Phosphoric acid ionizes in three steps with their ionization constant values K_a ,K_a2 and K_a3 , respectively, while K is the overall ionization constant. Which of the following statements are true?

A. log K = log K_a1 + log K_a2 + log K_a3

B. H₃PO₄ is stronger acid than H₂PO₄⁻ and HPO₄²⁻.

C. K_a1 > K_a2 > K_a3

D. K_a1 = (K_a2 + K_a3) / 2

Choose the correct answer from the options given below

The correct answer is A, B and C only.

Let us analyze each statement step-by-step to understand the behavior of phosphoric acid ($H_3{\mathrm{PO}}_4$) during its ionization in aqueous solution.

Phosphoric acid ($H_3{\mathrm{PO}}_4$) is a triprotic acid, which means it can donate three protons (hydrogen ions) in three successive steps. The ionization steps and their corresponding equilibrium constants are:
Step 1: $H_3{\mathrm{PO}}_4\rightleftharpoons H^{+}+H_2{\mathrm{PO}}_4^{-}$ with ionization constant $K_{a1}$
Step 2: $H_2{\mathrm{PO}}_4^{-}\rightleftharpoons H^{+}+{\mathrm{HPO}}_4^{2-}$ with ionization constant $K_{a2}$
Step 3: ${\mathrm{HPO}}_4^{2-}\rightleftharpoons H^{+}+{\mathrm{PO}}_4^{3-}$ with ionization constant $K_{a3}$

The overall ionization equation is the sum of these three individual steps:
Overall: $H_3{\mathrm{PO}}_4\rightleftharpoons 3H^{+}+{\mathrm{PO}}_4^{3-}$ with overall ionization constant $K$

Analysis of Statement A:
When chemical equations are added to get a net equation, their equilibrium constants are multiplied. Therefore, the overall ionization constant $K$ is the product of the individual step constants:
$K=K_{a1}\times K_{a2}\times K_{a3}$
Taking the logarithm on both sides of the equation:
$logK=log(K_{a1}\times K_{a2}\times K_{a3})$
Using the logarithmic property $log\left(xyz\right)=logx+logy+logz$:
$logK=log{K}_{a1}+log{K}_{a2}+log{K}_{a3}$
Hence, Statement A is true.

Analysis of Statement B:
In the first step, a proton is lost from a neutral molecule ($H_3{\mathrm{PO}}_4$). In the second step, a proton must be removed from a negatively charged species ($H_2{\mathrm{PO}}_4^{-}$). Due to electrostatic attraction, it is much more difficult to remove a positively charged proton ($H^{+}$) from a negatively charged anion than from a neutral molecule. Similarly, in the third step, it is even harder to remove a proton from a doubly negatively charged species (${\mathrm{HPO}}_4^{2-}$).
Consequently, $H_3{\mathrm{PO}}_4$ releases protons most readily, making it a stronger acid than $H_2{\mathrm{PO}}_4^{-}$ and ${\mathrm{HPO}}_4^{2-}$.
Hence, Statement B is true.

Analysis of Statement C:
Since the ease of losing a proton decreases significantly with each successive ionization step, the ionization constants follow the order:
$K_{a1}>K_{a2}>K_{a3}$
For phosphoric acid, the actual values are approximately:
$K_{a1}\approx 7.5\times {10}^{-3}$, $K_{a2}\approx 6.2\times {10}^{-8}$, and $K_{a3}\approx 4.2\times {10}^{-13}$.
Hence, Statement C is true.

Analysis of Statement D:
Since the successive ionization constants differ by several orders of magnitude, there is no simple arithmetic relation such as $K_{a1}=\frac{K_{a2}+K_{a3}}{2}$.
Hence, Statement D is false.

In conclusion, statements A, B, and C are correct, corresponding to the option A, B and C only.