Problem 91 - Chemistry: Atoms First

Question

A sample of solid calcium hydroxide, \(\mathrm{Ca}(\mathrm{OH})_{2},\) is allowed to stand in water until a saturated solution is formed. A titration of \(75.00 \mathrm{mL}\) of this solution with \(5.00 \times 10^{-2} \mathrm{M}\) HCl requires \(36.6 \mathrm{mL}\) of the acid to reach the end point. \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{CaCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)\) What is the molarity?

Step-by-Step Solution

Answer

The molarity of the calcium hydroxide solution is 0.024 M.

Step 1: Calculate moles of HCl used in titration

Multiply the molarity of HCl by the volume in liters used in the titration to find the moles of HCl that reacted. The molarity of HCl is given as 5.00 x 10^-2 M and the volume is 36.6 mL, which must be converted to liters by dividing by 1000. Moles of HCl = Molarity of HCl x Volume of HCl (in liters).

Step 2: Calculate moles of calcium hydroxide

Use the stoichiometry of the reaction to find the moles of Ca(OH)2 that reacted with the HCl. According to the balanced chemical equation, 2 moles of HCl react with 1 mole of Ca(OH)2. Moles of Ca(OH)2 = Moles of HCl / 2.

Step 3: Calculate the molarity of calcium hydroxide solution

Divide the moles of Ca(OH)2 by the volume of the saturated solution in liters to find its molarity. The volume of the saturated calcium hydroxide solution is 75.00 mL, which we need to convert to liters. Molarity of Ca(OH)2 = Moles of Ca(OH)2 / Volume of solution (in liters).

Key Concepts

Titration

Titration is a laboratory technique used to determine the concentration of a given substance by reacting it with a solution of known concentration. It is commonly used for acid-base reactions, where an acid or base of unknown concentration is titrated with a base or acid of known concentration, respectively. The point at which the reaction is complete is known as the end point, and it is often indicated by a color change with an indicator or by reaching a particular pH value.

Using titration in the original exercise, we're able to find out how much of the saturated calcium hydroxide solution reacts with a known volume and concentration of hydrochloric acid. The calculations follow this process: we first find the moles of HCl used, then stoichiometrically derive the moles of calcium hydroxide, and finally calculate its molarity.

Stoichiometry

Stoichiometry is the field of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It's based on the principle of the conservation of mass, where the quantity of each element must be the same before and after a chemical reaction.

In the context of the original problem, we use stoichiometry to relate the moles of hydrochloric acid to the moles of calcium hydroxide. Based on the balanced chemical equation, two moles of HCl react with one mole of Ca(OH)₂. This 2:1 ratio allows us to accurately determine the amount of calcium hydroxide present in our saturated solution and thus calculate its molarity.

Saturated Solutions

A saturated solution is one in which the maximum amount of solute has been dissolved into the solvent at a given temperature. No more solute can be dissolved at this point, and any added solute will remain undissolved. In some cases, such a solution may have undissolved solute present, which is in dynamic equilibrium with the dissolved ions.

Understanding saturation is crucial in the exercise, as we are dealing with a saturated solution of calcium hydroxide. The concentration of calcium hydroxide in the solution directly impacts the calculation of molarity, after performing titration. Knowing that the solution is saturated ensures that the calculated molarity is the maximum that can be achieved under the given conditions.

Acid-Base Reactions

Acid-base reactions are chemical reactions that occur between acids and bases. An acid is a substance that can donate a hydrogen ion (H⁺), whereas a base can accept a hydrogen ion. The reaction between an acid and a base typically results in the formation of water and a salt. This kind of reaction is central to many processes in chemistry, from analytical methods like titration to biological systems.

In the exercise, calcium hydroxide, a strong base, reacts with hydrochloric acid, a strong acid, to form water and calcium chloride, a salt. It's an example of a neutralization reaction, which is a specific type of acid-base reaction. Appreciating the nature of acid-base reactions helps us understand why certain indicators, like phenolphthalein, work to show the endpoint in titration and predict the products of the reaction.