Solid Ba(NO₃)₂ is gradually dissolved in a 1.0 $$\times$$ 10^-4 M Na₂CO₃ solution. At what concentration of Ba²⁺ will a precipitate begin to form ?
(K_sp for BaCO₃ = 5.1 $$\times$$ 10⁻⁹ )

On the basis of the following thermochemical data :
($$\Delta _fG^oH^+_{(aq)}$$ = 0)

H₂O(l) $$\to$$ H⁺(aq) + OH^-(aq); $$\Delta H$$ = 57.32 kJ
H₂(g) + $${1 \over 2} O_2(g) \to$$ H₂O(l); $$\Delta H$$ = -286.20 kJ

The value of enthalpy of formation of OH⁻ ion at 25^oC is :

Two liquids X and Y form an ideal solution. At 300K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this solution, vapour pressure of the solution increases by 10 mm Hg. Vapour pressure (in mm Hg) of X and Y in their pure states will be, respectively :

In Cannizzaro reaction given below
2PhCHO $$\buildrel {\mathop {:OH}\limits^{\left( - \right)} } \over \longrightarrow $$ PhCH₂OH + $$PhC\mathop O\limits^{..} $$₂^(-)
the slowest step is :