Answer :
[tex]Determine\ the \ concentration \ of \ $\mathrm{H}_3 \mathrm{O}^{+}$:$\begin{aligned}{\left[\mathrm{H}_3 \mathrm{O}^{+}\right] } &=10^{-\mathrm{pH}} \\&=10^{-55} \\&=3 \times 10^{-6} \mathrm{M}\end{aligned}$[/tex]
[tex]This\ range\ does\ not \ match \ with\ the \ available \ acids.[/tex]
[tex]Determine \ the \ concentration \ of \ $\mathrm{OH}^{-}$:$\begin{aligned}\mathrm{OH}^{-} &=\frac{K_w}{\left[\mathrm{H}_3 \mathrm{O}^{+}\right]} \\&=\frac{1.0 \times 10^{-14}}{3 \times 10^{-6}} \\&=3 \times 10^{-4} \mathrm{M}\end{aligned}$[/tex]
[tex]This \ range \ matches \ with \ $\mathrm{C}_5 \mathrm{H}_5 \mathrm{~N}, K_{\mathrm{b}}=1.7 \times 10^{-9}$. Write the conjugate acid of the base by adding one hydrogen atom as $\mathrm{C}_5 \mathrm{H}_5 \mathrm{NH}^{+}$. Write the conjugate acid-base pair for the required $\mathrm{pH}$ :$\mathrm{C}_5 \mathrm{H}_5 \mathrm{NH}^{-} / \mathrm{C}_5 \mathrm{H}_5 \mathrm{~N}$[/tex]
What is a conjugate acid and base pair?
An acid-base pair that differs by one proton is referred to as a conjugate pair. A conjugate acid-base pair is a pair of substances that can both absorb and donate hydrogen ions to one another. A proton is added to the compound to create the conjugate acid, and a proton is taken out to create the conjugate base. When a proton is supplied to a base, a conjugate acid is created, and vice versa when a proton is taken away from an acid, a conjugate base is created.
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