Animated Solution for Chemistry - Ionic Equilibrium: Which one of the following statements is not true?

The journey to solving this problem is a beautiful exercise in critical thinking. In multiple-choice questions asking for the "incorrect" statement, we must act as detectives, interrogating each option until one breaks under the laws of chemistry. Let's dive into the investigation!

Options A, B, and D

Let's start by clearing the innocent statements.

Option A claims that the conjugate base of ${\text{H}}_2{\text{PO}}_4^{-}$ is ${\text{HPO}}_4^{2-}$. According to the Brønsted-Lowry theory, a conjugate base is simply what remains after an acid donates a single proton (${\text{H}}^{+}$). If we mathematically subtract an ${\text{H}}^{+}$ from ${\text{H}}_2{\text{PO}}_4^{-}$, the charge drops by one, leaving us perfectly with ${\text{HPO}}_4^{2-}$. This statement is absolutely true.

Option B states that $\text{pH}+\text{pOH}=14$ for all aqueous solutions. Now, a sharp student might argue, "Wait! The ionic product of water, $K_w$, is temperature-dependent. This is only true at $25^{\circ }\text{C}$!" And you would be right. However, in standard chemistry problems, unless a different temperature is explicitly stated, we assume standard room temperature ($25^{\circ }\text{C}$). Under this standard assumption, the statement holds true.

Option D brings in Faraday's First Law of Electrolysis, stating that $96,500\text{ C}$ of electricity deposits $1\text{ g}$ equivalent of copper. Since $96,500\text{ C}$ is exactly $1\text{ Faraday}$ (the charge of one mole of electrons), and $1\text{ Faraday}$ always deposits exactly $1\text{ gram equivalent}$ of any substance, this statement is a fundamental truth of electrochemistry.

Option C

Now we arrive at Option C, which claims that the pH of a $1\times 10^{-8}\text{ M HCl}$ solution is $8$.

At first glance, if you blindly plug the concentration into the pH formula, you get:

But stop and think about the physical reality of what you just calculated. HCl is a strong acid. Can an aqueous solution of an acid ever be basic? Can adding acid to neutral water suddenly turn it into a base with a pH of 8? Absolutely not! This is a classic, high-yield trap designed to catch students who rely purely on formulas without visualizing the chemistry.

Water's Auto-ionization

So, where did the math go wrong? The flaw lies in assuming that the only source of ${\text{H}}^{+}$ ions in the beaker is the HCl.

In a normal, concentrated acid solution (like $0.1\text{ M}$), the ${\text{H}}^{+}$ provided by the acid completely overwhelms anything else. But when the acid is extremely dilute (concentration $<10^{-6}\text{ M}$), we can no longer ignore the solvent itself: Water.

Water undergoes self-ionization:

Pure water naturally provides an ${\text{H}}^{+}$ concentration of $10^{-7}\text{ M}$. Notice that $10^{-7}\text{ M}$ is actually ten times larger than the $10^{-8}\text{ M}$ provided by our highly dilute HCl!

To find the true pH, we must calculate the total hydrogen ion concentration:

While the exact calculation requires solving a quadratic equation due to the common ion effect suppressing water's ionization slightly, we don't even need to do that to prove the statement false.

We know for a fact that:

Because the total concentration of ${\text{H}}^{+}$ is greater than $10^{-7}\text{ M}$, the pH must be less than 7 (specifically, it turns out to be around $6.98$).

Therefore, the claim that the pH is 8 is a physical impossibility. Statement (c) is the definitively incorrect statement, making it our correct answer!