Problem 99 - A Complete Resource Book in Chemistry for JEE Main

Question

\(100 \mathrm{ml}\) of \(0.015 \mathrm{M} \mathrm{HCl}\) solution is mixed with 100 \(\mathrm{ml}\) of \(0.005 \mathrm{M} \mathrm{HCl}\). What is the \(\mathrm{pH}\) of the resultant solution? (a) \(2.5\) (b) \(1.5\) (c) 2 (d) 1

Step-by-Step Solution

Answer

The pH of the resultant solution is 2 (option c).

Step 1: Calculate moles of HCl in each solution

First, calculate the moles of HCl in the first solution using the formula: moles = concentration \(\times\) volume. For 100 ml of 0.015 M HCl: \[ \text{Moles in solution 1} = 0.015 \times \frac{100}{1000} = 0.0015 \text{ moles} \] Next, calculate the moles of HCl in the second solution. For 100 ml of 0.005 M HCl: \[ \text{Moles in solution 2} = 0.005 \times \frac{100}{1000} = 0.0005 \text{ moles} \]

Step 2: Calculate total moles of HCl

Add the moles of HCl from both solutions to find the total moles in the mixture: \[ \text{Total moles of HCl} = 0.0015 + 0.0005 = 0.0020 \text{ moles} \]

Step 3: Calculate total volume of solution

Since the two solutions are mixed, the total volume is the sum of both volumes: \[ \text{Total volume} = 100 \text{ ml} + 100 \text{ ml} = 200 \text{ ml} = 0.2 \text{ L} \]

Step 4: Calculate concentration of HCl in the resultant solution

Use the total moles of HCl and the total volume to find the concentration of the resultant solution: \[ \text{Concentration} = \frac{0.0020}{0.2} = 0.01 \text{ M} \]

Step 5: Calculate the pH of the resultant solution

Since HCl is a strong acid, it dissociates completely in solution. The concentration of \(\text{H}^+\) ions is therefore equal to the concentration of HCl: \[ \text{pH} = -\log_{10}[\text{H}^+] = -\log_{10}(0.01) = 2 \]

Step 6: Verify the solution aligns with answer choices

The calculated pH value is 2. This matches answer choice (c).

Key Concepts

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept in chemistry that involves the study of acids and bases and how they interact with each other. Acids are substances that can donate protons (10 ions) in a solution, while bases can accept these protons.
When an acid and a base react, they can neutralize each other, forming water and a salt. This reaction is crucial in many chemical processes.

• Acids are often understood through the concept of pH, a scale that measures the acidity of a solution.
  
• The pH scale ranges from 0 to 14, with 7 being neutral. Values below 7 indicate acidic solutions, and values above 7 indicate basic solutions.
  

Understanding acid-base chemistry allows us to predict the outcomes of mixing different chemicals, like determining the pH of a resultant solution after mixing acids.

Strong Acids

Strong acids are a category of acids that dissociate completely in water to produce ions. This complete dissociation is what distinguishes strong acids from weak acids, which only partially dissociate.

• Examples of strong acids include hydrochloric acid (HCl), sulfuric acid (32SO4), and nitric acid (HNO3).
  
• When strong acids are dissolved in water, they release all of their hydrogen ions, significantly affecting the pH of the solution.
  

The ability of strong acids to fully dissociate makes them powerful agents in chemical reactions and important in various industrial applications. Knowing how strong acids behave helps us calculate pH levels accurately after mixing solutions, as shown in the exercise where HCl is used.

Molar Concentration

Molar concentration, often referred to as molarity, is a way to express the concentration of a solute in a solution. It is defined as the number of moles of a substance (the solute) divided by the volume of the solution in liters.
This measurement is crucial when working with chemical solutions because it provides a clear understanding of the solution's strength.

• The formula for molarity is: \( M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \)
  
• In the context of mixing two solutions, calculating the molarity of the resultant mixture helps in determining how the mixture will behave chemically.
  

Molar concentration is especially important in pH calculations, as the pH is directly dependent on the concentration of hydrogen ions produced by acids in the solution.

HCl Dissociation

HCl, or hydrochloric acid, is a prime example of a strong acid, meaning it dissociates completely in water. When HCl is added to water, it breaks down into hydrogen ions (10) and chloride ions (11) instantly.
This complete dissociation is crucial for understanding how the pH is affected by the presence of HCl.

• Because every molecule of HCl produces a hydrogen ion, the concentration of HCl directly equals the concentration of hydrogen ions in the solution.
  
• This is why the pH of a hydrochloric acid solution can be calculated simply by taking the negative logarithm of its concentration as shown in the exercise.
  

HCl's behavior in water highlights the concept of strong acids and their role in altering the acidity of solutions.