Problem 279 - A Complete Resource Book in Chemistry for JEE Main

Question

How many litres of water must be added to litre of an aqueous solution of \(\mathrm{HCl}\) with a \(\mathrm{pH}\) of 1 to create an aqueous solution with \(\mathrm{pH}\) of 2 ? [2013] (a) \(2.0 \mathrm{~L}\) (b) \(9.0 \mathrm{~L}\) (c) \(0.1 \mathrm{~L}\) (d) \(0.9 \mathrm{~L}\)

Step-by-Step Solution

Answer

Add 9.0 L of water to achieve the desired pH.

Step 1: Understand pH and Concentration

pH is a measure of the hydrogen ion concentration (100).When pH decreases by 1 unit, the concentration of 10c increases tenfold.The initial pH of the solution is 1, meaning it has a hydrogen ion concentration of \([ ext{H}^+]=10^{-1} ext{M}\). We want to make a solution with pH 2, which corresponds to \([ ext{H}^+]=10^{-2} ext{M}\). This will require diluting the solution to attain the desired concentration.

Step 2: Determine the Initial and Final Volume Needed

Let's assume we have 1 L of the initial solution with a pH of 1 ((\([ ext{H}^+]=10^{-1} ext{M}\)).In order to reduce the concentration of hydrogen ions by a factor of 10 (pH from 1 to 2), the volume of solution needs to be increased by a factor of 10.Thus, if the initial solution has a volume of 1 L, the final solution should be 10 L.

Step 3: Calculate the Amount of Water to Add

The final volume of water needed is 10 L to achieve a pH of 2.The original solution volume is 1 L.Thus, the amount of water that needs to be added is: \(10 ext{ L} - 1 ext{ L} = 9 ext{ L}\).We need to add 9 L of water to the original solution.

Key Concepts

Dilution

Dilution is a common practice in chemistry to decrease the concentration of a solute in a solution by adding more solvent, usually water. This process does not change the amount of solute present; it only changes the concentration by increasing the volume.
For example, if you have 1 liter of a hydrochloric acid (HCl) solution, diluting it with water will spread out the hydrogen ions over a greater volume. In pH terms, the concentration of hydrogen ions lowers, which means the pH increases (since pH is inversely related to hydrogen ion concentration).
Calculating how much water to add involves understanding that each pH unit change, like going from pH 1 to pH 2, represents a tenfold change in hydrogen ion concentration. Therefore, achieving this requires multiplying the original volume by ten. The formula used here for calculating pH change through dilution is:

• Initial concentration x Initial volume = Final concentration x Final volume
• Solving for the unknown volume gives us the amount of water to add

To achieve a new concentration for the desired pH, ensure the final volume is ten times the original.

Hydrogen Ion Concentration

Hydrogen ion concentration in a solution is a crucial aspect of determining its acidity, which is measured by the pH scale. The pH value is logarithmic, calculated as \(-\log[H^+]\), so each whole number on the pH scale represents a tenfold change in hydrogen ion concentration.
For instance, at pH 1, there is a concentration of hydrogen ions measuring \(10^{-1}\) M, meaning 0.1 moles per liter. At pH 2, this concentration decreases to \(10^{-2}\) M or 0.01 moles per liter, indicating the solution is ten times less acidic.
To transition from pH 1 to pH 2, the concentration of hydrogen ions must decrease by one order of magnitude. This change occurs through dilution, effectively spreading a fixed number of hydrogen ions across a larger volume.

• To adjust pH by increasing the liquid volume, establish the desired hydrogen ion concentration
• Use the relationship between initial and final hydrogen ion concentrations to determine the necessary volume increase

Thus, understanding this relationship is key to manipulating concentration levels in chemical solutions.

Aqueous Solution of HCl

An aqueous solution of HCl refers to hydrochloric acid dissolved in water. It is a strong acid that fully dissociates in water, meaning it separates into hydrogen ions \(H^+\) and chloride ions \(Cl^-\). This characteristic results in a high concentration of hydrogen ions and, consequently, a low pH.
For example, a 1 molar solution of HCl will have a \(H^+\) concentration equal to its molarity, which explains its intense acidic behavior and pH of 0 for a highly concentrated solution.
Changing the properties of an HCl solution, such as its pH, involves altering its hydrogen ion concentration through processes like dilution. By adding water to an HCl solution, the concentration of \(H^+\) decreases, increasing the pH making it less acidic.
Important points to remember include:

• HCl is a strong acid and fully dissociates in water
• Change in solution's pH is due to changes in \(H^+\) concentration
• Decreasing the concentration results in a higher pH owing to the dilution process

Understanding these aspects allows better control over the acidity of the solution through dilution, vital for chemical handling and reactions involving a change in acid concentration.