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**Problem**: Codeine (C18H21NO3) is a narcotic pain reliever that forms a salt with HCl. What is the pH of 0.050 M codeine hydrochloride (pKb of codeine = 5.80)?

###### FREE Expert Solution

###### FREE Expert Solution

Codeine hydrochloride → salt

HC_{18}H_{21}NO_{3}Cl → **HC _{18}H_{21}NO_{3}**

^{+}+ Cl

^{-}

**Equilibrium reaction:** **HC _{18}H_{21}NO_{3}**

^{+}

_{(aq)}+ H_{2}O_{(l)}**⇌ C**

_{18}H_{21}NO_{3}_{(aq)}+ H_{3}O^{+}_{(aq)}*****HC _{18}H_{21}NO_{3}**

^{+}conjugate acid of

**C**

_{18}H_{21}NO_{3}**Step 1:**** **Construct an ICE chart for the reaction.

**Step 2:** Write the K_{a} expression and calculate for K_{a}.

$\overline{){{\mathbf{K}}}_{{\mathbf{a}}}{\mathbf{=}}\frac{\mathbf{products}}{\mathbf{reactants}}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{\mathbf{\left[}{\mathbf{C}}_{\mathbf{18}}{\mathbf{H}}_{\mathbf{21}}{\mathbf{NO}}_{\mathbf{3}}\mathbf{\right]}\mathbf{\left[}{\mathbf{H}}_{\mathbf{3}}{\mathbf{O}}^{\mathbf{+}}\mathbf{\right]}}{\left[{\mathrm{HC}}_{18}{H}_{21}{{\mathrm{NO}}_{3}}^{+}\right]}$

*Solids and liquids are not included in the expression*

${\mathbf{K}}_{\mathbf{b}}\mathbf{=}{\mathbf{10}}^{\mathbf{-}{\mathbf{pK}}_{\mathbf{b}}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{b}}\mathbf{=}{\mathbf{10}}^{\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{80}}$

**K _{b} = 1.5849x10^{–6}**

$\frac{{\mathbf{K}}_{\mathbf{w}}}{{\mathbf{K}}_{\mathbf{b}}}\mathbf{=}\frac{{\mathbf{K}}_{\mathbf{a}}\mathbf{\xb7}\overline{){\mathbf{K}}_{\mathbf{b}}}}{\overline{){\mathbf{K}}_{\mathbf{b}}}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{14}}}{\mathbf{1}\mathbf{.}\mathbf{5849}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}}$

**K _{a} = 6.3096x10^{–9}**

**Step 3:**** **Calculate the equilibrium concentrations.

${\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{\left[\mathbf{x}\right]\left[\mathbf{x}\right]}{\left[\mathbf{0}\mathbf{.}\mathbf{050}\mathbf{-}\mathbf{x}\right]}\phantom{\rule{0ex}{0ex}}\overline{){{\mathbf{K}}}_{{\mathbf{a}}}{\mathbf{=}}\frac{{\mathbf{x}}^{\mathbf{2}}}{\mathbf{0}\mathbf{.}\mathbf{050}\mathbf{-}\mathbf{x}}}$

###### Problem Details

Codeine (C_{18}H_{21}NO_{3}) is a narcotic pain reliever that forms a salt with HCl. What is the pH of 0.050 M codeine hydrochloride (p*K*_{b} of codeine = 5.80)?

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