# Problem: A 120.0 -mL buffer solution is 0.110 M in NH3 and 0.135 M in NH4Br. What mass of HCl can this buffer neutralize before the pH falls below 9.00?

###### FREE Expert Solution

Determine the moles of the weak acid and conjugate base:

0.0132 mol

0.0162 mol

Construct an ICF Chart:

$\overline{){\mathbf{pH}}{\mathbf{=}}{{\mathbf{pK}}}_{{\mathbf{a}}}{\mathbf{+}}{\mathbf{log}}\mathbf{\left(}\frac{{\mathbf{NH}}_{\mathbf{3}}}{{{\mathbf{NH}}_{\mathbf{4}}}^{\mathbf{+}}}\mathbf{\right)}}$

${\mathbf{pK}}_{\mathbf{a}}\mathbf{=}\mathbf{14}\mathbf{-}{\mathbf{pK}}_{\mathbf{b}}$

${\mathbf{pK}}_{\mathbf{a}}\mathbf{=}\mathbf{14}\mathbf{-}\mathbf{4}\mathbf{.}\mathbf{75}\mathbf{=}$9.25

${\mathbf{9}}{\mathbf{=}}{\mathbf{9}}{\mathbf{.}}{\mathbf{25}}{\mathbf{+}}{\mathbf{log}}\mathbf{\left(}\frac{{\mathbf{NH}}_{\mathbf{3}}}{{{\mathbf{NH}}_{\mathbf{4}}}^{\mathbf{+}}}\mathbf{\right)}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{log}}\mathbf{\left(}\frac{{\mathbf{NH}}_{\mathbf{3}}}{{{\mathbf{NH}}_{\mathbf{4}}}^{\mathbf{+}}}\mathbf{\right)}{\mathbf{=}}{\mathbf{9}}{\mathbf{-}}{\mathbf{9}}{\mathbf{.}}{\mathbf{25}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{log}}\mathbf{\left(}\frac{{\mathbf{NH}}_{\mathbf{3}}}{{{\mathbf{NH}}_{\mathbf{4}}}^{\mathbf{+}}}\mathbf{\right)}{\mathbf{=}}{\mathbf{-}}{\mathbf{0}}{\mathbf{.}}{\mathbf{25}}$

$\mathbf{\left(}\frac{{\mathbf{NH}}_{\mathbf{3}}}{{{\mathbf{NH}}_{\mathbf{4}}}^{\mathbf{+}}}\mathbf{\right)}{\mathbf{=}}{{\mathbf{10}}}^{\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{25}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{\left(}\frac{{\mathbf{NH}}_{\mathbf{3}}}{{{\mathbf{NH}}_{\mathbf{4}}}^{\mathbf{+}}}\mathbf{\right)}{\mathbf{=}}{\mathbf{0}}{\mathbf{.}}{\mathbf{5623}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{\left(}\frac{\mathbf{0}\mathbf{.}\mathbf{0132}\mathbf{-}\mathbf{x}}{\mathbf{0}\mathbf{.}\mathbf{0162}\mathbf{+}\mathbf{x}}\mathbf{\right)}{\mathbf{=}}{\mathbf{0}}{\mathbf{.}}{\mathbf{5623}}$

$\mathbf{\left(}\frac{\mathbf{0}\mathbf{.}\mathbf{0132}\mathbf{-}\mathbf{x}}{\mathbf{0}\mathbf{.}\mathbf{0162}\mathbf{+}\mathbf{x}}\mathbf{\right)}{\mathbf{=}}{\mathbf{0}}{\mathbf{.}}{\mathbf{5623}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{0}}{\mathbf{.}}{\mathbf{5623}}\left(0.0162+x\right){\mathbf{=}}{\mathbf{0}}{\mathbf{.}}{\mathbf{0132}}{\mathbf{-}}{\mathbf{x}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{9}}{\mathbf{.}}{\mathbf{10926}}{\mathbf{×}}{{\mathbf{10}}}^{\mathbf{-}\mathbf{3}}{\mathbf{+}}{\mathbf{0}}{\mathbf{.}}{\mathbf{5623}}\left(x\right){\mathbf{=}}{\mathbf{0}}{\mathbf{.}}{\mathbf{0132}}{\mathbf{-}}{\mathbf{x}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{0}}{\mathbf{.}}{\mathbf{5623}}\left(x\right)+x={\mathbf{0}}{\mathbf{.}}{\mathbf{0132}}{\mathbf{-}}{\mathbf{9}}{\mathbf{.}}{\mathbf{10926}}{\mathbf{×}}{{\mathbf{10}}}^{\mathbf{-}\mathbf{3}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{\overline{)\mathbf{1}\mathbf{.}\mathbf{5623}}\mathbf{x}}{\overline{)\mathbf{1}\mathbf{.}\mathbf{5623}}}{\mathbf{=}}\frac{\mathbf{4}\mathbf{.}\mathbf{09074}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}}{\mathbf{1}\mathbf{.}\mathbf{5623}}$

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###### Problem Details

A 120.0 -mL buffer solution is 0.110 M in NH3 and 0.135 M in NH4Br. What mass of HCl can this buffer neutralize before the pH falls below 9.00?