An 8.65 -g sample of an unknown group 2 A metal hydroxide is dissolved in 85.0 \(\mathrm{mL}\) of water. An acid-base indicator is added and the resulting solution is titrated with 2.50 \(\mathrm{M}\) \(\mathrm{HCl}(a q)\) solution. The indicator changes color, signaling that the equivalence point has been reached, after 56.9 \(\mathrm{mL}\) of the hydrochloric acid solution has been added. (a) What is the molar mass of the metal hydroxide? (b) What is the identity of the metal cation: \(\mathrm{Ca}^{2+}, \mathrm{Sr}^{2+},\) or \(\mathrm{Ba}^{2+?}\) ?

Based on the provided step-by-step solution, the short answer to the question is as follows. (a) To find the molar mass of the metal hydroxide, first, calculate the moles of HCl used in the titration: \(Moles_{HCl} = 2.50 M * 0.0569 L\) Next, use stoichiometry to find the moles of metal hydroxide (MH): \(Moles_{MH} = \frac{Moles_{HCl}}{2}\) Then, calculate the molar mass of the metal hydroxide: \(Molar\,mass_{MH} = \frac{8.65 g}{Moles_{MH}}\) (b) To identify the metal cation, compare the calculated molar mass with the known molar masses of Group 2A metal hydroxides (Ca(OH)2, Sr(OH)2, and Ba(OH)2) to find the metal hydroxide with the closest molar mass. This will determine the identity of the metal cation (Ca2+, Sr2+, or Ba2+).