What are the major species present in 0.015\(M\) solutions of each of the following bases? a. \(\mathrm{KOH}\) b. \(\mathrm{Ba}(\mathrm{OH})_{2}\) What is \(\left[\mathrm{OH}^{-}\right]\) and the pH of each of these solutions?

First, we need to identify the major species present in the solutions of the given bases. The major species are the components that exist in the solution after dissociation. a. KOH Upon dissociation, KOH will release OH⁻ ions: \[ \mathrm{KOH} \rightarrow \mathrm{K}^{+} + \mathrm{OH}^{-} \] So the major species in the solution of KOH are K⁺ and OH⁻. b. Ba(OH)₂ Upon dissociation, Ba(OH)₂ releases two OH⁻ ions: \[ \mathrm{Ba(OH)_{2}} \rightarrow \mathrm{Ba}^{2+} + 2\mathrm{OH}^{-} \] So the major species in the solution of Ba(OH)₂ are Ba²⁺ and OH⁻.

Next, we need to calculate the concentration of hydroxide ions present in each solution. For this, we must consider the stoichiometry of the dissociation. a. KOH Since one mole of KOH dissociates to produce one mole of OH⁻, the concentration of OH⁻ is the same as the concentration of KOH: \[ \left[ \mathrm{OH}^{-} \right] = 0.015 \,M \] b. Ba(OH)₂ Since one mole of Ba(OH)₂ dissociates to produce two moles of OH⁻, the concentration of OH⁻ is twice the concentration of Ba(OH)₂: \[ \left[ \mathrm{OH}^{-} \right] = 2 \times 0.015 \,M = 0.030 \,M \]

To find the pH of each solution, we first need to calculate the pOH, which is the negative logarithm (base 10) of the hydroxide concentration: \[ \mathrm{pOH} = -\log_{10} \left[\mathrm{OH}^{-}\right] \] Then, using the relationship between pH and pOH: \[ \mathrm{pH + pOH} = 14\] We can calculate the pH of each solution: a. KOH Calculating the pOH: \[ \mathrm{pOH} = -\log_{10} \left(0.015\right) = 1.82 \] Calculating the pH: \[ \mathrm{pH} = 14 - \mathrm{pOH} = 14 - 1.82 = 12.18 \] b. Ba(OH)₂ Calculating the pOH: \[ \mathrm{pOH} = -\log_{10} \left(0.030\right) = 1.52 \] Calculating the pH: \[ \mathrm{pH} = 14 - \mathrm{pOH} = 14 - 1.52 = 12.48 \] In summary, the major species in a solution of KOH are K⁺ and OH⁻ with an \(\left[ \mathrm{OH}^{-} \right]\) of 0.015 M and a pH of 12.18. The major species in a solution of Ba(OH)₂ are Ba²⁺ and OH⁻ with an \(\left[ \mathrm{OH}^{-} \right]\) of 0.030 M and a pH of 12.48.