An 8.65-g sample of an unknown group 2 metal hydroxide is dissolved in 85.0 mL of water. An acid–base indicator is added and the resulting solution is titrated with 2.50 M HCl(aq) solution. The indicator changes color, signaling that the equivalence point has been reached, after 56.9 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: Ca2+, Sr2+, or Ba2+?
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Determine the moles of HCl used in the titration by using the formula: \( \text{moles of HCl} = \text{volume (L)} \times \text{molarity (M)} \). Convert the volume of HCl from mL to L before using it in the calculation.
Write the balanced chemical equation for the reaction between the group 2 metal hydroxide \( M(OH)_2 \) and HCl: \( M(OH)_2 + 2 \text{HCl} \rightarrow MCl_2 + 2 \text{H}_2\text{O} \).
Use the stoichiometry of the balanced equation to determine the moles of \( M(OH)_2 \) that reacted. Since 2 moles of HCl react with 1 mole of \( M(OH)_2 \), divide the moles of HCl by 2 to find the moles of \( M(OH)_2 \).
Calculate the molar mass of the unknown metal hydroxide \( M(OH)_2 \) using the formula: \( \text{molar mass} = \frac{\text{mass of sample (g)}}{\text{moles of } M(OH)_2} \).
Compare the calculated molar mass of \( M(OH)_2 \) with the known molar masses of \( \text{Ca(OH)}_2 \), \( \text{Sr(OH)}_2 \), and \( \text{Ba(OH)}_2 \) to identify the metal cation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Titration and Equivalence Point
Titration is a quantitative analytical method used to determine the concentration of a solute in a solution. The equivalence point is reached when the amount of titrant added is stoichiometrically equivalent to the amount of substance in the sample. In this case, the color change of the indicator signals that all the metal hydroxide has reacted with the hydrochloric acid, allowing for calculations to determine the identity of the metal cation.
Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. For the reaction between a metal hydroxide and hydrochloric acid, the stoichiometric coefficients indicate the molar ratios of the reactants. Understanding these ratios is essential to determine the number of moles of the metal hydroxide present, which can then be used to identify the metal cation based on its molar mass.
Group 2 metal hydroxides, such as calcium hydroxide (Ca(OH)2), strontium hydroxide (Sr(OH)2), and barium hydroxide (Ba(OH)2), are characterized by their solubility and molar masses. Each metal hydroxide has a distinct molar mass that can be calculated from the mass of the sample and the moles of acid used in the titration. By comparing the calculated molar mass of the unknown hydroxide to known values, one can identify the specific metal cation present.
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