Question

At \(90^{\circ} \mathrm{C}\), pure water has \(\left[\mathrm{H}^{+}\right]=10^{-6} M\), if \(100 \mathrm{~mL}\) of \(0.2 \mathrm{M} \mathrm{HCl}\) is added to \(200 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) \(\mathrm{KOH}\) at \(90^{\circ} \mathrm{C}\) then \(\mathrm{pH}\) of the resulting solution will be : (a) 5 (b) 6 (c) 7 (d) None of these

Short answer

The pH of the resulting solution will be 6.

Step-by-step solution

Calculate the moles of HCl and KOH

First, find the number of moles of HCl and KOH initially present. For HCl: Moles of HCl = concentration (M) * volume (L) = 0.2 M * 0.1 L = 0.02 moles. For KOH: Moles of KOH = 0.1 M * 0.2 L = 0.02 moles.

Determine the neutralization reaction

The reaction between HCl and KOH is a neutralization reaction where HCl (acid) reacts with KOH (base) to form KCl (salt) and water (H2O). The reaction consumes equal moles of H+ and OH- ions, so they will completely neutralize each other, leaving no excess of H+ or OH- in the solution.

Calculate the concentration of remaining ions

Since the moles of HCl and KOH are equal and they neutralize each other, no excess H+ from HCl or OH- from KOH will remain. However, the water at 90°C has an autoionization constant with concentration [H+] = 10^-6 M. This will be the concentration of H+ ions in the solution after the reaction.

Calculate the pH of the solution

pH is calculated using the formula pH = -log[H+]. Substitute the remaining H+ concentration to find the pH: pH = -log(10^-6) = 6.

Key concepts

Neutralization Reaction

A neutralization reaction is a chemical process wherein an acid and a base react with each other to produce a salt and water. This type of reaction is fundamental in acid-base chemistry. When an acid like HCl (hydrochloric acid) is mixed with a base such as KOH (potassium hydroxide), they react to form KCl (potassium chloride) and H₂O (water).

An essential aspect of a neutralization reaction to understand is that it typically results in the pH of the solution moving towards neutral, which is a pH value of 7. However, this isn't always the case as the resulting pH can depend on the strength of the acid and base involved. In our exercise, both the moles of HCl and KOH used are equal; hence their effects cancel out, leaving only the impact of autoionized water on the pH of the solution.

Autoionization of Water

Autoionization of water is the process by which water spontaneously forms low concentrations of hydrogen ions (H⁺) and hydroxide ions (OH^-) by the chemical reaction where two water molecules react to produce a hydronium ion (H₃O⁺) and a hydroxide ion. The product of the concentrations of these ions is known as the water's autoionization constant (K_w), which changes with temperature.

At standard conditions (25°C), K_w is typically 1.0 x 10^-14, but at elevated temperatures like 90°C, as mentioned in the exercise, the concentration of H⁺ and OH^- increases due to higher autoionization, hence the given value [H⁺] = 10^-6 M for pure water at this temperature. This elevated autoionization plays a significant role in determining the pH of the solution after the neutralization reaction.

Molarity and Concentration

Molarity is a measure of the concentration of a solute in a solution, defined as the number of moles of the solute divided by the volume of the solution in liters (L). It is denoted with the unit M (molar). For example, a 0.2 M HCl solution indicates that there are 0.2 moles of HCl in every liter of the solution.

In the context of our exercise, we calculated the number of moles of HCl and KOH used in the reaction by multiplying their molarity by the volume in liters. Understanding molarity is pivotal because it enables us to calculate how much of each reactant participates in a reaction, which is crucial for predicting the outcome of the reaction and, subsequently, the pH of the resulting solution.

Logarithmic Scale in pH

pH is a scale used to specify the acidity or basicity of an aqueous solution. It is a logarithmic scale based on the concentration of hydrogen ions (H⁺) in the solution. The pH scale ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are acidic, and those with a pH greater than 7 are basic.

Calculating pH involves taking the negative logarithm (base 10) of the H⁺ ion concentration. This means if the H⁺ ion concentration increases by a factor of 10, the pH value would decrease by one, demonstrating the inverse relationship between H⁺ ion concentration and pH value. In our case, the pH is calculated as pH = -log(10^-6) = 6, which indicates that the resulting solution is slightly acidic.