Phosphoric acid ionizes in three steps with their ionization constant values Ka₁ , Ka₂ and Ka₃ , respectively, while K is the overall ionization constant. Which of the following statements are true?

log K= log Ka₁ + logKa₂ + log Ka₃

H₃PO₄ is a stronger acid than H₂PO^-₄  and HPO^2-₄

Ka₁ > Ka₂ > Ka₃

Ka₁=Ka₃ +Ka₂/2

Choose the correct answer from the options given below :

To determine which statements are true for the ionization of phosphoric acid ($H_{3}P{O}_4$), let us analyze each statement step-by-step:

Phosphoric acid ($H_{3}P{O}_4$) is a weak triprotic acid that ionizes in three successive steps in aqueous solution:
1. First ionization step:
$H_{3}P{O}_4\rightleftharpoons H^{+}+H_{2}P{O}_4^{-}$, with ionization constant $K{a}_1=\frac{\left[H^{+}\right]\left[H_{2}P{O}_4^{-}\right]}{\left[H_{3}P{O}_4\right]}$
2. Second ionization step:
$H_{2}P{O}_4^{-}\rightleftharpoons H^{+}+HP{O}_4^{2-}$, with ionization constant $K{a}_2=\frac{\left[H^{+}\right]\left[HP{O}_4^{2-}\right]}{\left[H_{2}P{O}_4^{-}\right]}$
3. Third ionization step:
$HP{O}_4^{2-}\rightleftharpoons H^{+}+P{O}_4^{3-}$, with ionization constant $K{a}_3=\frac{\left[H^{+}\right]\left[P{O}_4^{3-}\right]}{\left[HP{O}_4^{2-}\right]}$

The overall ionization equation of phosphoric acid is the sum of these three steps:
$H_{3}P{O}_4\rightleftharpoons 3H^{+}+P{O}_4^{3-}$, with overall constant $K=\frac{{\left[H^{+}\right]}^3\left[P{O}_4^{3-}\right]}{\left[H_{3}P{O}_4\right]}$

When chemical reactions are added, their equilibrium constants are multiplied. Therefore:
$K=K{a}_1\times K{a}_2\times K{a}_3$
Taking the logarithm on both sides yields:
$logK=logK{a}_1+logK{a}_2+logK{a}_3$
Thus, Statement A is true.

Next, let us analyze the relative acid strengths of the species. It is significantly easier to remove a positively charged proton ($H^{+}$) from a neutral molecule ($H_{3}P{O}_4$) than from a negatively charged ion ($H_{2}P{O}_4^{-}$), which in turn is easier than removing it from a doubly negatively charged ion ($HP{O}_4^{2-}$) due to increasing electrostatic attraction. Consequently, $H_{3}P{O}_4$ is a stronger acid than $H_{2}P{O}_4^{-}$, which is stronger than $HP{O}_4^{2-}$.
Thus, Statement B is true.

Since the acid strength decreases in each successive ionization step, the corresponding acid dissociation constants decrease as well:
$K{a}_1>K{a}_2>K{a}_3$
Thus, Statement C is true.

Statement D ($K{a}_1=K{a}_3+\frac{K{a}_2}{2}$) is incorrect because ionization constants of successive steps for polyprotic acids differ by several orders of magnitude (typically ${10}^5$ to ${10}^6$ fold) rather than having simple linear algebraic relationships.

Hence, statements A, B, and C are true.