Question

write the expression for the $k_b$ for each of the following reactions
$\ce{hco3^{-1} + h2o <-> oh^{-1} + h2co3}$
\\k_b = \frac{\ce{oh^{-1}} \\_\\_1\\_\\_}{\\_\\_2\\_\\_}\\

$\ce{hpo4^{-2} + h2o <-> oh^{-1} + h2po4^{-1}}$\\k_b = \frac{\ce{oh^{-1}} \\_\\_3\\_\\_}{\\_\\_4\\_\\_}\\

a. $\ce{h2o_{(liq)}}$ b. $\ce{oh^{-1}}$ c. $\ce{h3o^{+1}}$ d. $\ce{so4^{-2}}$ e. $\ce{mg^{+2}}$ f. $\ce{cl^{-1}}$
g. $\ce{hpo4^{-2}}$ h. $\ce{h2po4^{-1}}$ i. $\ce{co3^{-2}}$ j. $\ce{hco3^{-1}}$ k. $\ce{h2s}$ l. $\ce{hs^{-1}}$
m. $\ce{s^{-2}}$ n. $\ce{h2o}$ o. $\ce{h2co3}$ p. $\ce{h3po4}$ q. $\ce{hc2h3o2}$
r. $\ce{c2h3o2^{-1}}$ s. $\ce{po4^{-3}}$ t. $\ce{so4^{-2}}$ u. $\ce{caco3_{(s)}}$ v. $\ce{hf_{(aq)}}$

Explanation:

Step1: Recall \( K_b \) expression rule

For a base hydrolysis reaction \( \text{Base} + \text{H}_2\text{O}
ightleftharpoons \text{OH}^- + \text{Conjugate Acid} \), the \( K_b \) expression is \( K_b=\frac{[\text{OH}^-][\text{Conjugate Acid}]}{[\text{Base}]} \) (water is a liquid, so its concentration is not included).

Step2: Solve for first reaction (\( \text{HCO}_3^- + \text{H}_2\text{O}

ightleftharpoons \text{OH}^- + \text{H}_2\text{CO}_3 \))

• Identify Conjugate Acid and Base: The base is \( \text{HCO}_3^- \) (reactant, not \( \text{H}_2\text{O} \)), and the conjugate acid is \( \text{H}_2\text{CO}_3 \).
• So, for \( K_b \) of \( \text{HCO}_3^- \):
• Numerator: \( [\text{OH}^-][\text{H}_2\text{CO}_3] \) (so \(_1\) is \( \text{H}_2\text{CO}_3 \) (option O), \(_2\) is \( \text{HCO}_3^- \) (option J)).

Step3: Solve for second reaction (\( \text{HPO}_4^{2-} + \text{H}_2\text{O}

ightleftharpoons \text{OH}^- + \text{H}_2\text{PO}_4^- \))

• Identify Conjugate Acid and Base: The base is \( \text{HPO}_4^{2-} \), and the conjugate acid is \( \text{H}_2\text{PO}_4^- \).
• So, for \( K_b \) of \( \text{HPO}_4^{2-} \):
• Numerator: \( [\text{OH}^-][\text{H}_2\text{PO}_4^-] \) (so \(_3\) is \( \text{H}_2\text{PO}_4^- \) (option H), \(_4\) is \( \text{HPO}_4^{2-} \) (option G)).

Answer:

\(_1\): O. \( \text{H}_2\text{CO}_3 \)
\(_2\): J. \( \text{HCO}_3^{-1} \)
\(_3\): H. \( \text{H}_2\text{PO}_4^{-1} \)
\(_4\): G. \( \text{HPO}_4^{-2} \)