Problem 84 - A Complete Resource Book in Chemistry for JEE Main

Question

A solution has hydrogen ion concentration \(0.0005 \mathrm{M}\), its \(\mathrm{pOH}\) is (a) \(8.2798\) (b) \(10.6990\) (c) \(12.7854\) (d) \(13.3344\)

Step-by-Step Solution

Answer

The pOH is 10.6990, which corresponds to option (b).

Step 1: Calculate pH

The concentration of hydrogen ions \([H^+]\) is given as 0.0005 M. To find the pH, use the formula \(\text{pH} = -\log[H^+]\). So, \(\text{pH} = -\log(0.0005)\). Calculate the logarithm to get \(\text{pH} \approx 3.3010\).

Step 2: Use the relationship between pH and pOH

Recall that \(\text{pH} + \text{pOH} = 14\). We already have the pH from Step 1. Substitute \([\text{pH} = 3.3010]\) into the equation to find pOH: \(\text{pOH} = 14 - \text{pH}\). Therefore, \(\text{pOH} = 14 - 3.3010 = 10.6990\).

Key Concepts

Understanding Hydrogen Ion Concentration

Hydrogen ion concentration \([H^+]\) is pivotal in determining the acidity or basicity of a solution. \([H^+]\) is a measure of how many hydrogen ions are present in a given volume of solution. The concentration is typically expressed in molarity (M), which stands for moles per liter.
The formula \([H^+] = 10^{-\text{pH}}\) is essential for calculating the hydrogen ion concentration when the pH is known, or vice versa. The higher the \([H^+]\), the more acidic the solution becomes. Conversely, lower hydrogen ion concentrations indicate a more basic or alkaline solution.
In the given exercise, the \([H^+]\) concentration is 0.0005 M, highlighting an acidic environment because it is lower than the neutral concentration typically described by a pH of 7.

Steps to Calculate pH

Calculating pH involves using the formula \(\text{pH} = -\log[H^+]\). The pH scale is logarithmic, meaning every whole pH value less than 7 is ten times more acidic than the next higher value. Similarly, each whole pH value greater than 7 becomes ten times more basic as the number increases.
To solve for pH with an \([H^+]\) of 0.0005 M:

• Compute the logarithm of the hydrogen ion concentration: \(-\log(0.0005)\).
• This calculation yields a pH of approximately 3.3010, indicating an acidic solution.

Understanding the logarithmic nature of the pH scale is crucial because it shows how even a small change in hydrogen ion concentration can result in a significant change in pH.

Logarithmic Functions in Chemistry

Logarithms play a vital role in calculating pH and other chemical properties. In chemistry, logarithms help convert numbers across multiple scales to make them manageable.
A logarithm, expressed as \(\log_b(x)\), corresponds to the exponent to which the base \(b\) must be raised to yield \(x\). For pH, the base is 10, simplifying the conversion of hydrogen ion concentration to pH.
Why use logarithms in chemistry?

• They simplify multiplicative relationships into additive ones, making complex equations easier to work with.
• The logarithmic scale allows chemists to handle the vast and often minute differences in compound concentrations effectively.

Understanding logarithms is integral for comprehending how large or tiny changes in concentration translate into the pH scale.

Exploring the Relationship between pH and pOH

The relationship between pH and pOH is governed by the equation \(\text{pH} + \text{pOH} = 14\). This connection reflects the dual nature of aqueous solutions, where both hydrogen ions and hydroxide ions coexist.
Key Points:

• pH relates directly to the concentration of hydrogen ions.
• pOH is analogous but measures the concentration of hydroxide ions \([OH^-]\).
• The sum 14 comes from the ionic product of water, \(K_w\), which remains constant at 1 x 10\(^{-14}\) at 25°C.
• For the given problem, once you calculate the pH, finding the pOH involves a straightforward subtraction from 14.
• In the exercise above, after determining pH as 3.3010, calculating \(\text{pOH} = 14 - \text{pH}\) yields a pOH of 10.6990.

This relationship is fundamental in understanding how acidic or basic a solution is based on either parameter.