Problem 26 - Chemistry in 30 days

Question

Twenty-five millilters of a solution of barium hydroxide on titration with a \(0.1\) molar solution of hydrochloric acid gave a titre value of \(35 \mathrm{ml}\). The molarity of barium hydroxide solution was (a) \(0.14\) (b) \(0.28\) (c) \(0.35\) (d) \(0.07\)

Step-by-Step Solution

Answer

The molarity of the barium hydroxide solution is 0.07 M. The correct answer is (d).

Step 1: Understanding the Reaction

Barium hydroxide, Ba(OH)_2, reacts with hydrochloric acid, HCl, in a neutralization reaction to form barium chloride and water. The balanced equation for this reaction is: \[ \text{Ba(OH)}_2 + 2 \text{HCl} \to \text{BaCl}_2 + 2 \text{H}_2\text{O} \] From the equation, we see that 1 mole of Ba(OH)_2 reacts with 2 moles of HCl.

Step 2: Calculate Moles of HCl Used

We know the molarity and volume of the HCl solution used. The number of moles of HCl can be calculated using the formula:\[ n = C \times V \]where \( n \) is the number of moles, \( C \) is the concentration, and \( V \) is the volume in liters.Given that \( C_{\text{HCl}} = 0.1 \) M and \( V_{\text{HCl}} = 35 \) mL (or 0.035 L), we have:\[ n_{\text{HCl}} = 0.1 \times 0.035 = 0.0035 \text{ moles} \]

Step 3: Relate Moles of HCl to Moles of Ba(OH)_2

According to the balanced chemical equation, 1 mole of Ba(OH)_2 reacts with 2 moles of HCl. Therefore, the moles of Ba(OH)_2 is half that of HCl:\[ n_{\text{Ba(OH)}_2} = \frac{n_{\text{HCl}}}{2} = \frac{0.0035}{2} = 0.00175 \text{ moles} \]

Step 4: Calculate Molarity of Ba(OH)_2 Solution

The molarity, \( M \), of the Ba(OH)_2 solution is given by:\[ M = \frac{n}{V} \]where \( n \) is the number of moles calculated in Step 3 and \( V \) is the volume of the solution in liters. Here, \( V = 25 \) mL (or 0.025 L):\[ M_{\text{Ba(OH)}_2} = \frac{0.00175}{0.025} = 0.07 \text{ M} \]

Step 5: Choose the Correct Answer

Based on our calculations, the molarity of the Ba(OH)_2 solution is 0.07 M. Therefore, the correct answer is (d) \(0.07\).

Key Concepts

Neutralization Reaction

A neutralization reaction occurs when an acid and a base react to form water and a salt. In such reactions, the acidic and basic properties cancel each other out, resulting in neutral solutions. In the exercise, barium hydroxide ( \( \text{Ba(OH)}_2 \) ) which is a strong base, reacts with hydrochloric acid ( \( \text{HCl} \) ), a strong acid.The products of this neutralization reaction are water and barium chloride ( \( \text{BaCl}_2 \) ), the salt. The reaction can be represented by this balanced chemical equation:

• \( \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \)

This equation shows how one mole of barium hydroxide combines with two moles of hydrochloric acid to complete the reaction.

Molarity Calculation

Molarity is a way to express the concentration of a solution. It is the number of moles of solute dissolved in one liter of solution. In the context of titration, calculating molarity involves understanding the stoichiometry of the reaction as outlined by the balanced equation.In the given exercise, the molarity of the hydrochloric acid ( \( \text{HCl} \) ) is known (\(0.1 \text{ M}\)), along with the volume of acid used, \(35 \text{ mL}\) or \(0.035 \text{ L}\). The equation for calculating moles is:

• \( n = C \times V \)

where \(n\) is the number of moles, \(C\) is concentration in molarity, and \(V\) is volume in liters.Plugging the given values into this equation gives the moles of HCl:

• \( n_{\text{HCl}} = 0.1 \times 0.035 = 0.0035 \text{ moles} \)

With this, we can determine the corresponding moles of barium hydroxide since their reaction ratio from the balanced equation is 2:1.

Balanced Chemical Equation

A balanced chemical equation is crucial for accurately representing a chemical reaction. It ensures that the number of atoms for each element is the same on both sides of the equation. This reflects the principle of the conservation of mass, stating that matter cannot be created or destroyed in a chemical reaction.In the given example, the balanced equation is:

• \( \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \)

This indicates that one molecule of barium hydroxide reacts with two molecules of hydrochloric acid to form one molecule of barium chloride and two molecules of water.Balancing involves ensuring that you have:

• The same number of each type of atom on both sides.
• The same total charge on both sides (for reactions with ionic compounds).

Balancing chemical equations is essential when performing molarity calculations in titrations, as it allows us to correctly relate the moles of reactants and products in the reaction.