${K_{{a_1}}}$, ${K_{{a_2}}}$ 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 :

Question

${K_{{a_1}}}$, ${K_{{a_2}}}$ 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 :

${K_{{a_3}}}$ $=$ ${K_{{a_1}}}$ $+$ ${K_{{a_2}}}$

${K_{{a_3}}}$ $=$ ${K_{{a_1}}}$ $-$ ${K_{{a_2}}}$

${K_{{a_3}}}$ $=$ ${K_{{a_1}}}$ $/$ ${K_{{a_2}}}$

${K_{{a_3}}}$ $=$ ${K_{{a_1}}}$ $\times$ ${K_{{a_2}}}$

Solution

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