The pKb of ammonia solution, NH3(aq) is 4.76. A buffer solution contains NH4Cl and NH3, has a pH of 9.45, and a total ammonia concentration (all forms) of 0.400 M. What is the concentration of NH4+?
(Hint: [NH4+] + [NH3] = 0.400 M)
3.0
To find the concentration of NH4+, we can use the equation for the pH of a buffer solution:
pH = pKa + log([A-]/[HA])
In this case, NH3 is the base (A-) and NH4+ is the conjugate acid (HA). We are given the pH of 9.45. We also know that the pKa of NH4+ is related to the pKb of NH3 through the equation:
pKa + pKb = 14
So, we can find the pKa:
pKa = 14 - pKb
= 14 - 4.76
= 9.24
Now, we can plug in the values into the pH equation:
9.45 = 9.24 + log([NH3]/[NH4+])
We are given that the total ammonia concentration is 0.400 M, which is the sum of the concentrations of NH3 and NH4+. So, we can rewrite the equation as:
9.45 = 9.24 + log([NH3] + [NH4+])
Now, we can rearrange the equation to solve for [NH4+]:
log([NH3] + [NH4+]) = 9.45 - 9.24
[NH3] + [NH4+] = 10^(9.45 - 9.24)
[NH3] + [NH4+] = 10^0.21
[NH3] + [NH4+] = 1.581
We are also given the equation: [NH3] + [NH4+] = 0.400
So, we can rewrite the equation as:
0.400 = 1.581 - [NH4+]
Solving for [NH4+], we get:
[NH4+] = 1.581 - 0.400
= 1.181
Therefore, the concentration of NH4+ in the buffer solution is 1.181 M.