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 solution's \(\text{pOH}\) is (b) 10.6990.

Step 1: Understanding the Relationship

First, recognize that pH and pOH are related through the formula: \[ ext{pH} + ext{pOH} = 14\]where 14 is the pH scale's neutral value at 25°C.

Step 2: Calculate pH from Hydrogen Ion Concentration

Given the hydrogen ion concentration \([H^+] = 0.0005 \, \text{M}\), calculate the pH using the formula: \[ ext{pH} = -\log([H^+])\]Substituting in the given concentration:\[ ext{pH} = -\log(0.0005) = 3.3010\]

Step 3: Calculate pOH Using the Relationship

Use the relationship between pH and pOH to find the pOH:\[ ext{pOH} = 14 - ext{pH}\]Substitute the calculated pH value:\[ ext{pOH} = 14 - 3.3010 = 10.6990\]

Step 4: Verify pOH Against Options

Now, compare the calculated pOH (10.6990) to the given options. The matching option is (b) 10.6990.

Key Concepts

Understanding Hydrogen Ion Concentration

The concept of hydrogen ion concentration is fundamental to understanding acid-base chemistry. The concentration of hydrogen ions \([H^+]\) in a solution determines its acidity. A higher concentration of hydrogen ions indicates a more acidic solution, while a lower concentration suggests a more basic or neutral environment.

• Acids release hydrogen ions into a solution, increasing the \([H^+]\).
• Bases, on the other hand, can accept hydrogen ions, reducing the \([H^+]\).
• Neutral solutions have balanced hydrogen ion and hydroxide ion \([OH^-]\) concentrations.

The formula \[ \text{pH} = -\log([H^+]) \] directly links the hydrogen ion concentration to the pH of the solution. This relationship makes it possible to quantify acidity in a precise and convenient manner.

Relationship Between pH and pOH

The pH and pOH scales are intimately connected in the chemistry of aqueous solutions. They are complementary measures that together describe a solution's acidity and basicity.

• The pH scale measures how acidic or basic a solution is, with lower values being more acidic and higher values more basic.
• The pOH scale, conversely, measures the concentration of hydroxide ions \([OH^-]\).

At 25°C, the relationship is given by the equation: \[ \text{pH} + \text{pOH} = 14 \]This relationship highlights that in a neutral solution at this temperature, the pH and pOH levels sum to 14. When the solution becomes more acidic \(\text{higher } [H^+]\), the pH decreases, and consequently, the pOH rises to maintain this balance.

Logarithmic pH Calculation

The calculation of pH using a logarithmic scale is a critical concept in chemistry. The formula \[ \text{pH} = -\log([H^+]) \] allows us to find the pH of a solution based on its hydrogen ion concentration.

• Logarithms help simplify the large range of hydrogen ion concentrations into a manageable scale from 0 to 14.
• The use of a negative sign indicates that as the hydrogen ion concentration increases, the pH value decreases, signifying increased acidity.

For example, with a hydrogen ion concentration of \[0.0005 \ \text{M}\], the pH is calculated as \[ \text{pH} = -\log(0.0005) = 3.3010 \]. Understanding how to perform these calculations is important for predicting how changes in concentration will affect the acidity or basicity of a solution.