# Problem: Calculate the pH of a solution formed by mixing 250.0 mL of 0.15 M NH4CI with 100.0 mL of  0.20 M NH3. The Kb for NH3 is 1.8 x 10-5. A) 8.98 B) 9.25 C) 9.53 D) 9.13 E) 4.74

###### FREE Expert Solution

Henderson-Hasselbalch equation.

Determine the composition of the solution.

NH4Cl → breaks up in the solution

NH4Cl → NH4+ + Cl-

Equilibrium reaction:  NH4+ + H2O ⇌ NH3 + H3O+

NH4+ → weak acid

NH3 → conjugate base

• The solution is composed of a weak acid and its conjugate base, therefore we have a buffer.

Calculate the pKa of the NH4+.

$\frac{{\mathbf{K}}_{\mathbf{w}}}{{\mathbf{K}}_{\mathbf{b}}}\mathbf{=}\frac{{\mathbf{K}}_{\mathbf{a}}\mathbf{·}\overline{){\mathbf{K}}_{\mathbf{b}}}}{\overline{){\mathbf{K}}_{\mathbf{b}}}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{{\mathbf{K}}_{\mathbf{w}}}{{\mathbf{K}}_{\mathbf{b}}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{14}}}{\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{5}}}$

Ka = 5.555x10-10

pKa = 9.25

Determine the initial moles of the weak acid and conjugate base present.

Recall molarity is:

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###### Problem Details

Calculate the pH of a solution formed by mixing 250.0 mL of 0.15 M NH4CI with 100.0 mL of  0.20 M NH3. The Kb for NH3 is 1.8 x 10-5

A) 8.98

B) 9.25

C) 9.53

D) 9.13

E) 4.74