Exercises: pH, Ka, Kb and degree of dissociation

In the chemistry lab there is an aqueous solution of nitric acid, $\mathrm{HNO_3}$, of concentration $0.025\,\mathrm{mol\times L^{-1}}$ at $25\,^\circ\mathrm{C}$. Given that nitric acid behaves as a strong monoprotic acid that dissociates completely in water and that the ionic product of water is $K_\mathrm{w} = 1.0\times 10^{-14}$ at that temperature, assume ideal behavior where $\mathrm{pH} = -\log[\mathrm{H_3O^+}]$. Calculate: a) The concentration of hydronium ions, $[\mathrm{H_3O^+}]$, and the value of the $\mathrm{pH}$ of the solution. b) The concentration of hydroxide ions, $[\mathrm{OH^-}]$, present in the medium. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.

An aqueous solution is prepared by dissolving $0.171\,\mathrm{g}$ of barium hydroxide, $\mathrm{Ba(OH)_2}$, in distilled water to make an exact volume of $500\,\mathrm{mL}$ at $25\,^\circ\mathrm{C}$. This compound is assumed to be a strong base that dissociates completely according to the process $\mathrm{Ba(OH)_2(s) \rightarrow Ba^{2+}(aq) + 2\,OH^-(aq)}$. Molar mass of $\mathrm{Ba(OH)_2}$: $171.3\,\mathrm{g\times mol^{-1}}$; $K_\mathrm{w} = 1.0\times 10^{-14}$. Under the ideal approximation, determine: a) The molar concentration of $\mathrm{OH^-}$ ions in the resulting solution. b) The $\mathrm{pOH}$ and the $\mathrm{pH}$ of the final solution. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.

A laboratory reactor is filled with a mixture of $250\,\mathrm{mL}$ of an aqueous solution of hydrochloric acid, $\mathrm{HCl}$, of concentration $0.060\,\mathrm{mol\times L^{-1}}$ and $150\,\mathrm{mL}$ of an aqueous solution of barium hydroxide, $\mathrm{Ba(OH)_2}$, of concentration $0.040\,\mathrm{mol\times L^{-1}}$ at $25\,^\circ\mathrm{C}$. Assume that the volumes are additive (final volume $400\,\mathrm{mL}$), that both substances behave as strong electrolytes that are fully dissociated, and that $K_\mathrm{w} = 1.0\times 10^{-14}$ at that temperature in an ideal solution. a) Write the net ionic neutralization reaction and determine, with justification, which reagent is in excess, quantifying the moles remaining. b) Calculate the molar concentration of all the ionic species present in the resulting mixture ($\mathrm{H_3O^+}$, $\mathrm{OH^-}$, $\mathrm{Ba^{2+}}$ and $\mathrm{Cl^-}$) and determine the $\mathrm{pH}$ of the final solution. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.