Question
Phosphoric acid ionizes in three steps with their ionization constant values $K_{a_{1}},K_{a_{2}}$ and $K_{a_{3}}$, respectively, while $K$ is the overall ionization constant. Which of the following statements are true?
A. $\ logK = logK_{a_{1}} + logK_{a_{2}} + logK_{a_{3}}$
B. $\ H_{3}{PO}_{4}$ is a stronger acid than $H_{2}{PO}_{4}^{-}$and ${HPO}_{4}^{2 -}$
C. $\ K_{a_{1}} > K_{a_{2}} > K_{a_{3}}$
D. $K_{a_{1}} = \frac{K_{a_{3}} + K_{a_{2}}}{2}$
Choose the correct answer from the options given below:
Options
Solution
Sol. [Key Concept: Stepwise ionisation constants of phosphoric acid (polyprotic acid)]
$H_{3}{PO}_{4}$ is a stronger acid than $H_{2}{PO}_{4}^{-}$and ${HPO}_{4}^{2 -}$
$H_{3}{PO}_{4}(aq) \rightleftharpoons H^{+}(aq) + H_{2}{PO}_{4}^{-}(aq)$ ;$K_{a_{1}} = 7.5 \times 10^{- 3}$
$$ H_{2}{PO}_{4}^{-}(aq) \rightleftharpoons H^{+}(aq) + {HPO}_{4}^{2 -}(aq)$$ ;$K_{a_{2}} = 6.2 \times 10^{- 8}$
$$ {HPO}_{4}^{2 -}(aq) \rightleftharpoons H^{+}(aq) + {PO}_{4}^{3 -}(aq)$$ ;$K_{a_{3}} = 1.7 \times 10^{- 12}$
$$ {K_{a_{1}} > K_{a_{2}} > K_{a_{3}}}$$
$$ {logK = logK_{a_{1}} + logK_{a_{2}} + logK_{a_{3}}}$$
Hence, A, B and C only are correct.
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