Problem 1 - Chemistry in 30 days

Question

The \(\mathrm{pH}\) value of decinormal solution of \(\mathrm{NH}_{4} \mathrm{OH}\), which is \(20 \%\) ionized, is (a) \(13.70\) (b) 14,70 (c) \(12.30\) (d) \(12.95\)

Step-by-Step Solution

Answer

The correct pH is 12.30.

Step 1: Understanding Key Concepts

To solve this problem, we need to understand what is being asked. The problem is about finding the pH of a decinormal (0.1 M) solution of \(\mathrm{NH_4OH}\), which is 20% ionized. \(\mathrm{NH_4OH}\) is a weak base, and when it ionizes, it produces \(\mathrm{OH^-}\) ions. The percentage of ionization will help us find the concentration of \(\mathrm{OH^-}\).

Step 2: Calculate Ionization

Given that \(\mathrm{NH_4OH}\) is 20% ionized and the solution is 0.1 M, we calculate the concentration of \(\mathrm{OH^-}\) ions. 20% of 0.1 M is \(0.02\, \text{M}\). Hence, \([\mathrm{OH^-}] = 0.02 \, \text{M}\).

Step 3: Find pOH

The \(\text{pOH}\) can be calculated using the formula: \(\text{pOH} = -\log{[\mathrm{OH^-}]}\). Thus, \(\text{pOH} = -\log{0.02}\). Calculating, we get \(\text{pOH} \approx 1.70\).

Step 4: Calculate pH

Using the relationship \(\text{pH} + \text{pOH} = 14\), we can find \(\text{pH}\). Substituting the \(\text{pOH}\) we found: \(\text{pH} = 14 - 1.70 = 12.30\).

Step 5: Verify Answer

Comparing the calculated pH \(12.30\) with the provided options, it matches option (c) which is \(12.30\). This confirms our calculations are correct.

Key Concepts

Ionization

Ionization is an important process in chemistry where molecules or atoms are converted to ions. For weak bases like ammonium hydroxide (NH4OH), ionization is a partial process, meaning only some of the molecules dissociate in water. In this exercise, NH4OH is 20% ionized, indicating that only 20% of the initial molecules break up into ions. This allows us to calculate the amount of hydroxide ions (OH-) produced. Understanding the percentage of ionization helps us in determining the concentrations needed for further calculations, such as the pH and pOH values.

Weak Base

A weak base is one that does not completely dissociate in a solution. Ammonium hydroxide (NH4OH) is a typical example of a weak base. It partially ionizes in water, meaning only a fraction of NH4OH molecules produces hydroxide ions. This limited ionization differentiates it from strong bases which fully dissociate. The degree of ionization of a weak base is typically given as a percentage, which in this exercise is 20%. Knowing a base is weak is crucial, as it directs our calculations and expectations for the concentration of ions produced.

pOH

The term pOH refers to the measure of hydroxide ion concentration in a solution and is akin to the concept of pH, which measures hydrogen ion concentration. They are related by the formula: 14 = pH + pOH. In this exercise, we calculated pOH from a known hydroxide ion concentration ([OH-]). The formula used is pOH = -log[OH-]]. Here, the pOH equates to 1.70, which helps us further calculate pH using the relationship between these two values.

NH4OH Solution

An NH4OH solution, also known as ammonium hydroxide, is a common example used in chemistry to illustrate principles of weak bases and ionization. Making a 0.1 M solution involves dissolving a specific mole amount of NH4OH in water. In this scenario, knowing the concentration is critical as it sets the starting point for calculating ionization and further pH-related values. NH4OH dissociating in solution forms NH4+ and OH- ions, and understanding this molecules behavior in solution is essential for solving a range of chemical problems.