Phosphoric acid ionizes in three steps with their ionization constant values $\mathrm{K}_{\mathrm{a}_1}, \mathrm{~K}_{\mathrm{a}_2}$ and $\mathrm{K}_{\mathrm{a}_3}$, respectively, While K is the overall ionization constant. Which of the following statements are true? A. $\log \mathrm{K}=\log \mathrm{K}_{\mathrm{a}_1}+\log \mathrm{K}_{\mathrm{a}_2}+\log \mathrm{K}_{\mathrm{a}_3}$ B. $\mathrm{H}_3 \mathrm{PO}_4$ is a stronger acid than $\mathrm{H}_2 \mathrm{PO}_4^{-}$and $\mathrm{HPO}_4^{2-}$ C. $K_{a_1}\gt K_{a_2}\gt K_{a_3}$ D. $\mathrm{K}_{\mathrm{a}_1}=\frac{\mathrm{K}_{\mathrm{a}_3}+\mathrm{K}_{\mathrm{a}_2}}{2}$ Choose the correct answer from the options given below:

• A

  $A$ and $B$ only
• B

  $A$ and $C$ only
• C

  $\mathrm{B}, \mathrm{C} \text { and } \mathrm{D} \text { only }$
• Correct answer
  D

  $\text { A, B and C only }$

Solution

For polybasic acid, order of ionization constant is $\mathrm{Ka}_1\gt\mathrm{Ka}_2\gt\mathrm{Ka}_3$ because as negative charge increases, tendency to loose $\mathrm{H}^{+}$ions decreases. Overall $\mathrm{K}=\mathrm{Ka}_1 \times \mathrm{Ka}_2 \times \mathrm{Ka}_3$ Taking log on both sides $\log \mathrm{K}=\log \mathrm{Ka}_1+\log \mathrm{Ka}_2+\log \mathrm{Ka}_3$

Hence, the correct answer is option: 'D'.