we can say:
pH = 9.2553 + log([base]/[acid])
We have 1 M ammonia, the base, and 1 M ammonium ions, the acid, so now we have:
pH = 9.2553 + log(1/1)
pH = 9.2553 + 0
pH = 9.2553
pH = pKa + log([base]/[acid])
We can find the pKa of the solution by finding Ka from Kb
Kb*Ka = 10^-14
Ka = (10^-14)/(1.8*10^-5)
Ka = 5.56*10^-10
pKa = -logKa
pKa = 9.2553
Now, we can say:
pH = 9.2553 + log([base]/[acid])
We have 1 M ammonia, the base, and 1 M ammonium ions, the acid, so now we have:
pH = 9.2553 + log(1/1)
pH = 9.2553 + 0
pH = 9.2553
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Because?