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Chapter 4: Problem 86

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: \(\mathrm{Ca}^{2+}, \mathrm{Sr}^{2+}, \mathrm{Ba}^{2+} ?\)

Short Answer

Expert verified
The molar mass of the unknown metal hydroxide is calculated as \(121.6 \,\mathrm{g/mol}\), and the metal cation is identified as \(\mathrm{Sr^{2+}}\), indicating that the metal hydroxide is \(\mathrm{Sr(OH)_2}\).

Step by step solution

01

Calculate the moles of \(\mathrm{HCl}\) used in the titration

We have the volume of the \(\mathrm{HCl}\) solution used in titration and its concentration, so we can calculate the number of moles by using the formula: Moles of \(\mathrm{HCl}=\mathrm{Volume\ of\ HCl\ used} \times \mathrm{Concentration\ of\ HCl}\) Moles of \(\mathrm{HCl} = (56.9 \times 10^{-3} \mathrm{L}) \times (2.50 \mathrm{M})\)
02

Calculate the moles of the unknown metal hydroxide

During titration, the \(\mathrm{HCl}\) reacts with the unknown metal hydroxide (\(\mathrm{M(OH)_2}\)), and the balanced chemical equation is: \(\mathrm{M(OH)_2 + 2HCl \rightarrow MCl_2 + 2H_2O}\) From the balanced equation, 1 mole of the metal hydroxide reacts with 2 moles of \(\mathrm{HCl}\). Applying the stoichiometry principles, we can calculate the moles of the metal hydroxide as follows: Moles of \(\mathrm{M(OH)_2} = \mathrm{\dfrac{moles\ of\ HCl}{2}}\)
03

Determine the molar mass of the metal hydroxide

We have the mass and moles of the metal hydroxide: Mass = \(8.65\,\mathrm{g}\) Moles = Moles of \(\mathrm{M(OH)_2}\) (calculated in Step 2) Molar mass of \(\mathrm{M(OH)_2} = \mathrm{\dfrac{mass}{moles}}\)
04

Identify the metal cation

Based on the molar mass of the metal hydroxide obtained in Step 3, we can compare it with the molar masses of the group 2A metal hydroxides and identify the metal cation. Group 2A metal hydroxides: - \(\mathrm{Ca(OH)_2}\): Molar mass = 74.1 g/mol - \(\mathrm{Sr(OH)_2}\): Molar mass = 121.6 g/mol - \(\mathrm{Ba(OH)_2}\): Molar mass = 171.3 g/mol Compare the molar mass obtained in Step 3 with the above values to determine which metal cation is present in the unknown metal hydroxide.

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