The first and second ionization constants of textH_2textX$\text{H}_2\text{X}$ are 2.5 times 10^-8$2.5 \times 10^{-8}$ and 1.0 times 10^-13$1.0 \times 10^{-13}$ respectively. The concentration of textX^2-$\text{X}^{2-}$ in 0.1text M textH_2textX$0.1\text{ M } \text{H}_2\text{X}$ solution is \_ times 10^-15text M$\_ \times 10^{-15}\text{ M}$. (Nearest Integer)

### Core Logic For a weak diprotic acid textH_2textX$\text{H}_2\text{X}$, the concentration of textX^2-$\text{X}^{2-}$ in a solution of concentration C$C$ is approximately equal to the second dissociation constant K_a_2$K_{a_2}$ under standard weak acid approximation conditions ([textX^2-] approx K_a_2 = 1.0 times 10^-13 text M$[\text{X}^{2-}] \approx K_{a_2} = 1.0 \times 10^{-13} \text{ M}$). Converting to the required format: 1.0 times 10^-13 = 100 times 10^-15 text M$1.0 \times 10^{-13} = 100 \times 10^{-15} \text{ M}$. ### Step 1: Final Calculation Thus, the integer value is 100. ### Pattern Recognition Sees: polyprotic acid dissociation equilibrium calculation for secondary anion concentration. Trap: Assuming complete dissociation for the second step. ### Chapter Mix Class 11 Chemistry: Equilibrium