Problem 30 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which of the following solutions will have \(\mathrm{pH}\) close to \(1.0 ?\) (a) \(100 \mathrm{ml}\) of \((\mathrm{M} / 10) \mathrm{HCl}+100 \mathrm{ml}\) of \((\mathrm{M} / 10) \mathrm{NaOH}\) (b) \(55 \mathrm{ml}\) of \((\mathrm{M} / 10) \mathrm{HCl}+45 \mathrm{ml}\) of \((\mathrm{M} / 10) \mathrm{NaOH}\) (c) \(10 \mathrm{ml}\) of \((\mathrm{M} / 10) \mathrm{HCl}+90 \mathrm{ml}\) of \((\mathrm{M} / 10) \mathrm{NaOH}\) (d) \(75 \mathrm{ml}\) of \((\mathrm{M} / 5) \mathrm{HCl}+25 \mathrm{ml}\) of \((\mathrm{M} / 5) \mathrm{NaOH}\)

Step-by-Step Solution

Answer

Option (d) will have a pH close to 1.0.

Step 1: Understand the pH Calculation

The pH of a solution is calculated using the formula \( \text{pH} = -\log_{10}[H^+] \). For a strong acid like HCl, which fully dissociates, the concentration of \([H^+]\) ions is equivalent to the concentration of HCl itself.

Step 2: Analyze Option (a)

In option (a), we mix \(100\, \text{ml}\) of \((M/10)\, \text{HCl}\) with \(100\, \text{ml}\) of \((M/10)\, \text{NaOH}\). Both are at equal concentration and volume, hence they completely neutralize each other. The resulting pH will be that of water, approximately \(7\).

Step 3: Analyze Option (b)

In option (b), we have \(55 \text{ ml}\) of \((M/10)\, \text{HCl}\) and \(45\, \text{ml}\) of \((M/10)\, \text{NaOH}\). First, find the moles of HCl and NaOH: \(C \times V = \frac{1}{10} \times \frac{55}{1000} = 0.0055\, \text{moles} \) and \( \frac{1}{10} \times \frac{45}{1000} = 0.0045\, \text{moles} \) respectively. The excess is \(0.0055 - 0.0045 = 0.0010\, \text{moles of HCl}\). The total volume is \(100 \text{ ml} = 0.1 \text{ L}\), giving an \([H^+]\) = \(\frac{0.001}{0.1} = 0.01\, \text{M}\), which gives a pH of \(2\).

Step 4: Analyze Option (c)

For option (c), \(10 \text{ ml}\) of \((M/10)\, \text{HCl}\) and \(90 \text{ml}\) of \((M/10)\, \text{NaOH}\) are mixed. Moles of HCl are \(\frac{1}{10} \times \frac{10}{1000} = 0.001\) and moles of NaOH are \(\frac{1}{10} \times \frac{90}{1000} = 0.009\). All of the HCl reacts, leaving NaOH in excess. The solution will be basic with a pH greater than 7.

Step 5: Analyze Option (d)

Option (d) involves \(75 \text{ ml}\) of \((M/5)\, \text{HCl}\) and \(25 \text{ml}\) of \((M/5)\, \text{NaOH}\). Calculating moles gives \(\frac{1}{5} \times \frac{75}{1000} = 0.015\, \text{moles of HCl}\) and \(\frac{1}{5} \times \frac{25}{1000} = 0.005\, \text{moles of NaOH}\). The excess HCl is \(0.015 - 0.005 = 0.01\, \text{moles of HCl}\). The total volume is \(100 \text{ ml} = 0.1 \text{ L}\), resulting in \([H^+] = \frac{0.01}{0.1} = 0.1\, \text{M}\), which gives a pH of \(1\).

Key Concepts

Strong Acids

Strong acids are powerful because they completely dissociate in water. This means that every molecule of the acid releases a hydrogen ion (H⁺), drastically increasing the H⁺ concentration in the solution.
Hydrochloric acid (HCl) is a common example of a strong acid. When dissolved, it separates entirely into H⁺ and Cl⁻ ions. This complete dissociation is what makes the solution highly acidic, easily lowering the pH.
Strong acids like HCl are often used in various chemical reactions, including those in laboratories, due to their predictability and ease of calculations in reactions. When calculating pH, the concentration of H⁺ ions for strong acids like HCl is equal to the original concentration of the acid itself.

Neutralization Reaction

A neutralization reaction occurs when an acid and a base interact to form water and a salt. This type of reaction is typically accompanied by the adjustment of the solution's pH towards 7, which is neutral on the pH scale.
In a typical neutralization reaction, the hydrogen ions (H⁺) from the acid mix with the hydroxide ions (OH⁻) from the base to create water (H₂O).

• For instance, when HCl (a strong acid) reacts with NaOH (a strong base), they neutralize each other.
• This reaction results in NaCl (table salt) and H₂O (water), effectively reducing the acidity or basicity of the solution.

This principle underlies the calculation of pH after mixing acids and bases; if they neutralize each other completely, the pH should be close to 7. However, if one component is in excess, the solution will lean towards being acidic or basic.

Molar Concentration

The molar concentration, also known as molarity, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of the solute per liter of solution.
In other words, if a solution has a molarity of \(M\/10\), this implies there is 1 mole of solute per 10 liters of solution or 0.1 mole per liter.
Molarity is crucial in chemical calculations as it provides a way to quantify reactants and products in reactions. For example:

• In the given solution, knowing the molarity of HCl and NaOH allows us to calculate how many moles of each are present before the reaction starts.
• This helps in determining the extent to which these compounds react and neutralize each other, providing insights into the resultant pH.

Accurate calculations of molar concentration can indicate whether a particular component will be in excess after an acid-base reaction, thereby influencing the final pH.

Acid-Base Reactions

Acid-base reactions involve the transfer of hydrogen ions between the acid and the base, which significantly alters the pH of a solution. These reactions are fundamental in both chemistry and biology, playing a crucial role in various physiological processes and industrial applications.
Such reactions proceed when acids like HCl donate protons (H⁺ ions) to bases such as NaOH, which accept them.

• This interaction often results in water and a salt, effectively changing the acidic or basic nature of the original solutions.
• When analyzing acid-base reactions, identifying the limiting reactant (the reactant that will be entirely consumed) is essential. It helps predict the outcome of the reaction and the resultant pH accurately.

The study of acid-base reactions includes understanding the concept of equilibrium and pH—a scale that measures the acidity or basicity of a solution. Through these reactions, we learn how solutions balance their pH as acids and bases neutralize each other.