Problem 167 - A Complete Resource Book in Chemistry for JEE Main

Question

\(25 \mathrm{~mL}\) of a solution of barium hydroxide on titration with \(0.1\) molar solution of hydrochloric acid gave a titre value of \(35 \mathrm{~mL}\). The molarity of barium hydroxide solution was (a) \(0.07\) (b) \(0.14\) (c) \(0.28\) (d) \(0.35\)

Step-by-Step Solution

Answer

The molarity of barium hydroxide solution is (a) 0.07.

Step 1: Understanding the Reaction

Barium hydroxide, Ba(OH)₂, reacts with hydrochloric acid, HCl, in a titration. The chemical reaction is: \[ \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \] This equation tells us that 1 mole of Ba(OH)₂ requires 2 moles of HCl for complete neutralization.

Step 2: Calculate Moles of HCl Used

Using the concentration and volume of HCl, calculate the moles: \[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume in Liters} = 0.1 \text{ M} \times 0.035 \text{ L} = 0.0035 \text{ moles} \] So, 0.0035 moles of HCl were used in the titration.

Step 3: Determine Moles of Ba(OH)₂ Reacted

Since the stoichiometry of the reaction requires 2 moles of HCl for every 1 mole of Ba(OH)₂, the moles of Ba(OH)₂ can be calculated from the moles of HCl: \[ \text{Moles of Ba(OH)₂} = \frac{\text{Moles of HCl}}{2} = \frac{0.0035 \text{ moles}}{2} = 0.00175 \text{ moles} \]

Step 4: Calculate Molarity of Ba(OH)₂ Solution

The molarity of Ba(OH)₂ is the number of moles per liter. Convert the 25 mL of solution to liters and calculate: \[ \text{Molarity} = \frac{\text{Moles of Ba(OH)₂}}{\text{Volume of Solution in Liters}} = \frac{0.00175 \text{ moles}}{0.025 \text{ L}} = 0.07 \text{ M} \]

Step 5: Select the Correct Answer

From the options provided, the correct molarity of the barium hydroxide solution is (a) 0.07.

Key Concepts

Barium Hydroxide

Barium hydroxide is a chemical compound typically denoted as Ba(OH)₂. It is an alkaline earth hydroxide that appears as a white granular powder. This compound is soluble in water and forms a strong alkaline solution, making it a common base in various chemical reactions.
In the context of titration, barium hydroxide acts as the base which reacts with an acid—in this case, hydrochloric acid—to form a salt and water.
Its use in titration stems from its ability to completely dissociate in water, which ensures a clear endpoint during the titration process.

Chemical Reaction

A chemical reaction involves the transformation of one or more substances into new substances, typically involving changes in energy and the making or breaking of bonds. In our context, we're looking at a neutralization reaction between an acid and a base.
Specifically, barium hydroxide reacts with hydrochloric acid in a classic acid-base titration. The reaction is defined by the chemical equation: \[ \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \]

• One mole of barium hydroxide reacts with two moles of hydrochloric acid.
• The products formed are barium chloride and water.

This balanced equation highlights the stoichiometric proportions needed for complete reaction.

Molarity Calculation

Molarity is a key concept in chemistry that measures the concentration of a solution. It is defined as the number of moles of a solute per liter of solution. For titrations, knowing the molarity of one reactant allows us to determine the molarity of the other reactant in the reaction.
To find the molarity of barium hydroxide, we first need to calculate the moles of hydrochloric acid used: \[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume in Liters} = 0.1 \text{ M} \times 0.035 \text{ L} = 0.0035 \text{ moles} \]Then, utilizing the balanced chemical equation, we determine moles of barium hydroxide from the moles of hydrochloric acid. Finally, using these moles and the volume of barium hydroxide solution, we calculate its molarity, confirming it to be 0.07 M.

Stoichiometry

Stoichiometry is the area of chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the conservation of mass and the concept that the quantity of each element is conserved in a reaction.
In our titration example, stoichiometry helps us determine the relation between barium hydroxide and hydrochloric acid:

• The balanced equation shows a 1:2 mole ratio between Ba(OH)₂ and HCl.
• This means that for each mole of barium hydroxide, two moles of hydrochloric acid are required for complete neutralization.

By applying stoichiometry, we can calculate the amount of each substance required or produced, which is crucial in laboratory settings and industrial applications.