JEE MAIN - Chemistry (2022 - 25th July Evening Shift - No. 3)
$${K_{{a_1}}}$$, $${K_{{a_2}}}$$ and $${K_{{a_3}}}$$ are the respective ionization constants for the following reactions (a), (b) and (c).
(a) $${H_2}{C_2}{O_4} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {H^ + } + H{C_2}O_4^ - $$
(b) $$H{C_2}O_4^ - \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {H^ + } + {C_2}O_4^{2 - }$$
(c) $${H_2}{C_2}O_4^{} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} 2{H^ + } + {C_2}O_4^{2 - }$$
The relationship between $${K_{{a_1}}}$$, $${K_{{a_2}}}$$ and $${K_{{a_3}}}$$ is given as :
$${K_{{a_3}}}$$ $$=$$ $${K_{{a_1}}}$$ $$+$$ $${K_{{a_2}}}$$
$${K_{{a_3}}}$$ $$=$$ $${K_{{a_1}}}$$ $$-$$ $${K_{{a_2}}}$$
$${K_{{a_3}}}$$ $$=$$ $${K_{{a_1}}}$$ $$/$$ $${K_{{a_2}}}$$
$${K_{{a_3}}}$$ $$=$$ $${K_{{a_1}}}$$ $$\times$$ $${K_{{a_2}}}$$
Explanation
$$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \rightleftharpoons 2 \mathrm{H}^{+}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \quad \mathrm{K}_{\mathrm{a}_{3}}$$
$$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \rightleftharpoons \mathrm{H}^{+}+\mathrm{HC}_{2} \mathrm{O}_{4}^{-} \quad \mathrm{K}_{\mathrm{a}_{1}}$$
$$\mathrm{HC}_{2} \mathrm{O}_{4}^{-} \rightleftharpoons \mathrm{H}^{+}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \quad \mathrm{K}_{\mathrm{a}_{2}}$$
$$\mathrm{K}_{\mathrm{a}_{3}}=\frac{\left[\mathrm{H}^{+}\right]^{2}\left[\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right]}{\left[\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right]}$$
$$\mathrm{K}_{\mathrm{a}_{1}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\right]}{\left[\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right]}, \mathrm{K}_{\mathrm{a}_{2}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{C}_{2} \mathrm{O}_{4}^{-}\right]}{\left[\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\right]}$$
$$\mathrm{K}_{\mathrm{a}_{3}}=\mathrm{K}_{\mathrm{a}_{1}} \times \mathrm{K}_{\mathrm{a}_{2}}$$
$$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \rightleftharpoons \mathrm{H}^{+}+\mathrm{HC}_{2} \mathrm{O}_{4}^{-} \quad \mathrm{K}_{\mathrm{a}_{1}}$$
$$\mathrm{HC}_{2} \mathrm{O}_{4}^{-} \rightleftharpoons \mathrm{H}^{+}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \quad \mathrm{K}_{\mathrm{a}_{2}}$$
$$\mathrm{K}_{\mathrm{a}_{3}}=\frac{\left[\mathrm{H}^{+}\right]^{2}\left[\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right]}{\left[\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right]}$$
$$\mathrm{K}_{\mathrm{a}_{1}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\right]}{\left[\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right]}, \mathrm{K}_{\mathrm{a}_{2}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{C}_{2} \mathrm{O}_{4}^{-}\right]}{\left[\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\right]}$$
$$\mathrm{K}_{\mathrm{a}_{3}}=\mathrm{K}_{\mathrm{a}_{1}} \times \mathrm{K}_{\mathrm{a}_{2}}$$
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