Correct option is (D) 1/2 (Y + Z - X)
\(\Lambda^0_{eq} (HCl) = \lambda ^0_{H^+} + \lambda^0_{Cl^-}\)
\(2 \times \Lambda^0_{eq} (HCl) = 2\lambda^0_{H^+} + 2\lambda^0_{Cl^-}\)
\(2 \times \Lambda^0_{eq} (HCl) = 2\lambda^0_{H^+} + \lambda ^0_{SO^{-2}_4}- \lambda ^0_{SO^{-2}_4}+2\lambda^0_{Cl^-} + \lambda^0_{Ba^{+2}} - \lambda^0_{Ba^{+2}}\)
\(2 \times \Lambda^0_{eq} (HCl) = \Lambda^0_{eq}(H_2SO_4) + \Lambda^0_{eq}(BaCl_2) - \Lambda^0_{eq}(BaSO_4) \)
\(2 \times \Lambda^0_{eq} (HCl) = Z + Y - X\)
\( \Lambda^0_{eq} (HCl) =\frac12( Z + Y - X)\)