Animated Solution for Chemistry - Basic Concepts in Chemistry: 25 mL of a solution of barium hydroxide on titration with 0.1 molar solution of hydrochloric acid gave a titre value of 35 mL. The molarity of barium hydroxide solution was

Welcome to the fascinating world of volumetric analysis! Today, we are stepping into the shoes of an analytical chemist to solve a classic titration puzzle. Titration is a technique where a solution of known concentration is used to determine the concentration of an unknown solution.

Imagine you are in the chemistry lab. We have a conical flask containing $25\text{ mL}$ of an unknown concentration of barium hydroxide, ${\text{Ba(OH)}}_2$. Above it, a burette is filled with $0.1\text{ M}$ hydrochloric acid, $\text{HCl}$. We slowly add the acid drop by drop until the indicator changes color, signaling that the reaction is complete. This happens exactly when $35\text{ mL}$ of acid has been added. This volume is known as the 'titre value'.

At the exact moment of neutralization, the law of equivalence states that the number of equivalents of the acid must perfectly match the number of equivalents of the base. This gives us our master equation:

Here, $N$ represents Normality and $V$ represents Volume. But wait, the problem gives us Molarity ($M$), not Normality. How do we bridge this gap?

Normality is simply the n-factor ($n$) multiplied by Molarity:

The n-factor is a crucial concept. For an acid, it's the number of replaceable $H^{+}$ ions (basicity). For a base, it's the number of replaceable $O{H}^{-}$ ions (acidity).

For barium hydroxide, ${\text{Ba(OH)}}_2$, it dissociates to give two hydroxide ions, so its n-factor is $2$. For hydrochloric acid, $\text{HCl}$, it gives one proton, so its n-factor is $1$.

Let's carefully substitute these values into our equivalence equation.

For the base (left side):

For the acid (right side):

Plugging it all together:

Now, it's just simple algebra. Two times twenty-five gives us fifty on the left. On the right, zero point one times thirty-five is three point five.

Dividing $3.5$ by $50$, we get our final answer:

The molarity of the barium hydroxide solution is exactly $0.07\text{ M}$. A beautiful and clean result that perfectly demonstrates the power of the law of equivalence!