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.

Step 1: Calculate moles of HCl in each solution

To find the total moles of \( ext{HCl}\), we start by calculating the moles in each solution separately. Use the formula \( ext{moles} = ext{concentration} \times ext{volume in liters}\). For the first solution, \( ext{moles of HCl} = 0.015 \text{ M} \times 0.1 \text{ L} = 0.0015 \text{ moles}\). For the second solution, \( ext{moles of HCl} = 0.005 \text{ M} \times 0.1 \text{ L} = 0.0005 \text{ moles}\).

Step 2: Total moles of HCl

Add the moles of HCl from both solutions to find the total moles. \( ext{Total moles of HCl} = 0.0015 + 0.0005 = 0.002 \text{ moles}\).

Step 3: Total volume of the mixed solution

The total volume is the sum of the volumes of both solutions, which is \(100 \text{ ml} + 100 \text{ ml} = 200 \text{ ml} = 0.2 \text{ L}\).

Step 4: Calculate the concentration of HCl in the mixed solution

Now, find the concentration of HCl in the mixed solution using \( \text{concentration} = \frac{\text{total moles}}{\text{total volume in liters}}\). So, \( \text{concentration of HCl} = \frac{0.002}{0.2} = 0.01 \text{ M}\).

Step 5: Calculate the pH of the resulting solution

Since HCl is a strong acid, it completely dissociates. Thus, the concentration of \([\text{H}^+]\) ions is the same as the concentration of HCl. The pH is given by \( \text{pH} = -\log_{10}([\text{H}^+])\). Substitute the concentration: \( \text{pH} = -\log_{10}(0.01) = 2\).

Key Concepts

Acid-Base Chemistry

In acid-base chemistry, it's essential to understand the behaviors of acids and bases. Acids like hydrochloric acid (HCl) are substances that increase the concentration of hydrogen ions

• Hydrochloric acid, being a strong acid, dissociates completely in water.
• It contributes to the hydrogen ion concentration directly.
• More hydrogen ions lead to a lower pH, which indicates a more acidic solution.

When you mix solutions that contain an acid, the total concentration of hydrogen ions is crucial in determining the resulting solution's acidity. HCl is a monoprotic acid, meaning it donates just one H⁺ ion per molecule. Hence, the concentration of HCl is equal to the concentration of hydrogen ions present.

Molarity

Molarity is a concept that helps us express the concentration of a solution. In simple terms, molarity (M) is the number of moles of solute (like HCl) per liter of solution.

• Molarity = Moles of solute / Volume of solution in liters.
• It gives insight into how concentrated or dilute a solution is.

When calculating molarity for each solution in a mixture, it's important to first determine the moles of solute in each solution. In our task, we multiply the given molarity by the volume of each solution to find out the total amount of HCl each contributes. Then, after mixing, we recalculate to find the molarity in the new, combined solution.

Solution Mixing

Solution mixing is a common practice to alter the properties of solutions by combining them. In this specific context, mixing changes both the volume and the solute concentration:

• When two solutions are mixed, their volumes add up.
• The total number of moles of the solute (HCl) from each solution combines.

After determining the entire moles of HCl, to find the resultant molarity, you should divide by the new total volume. Solution mixing allows us to accurately predict the properties of a new solution, like its pH, by considering the contributions from each original solution.

Logarithms in Chemistry

Logarithms in chemistry, specifically when calculating pH, help us manage the wide range of hydrogen ion concentrations found in solutions. pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration:

• The formula for pH is written as: pH = -log₁₀([H⁺]).
• This allows us to express acidity in a more comprehensible way.

For instance, a hydrogen ion concentration of 0.01 M simplifies to a pH of 2. This approach is invaluable since it condenses potentially vast concentrations into a more manageable scale, ranging typically from 0 (very acidic) to 14 (very basic), centering around 7 for neutral solutions.