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. \(0.35\)

Short answer

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

Step-by-step solution

Write the Balanced Chemical Equation

The reaction between barium hydroxide, \( \text{Ba(OH)}_2 \), and hydrochloric acid, \( \text{HCl} \), can be written as: \[ \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \]. This indicates that one mole of barium hydroxide reacts with two moles of hydrochloric acid.

Calculate Moles of Hydrochloric Acid

The molarity \( M \) is calculated using the formula \( M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \). Here, the volume of the \( \text{HCl} \) solution is 35 ml or 0.035 L. The molarity of \( \text{HCl} \) is 0.1 M, so the moles of \( \text{HCl} \) are \( 0.1 \times 0.035 = 0.0035 \) moles.

Determine Moles of Barium Hydroxide

From the balanced equation, one mole of \( \text{Ba(OH)}_2 \) reacts with two moles of \( \text{HCl} \). Therefore, the moles of \( \text{Ba(OH)}_2 \) that reacted are \( \frac{0.0035}{2} = 0.00175 \) moles.

Calculate the Molarity of Barium Hydroxide

The volume of the \( \text{Ba(OH)}_2 \) solution is 25 ml or 0.025 L. The molarity \( M \) of the barium hydroxide is calculated as \( M = \frac{\text{moles of } \text{Ba(OH)}_2}{\text{volume in L}} = \frac{0.00175}{0.025} = 0.07 \text{ M} \).

Key concepts

Molarity Calculation

Molarity is a way to express the concentration of a solution. It tells us how many moles of solute are present in one liter of solution.
The formula for calculating molarity (M) is:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]

• "Moles of solute" refers to the quantity of the substance dissolved in the solution.
• The "volume of solution" should always be converted into liters for this formula.

In our titration exercise, we used this formula to find the molarity of the barium hydroxide solution. First, we determined the moles of hydrochloric acid used and then found the moles of barium hydroxide through stoichiometry.
Finally, dividing these moles by the volume of the barium hydroxide solution in liters gave us the molarity.

Chemical Equation Balancing

Balancing chemical equations ensures that the mass and the charge are balanced on both sides of the equation. This means that the number of atoms for each element, as well as the total charge, must be the same in the reactants and products.
Here's the equation from the exercise:
\[ \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \]

• On the left side, we have one barium atom, two hydroxide ions, and two hydrogen chloride molecules.
• On the right side, we have one barium chloride molecule and two water molecules.

Notice that each type of atom (barium, hydrogen, oxygen, and chlorine) is present in equal amounts on both sides.

Stoichiometry

Stoichiometry involves using the balanced chemical equation to determine the proportions of reactants and products in a chemical reaction. It tells us how much of one substance reacts with another.
In this titration problem, stoichiometry helps us figure out how much barium hydroxide reacts with hydrochloric acid.
Since the balanced reaction equation shows that one mole of barium hydroxide reacts with two moles of hydrochloric acid, this ratio ( 1:2 ) helps calculate the moles of barium hydroxide reacting based on the moles of hydrochloric acid used.

• With 0.0035 moles of HCl , half of that amount ( 0.00175 moles ) is the amount of Ba(OH)_2 that reacted, since 1:2 is the required ratio.

This process ensures that all the chemical interactions in the equation remain consistent and predictable.

Solution Concentration

Understanding solution concentration is key to knowing how much solute is present in a solution. In this exercise, both barium hydroxide and hydrochloric acid have different concentrations.
Concentration is usually expressed in molarity, but it essentially tells us the amount of solute dissolved in a given volume of solvent.

• A more concentrated solution has more solute per volume.
• A less concentrated solution has less solute per volume.

In acid-base titrations, we often compare the concentration of the acid and the base to determine their reactivity ratios and eventually find unknown concentrations when they neutralize each other. By knowing the titration volume required to reach the endpoint, and the known concentration of one reactant, we can calculate the unknown concentration of the other (in this case, barium hydroxide).