What are the major species present in the following mixtures of bases? a. \(0.050 M \mathrm{NaOH}\) and \(0.050 \mathrm{M} \mathrm{LiOH}\) b. \(0.0010 M \mathrm{Ca}(\mathrm{OH})_{2}\) and \(0.020 \mathrm{M} \mathrm{RbOH}\) What is \(\left[\mathrm{OH}^{-}\right]\) and the \(\mathrm{pH}\) of each of these solutions?

In each mixture, we have to consider the dissociation of each base in water. The base dissociation reaction for a general base is given by: \[ B + H_2O \rightarrow BH^+ + OH^- \] We can apply this reaction for both the mixtures separately to find the major species present. a. Mixture with 0.050 M NaOH and 0.050 M LiOH \[ \mathrm{NaOH} \rightarrow \mathrm{Na}^+ + \mathrm{OH}^- \] \[ \mathrm{LiOH} \rightarrow \mathrm{Li}^+ + \mathrm{OH}^- \] Major species present: \(\mathrm{Na}^+\), \(\mathrm{Li}^+\), \(\mathrm{OH}^-\) b. Mixture with 0.0010 M Ca(OH)2 and 0.020 M RbOH \[ \mathrm{Ca(OH)_2} \rightarrow \mathrm{Ca}^{2+} + 2\mathrm{OH}^- \] \[ \mathrm{RbOH} \rightarrow \mathrm{Rb}^+ + \mathrm{OH}^- \] Major species present: \(\mathrm{Ca}^{2+}\), \(\mathrm{Rb}^+\), \(\mathrm{OH}^-\)

Now, we need to find the total concentration of hydroxide ions for each mixture by summing up the contributions from each base. a. For the first mixture, Total \(\left[\mathrm{OH}^-\right] = [\mathrm{OH}^-]_{\mathrm{NaOH}} + [\mathrm{OH}^-]_{\mathrm{LiOH}} = 0.050 + 0.050 = 0.100\ \mathrm{M}\) b. For the second mixture, Total \(\left[\mathrm{OH}^-\right] = [\mathrm{OH}^-]_{\mathrm{Ca(OH)_2}} + [\mathrm{OH}^-]_{\mathrm{RbOH}} = 2 (0.0010) + 0.020 = 0.022\ \mathrm{M}\)

Now, we can use the relationship between pOH and \(\left[ \mathrm{OH}^- \right]\) as well as the relationship between pH and pOH to find the pH of each mixture. The formula for pOH is: \[ \mathrm{pOH} = -\log_{10}[\mathrm{OH}^-] \] The relationship between pH and pOH is: \[ \mathrm{pH} + \mathrm{pOH} = 14 \] a. For the first mixture, pOH = \(-\log_{10}(0.100) = 1\) pH = \(14 - 1 = 13\) b. For the second mixture, pOH = \(-\log_{10}(0.022) \approx 1.66\) pH = \(14 - 1.66 \approx 12.34\) So, the pH values for the mixtures are approximately 13 and 12.34, respectively.