Problem 249 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{pOH}\) of an aqueous solution is \(5.0 .\) If the conc. of \(\left[\mathrm{H}^{+}\right]\) in that solution is \(10^{-\mathrm{x}} \mathrm{M}\), the value of \(\mathrm{x}\) is

Step-by-Step Solution

Answer

The value of \( x \) is 9.0

Step 1: Understand the Relationship Between pOH and pH

We know the relationship between pH and pOH is given by the equation: \( \text{pH} + \text{pOH} = 14 \). Since the pOH is given as 5.0, we can find the pH by rearranging the equation to \( \text{pH} = 14 - \text{pOH} \).

Step 2: Calculate the pH

Substitute the value of pOH into the equation: \( \text{pH} = 14 - 5.0 \). This simplifies to \( \text{pH} = 9.0 \).

Step 3: Understand the Relationship Between pH and Hydrogen Ion Concentration

The pH of a solution is related to the concentration of hydrogen ions by the equation: \( \text{pH} = -\log[\text{H}^+] \).

Step 4: Solve for \( [\text{H}^+] \) Concentration

Using the equation \( 9.0 = -\log[\text{H}^+] \), we find that \( [\text{H}^+] = 10^{-9.0} \) M.

Step 5: Identify the Value of x

The given concentration of \( [\text{H}^+] \) is \( 10^{-x} \) M. Since \( [\text{H}^+] = 10^{-9.0} \) M, this means \( x = 9.0 \).

Key Concepts

pH and pOH relationship

In chemistry, understanding the relationship between pH and pOH is vital when analyzing solutions. The sum of pH and pOH is always 14 in aqueous solutions at 25°C. This is a key concept, supporting the understanding of how acidic (pH) or basic (pOH) a solution is.
Knowing one value helps quickly determine the other. For example, if you know the pOH of a solution is 5.0, you can find the pH by using the formula:

• Calculate the pH: \[ \text{pH} = 14 - \text{pOH} = 14 - 5.0 = 9.0 \]

This quick conversion is regularly used in chemistry to further understand solution behavior and states of chemical reactions.

hydrogen ion concentration

The hydrogen ion concentration, often denoted as \( [\text{H}^+] \), is directly associated with the pH of a solution. In fact, pH describes the acidity of a solution quantitatively, defined as the negative logarithm of the hydrogen ion concentration:
\[\text{pH} = -\log[\text{H}^+]\]In practical scenarios, if you have a pH of 9.0, you calculate \( [\text{H}^+] \) like so:

• The pH equation tells us that \( [\text{H}^+] = 10^{-\text{pH}} \)
• Insert the pH value: \( [\text{H}^+] = 10^{-9.0} \)

This formula is central in calculations when determining how acidic or basic a solution is. Knowing the hydrogen ion concentration helps in predicting chemical reactions, especially when dealing with acids and bases.

logarithmic calculations in chemistry

Logarithmic calculations play a crucial role in chemistry, particularly when it comes to determining the acidity or basicity of solutions.
The logarithmic scale used in these calculations is the common log, which helps transform seemingly small-scale measurements into manageable numbers. For instance, pH and pOH values are calculated using base 10 logarithms.

• Example: \( \text{pH} = -\log[\text{H}^+] \)

This calculation simplifies complex ion concentration figures into clear and comprehensible pH values, often ranging from 0 to 14.
Understanding these steps:

• Convert ion concentrations using logarithms
• Use these results to determine chemical properties

This method provides clarity, making it easier to interpret how solution changes can impact chemical behaviors.