Problem 233 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{pH}\) of \(10^{-10} \mathrm{M} \mathrm{HCl}\) solution at \(25^{\circ} \mathrm{C}\) is approximately

Step-by-Step Solution

Answer

The pH is approximately 7.

Step 1: Understanding the problem

We need to determine the pH of a very dilute HCl solution, specifically a solution with a concentration of \(10^{-10} \text{ M}\) at \(25^{\circ} \text{C}\). Since this concentration is extremely low, we must take the \[H^+\] from water into consideration.

Step 2: Water contribution

Water autoionizes to produce hydrogen ions \[H^+\] and hydroxide ions \text{OH}^-\. At \(25^{\circ} \text{C},\) the concentration of hydrogen ions from water is \(10^{-7} \text{ M}.\)

Step 3: Combining contributions

The effective concentration of hydrogen ions \([H^+]_{\text{eff}}\) is the sum of contributions from both the water itself and the acid: \[ [H^+]_{\text{eff}} = [H^+]_{\text{water}} + [HCl] = 10^{-7} \text{ M} + 10^{-10} \text{ M}\] which simplifies to \([H^+]_{\text{eff}} \approx 10^{-7} \text{ M}\) since \(10^{-10} \text{ M}\) is negligible.

Step 4: Calculating pH

Since the effective concentration of hydrogen ions \([H^+]_{\text{eff}}\) is \(10^{-7} \text{ M},\) the pH is calculated using the formula: \[ \text{pH} = -\log_{10}([H^+]_{\text{eff}}) = -\log_{10}(10^{-7}) = 7.\]

Key Concepts

dilute solution

A dilute solution is defined as one with a relatively low concentration of solute compared to the solvent. In our exercise, we are examining a dilute solution of hydrochloric acid ( (HCl) ), with a concentration of just (10^{-10} ext{ M}). When solutions are this diluted, certain unique properties emerge because the impact of the solute molecules is minimal.

• The behavior of dilute solutions can significantly differ from more concentrated solutions.
• In such dilute solutions, additional factors, such as the self-ionization of water, become significant.
• The interaction between solute and solvent is often less impactful, leading to properties of the solvent playing a more dominant role.

In the case of the hydrochloric acid solution we are analyzing, we have to factor in not just the ions contributed directly by the acid, but also from the autoionization reaction of water itself. This is because the contribution of hydrogen ions due to the acid is extremely low, allowing the naturally occurring hydrogen ions in water to become relevant.

water autoionization

Water autoionization is a natural process where water ( (H_2O) ) molecules spontaneously split into hydrogen ions ( (H^+) ) and hydroxide ions ( (OH^-) ). This is an essential process to consider, especially in very dilute solutions like the one we're looking at with (10^{-10} ext{ M}) HCl.

• Even without any added solute, water itself can dissociate to produce ions.
• At (25^{ ext{o}} ext{C}), the concentration of (H^+) produced by water is around (10^{-7} ext{ M}).
• This means that in very dilute solutions, the quantity of hydrogen ions from water can outnumber those from the acid.

Therefore, in calculating the pH of our extremely dilute hydrochloric acid solution, the (H^+) from water autoionization is a key component, overshadowing the contribution from the acid itself.

hydrogen ion concentration

Hydrogen ion concentration in a solution is crucial to determining the pH, which measures how acidic or basic a solution is. For solutions at room temperature ( (25^{ ext{o}} ext{C})), the neutrality point is around a ([H^+] = 10^{-7} ext{ M}). In the context of this exercise:

• The initial concentration of (HCl) is negligible at (10^{-10} ext{ M}).
• Given the chemical environment, it's the hydrogen ions from water that primarily define the ([H^+]).
• The effective concentration of ([H^+]_{ ext{eff}}) used for pH calculation thus essentially remains heavily influenced by water autoionization.

By focusing on the more relevant ([H^+]) from this pathway, students can better understand that in such cases, traditional rules for acid behavior don't always apply and adjustment for water's properties becomes necessary.

hydrochloric acid dilution

Hydrochloric acid (HCl) is known as a strong acid, which means it dissociates completely into its ions in solution. However, when it's extremely dilute, as in this exercise with (10^{-10} ext{ M}), its behavior can be surprising.

• Despite being a strong acid, in highly dilute concentrations, its contribution of (H^+) ions is minimal.
• The stronger interaction is that of water itself, which generates more (H^+) ions through autoionization.
• Therefore, it's important for students to recognize that the dissociation power of strong acids like HCl can be overshadowed at extreme dilution.

In this scenario, calculating pH requires students to acknowledge not just the solute's dissociation, but also the broader context of the solution’s ionic contributions, leading to an understanding that often contradicts initial expectations of acid reactions.