Problem 86 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

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 1: 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 \(\mathrm{HCl} = (56.9 \times 10^{-3} \mathrm{L}) \times (2.50 \mathrm{M})\)

Step 2: 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 \(\mathrm{M(OH)_2} = \mathrm{\dfrac{moles\ of\ HCl}{2}}\)

Step 3: 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 \(\mathrm{M(OH)_2} = \mathrm{\dfrac{mass}{moles}}\)

Step 4: 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.

Key Concepts

Group 2A Metal Hydroxides

Group 2A metal hydroxides are a part of the alkaline earth metals in the periodic table. These metals include calcium, strontium, and barium, among others. When these metals combine with hydroxide ions, they form metal hydroxides like calcium hydroxide \(\mathrm{Ca(OH)_2}\), strontium hydroxide \(\mathrm{Sr(OH)_2}\), and barium hydroxide \(\mathrm{Ba(OH)_2}\). These compounds are characterized by being

• strong bases, which completely dissociate in water,
• relatively soluble in water, with solubility increasing down the group.

Understanding the properties of these metal hydroxides is crucial, especially in titration experiments, where their reaction with acids like hydrochloric acid \((\mathrm{HCl})\) is used to determine their molar masses and thus identify the metal involved. The process involves the hydroxide ions \((\mathrm{OH}^-)\) of these compounds reacting with \(\mathrm{H^+}\) ions from the acid to form water \((\mathrm{H_2O})\), leading to a neutralization of the solution.

Moles Calculation

Calculating moles is an essential concept when dealing with chemical reactions, especially in titration problems. In the context of the given exercise, it involves determining the amount of hydrochloric acid \((\mathrm{HCl})\) used in the titration process.
The formula used is:

• Moles of a solute = Volume of the solution \( \times \) Concentration of the solution

To find the moles of \(\mathrm{HCl}\), convert the volume from milliliters to liters, as the concentration is given in \(\mathrm{M}\) or moles per liter. For instance, if \(56.9\,\mathrm{mL}\) of \(\mathrm{HCl}\) was used, it should be converted to \(0.0569\,\mathrm{L}\). Then, multiply this by the molarity \((2.50\,\mathrm{M})\), yielding the number of moles of \(\mathrm{HCl}\).
In the given reaction, \(\mathrm{M(OH)_2}\) reacts in a 1:2 mole ratio with \(\mathrm{HCl}\). This ratio allows you to calculate the moles of the metal hydroxide by dividing the moles of \(\mathrm{HCl}\) by 2.

Molar Mass Determination

Determining the molar mass of a compound is a critical step in identifying the compound in various chemistry problems. In the context of the exercise, once you have calculated the moles for the unknown metal hydroxide \(\mathrm{M(OH)_2}\), the next step is to find its molar mass.
The molar mass \((\mathrm{M})\) is calculated using the formula:

• Molar mass = \(\dfrac{\text{mass}}{\text{moles}}\)

Given that the mass of the unknown metal hydroxide is \(8.65\,\mathrm{g}\), divide this by the moles you've calculated to find the molar mass.
Comparing this molar mass with the known molar masses of Group 2A metal hydroxides helps in identifying the cation present. For example, if the determined molar mass closely matches \(74.1\,\mathrm{g/mol}\), the hydroxide would likely be \(\mathrm{Ca(OH)_2}\).
This method provides a straightforward approach to identifying unknown compounds by their chemical properties and reactivity.