Question

\(\mathrm{pK}_{a}\) of \(\mathrm{NH}_{4}^{+}\) is \(9.26 .\) Hence, effective range for \(\mathrm{NH}_{4} \mathrm{OH}-\mathrm{NH}_{4} \mathrm{Cl}\) buffer is abouts (a) \(8.26\) to \(10.26\) (b) \(4.74\) to \(5.74\) (c) \(3.74\) to \(5.74\) (d) \(8.26\) to \(9.26\)

Short answer

The effective range for \(\mathrm{NH}_{4} \mathrm{OH}-\mathrm{NH}_{4} \mathrm{Cl}\) buffer is about 8.26 to 10.26.

Step-by-step solution

Understanding Buffer Range

The effective buffer range is typically within plus or minus 1 of the \(\mathrm{pK}_a\) value of the acid component of the buffer. In this case, the acid component is \(\mathrm{NH}_{4}^{+}\) and its \(\mathrm{pK}_a\) value is given as 9.26.

Calculating the Effective Buffer Range

To find the effective buffer range, subtract 1 from the \(\mathrm{pK}_a\) value to find the lower limit and add 1 to the \(\mathrm{pK}_a\) value to find the upper limit. Therefore, lower limit = \(\mathrm{pK}_a\) - 1 = 9.26 - 1 and upper limit = \(\mathrm{pK}_a\) + 1 = 9.26 + 1.

Determining the Answer

After calculation, the lower limit is 8.26 and the upper limit is 10.26. Therefore, the effective buffer range is from 8.26 to 10.26.

Key concepts

pKa Value

The pKa value is a critical property in understanding acid-base behavior in chemistry. It represents the strength of an acid in solution and is derived from the acid dissociation constant, Ka. In simple terms, a lower pKa value indicates a stronger acid because it dissociates more in water to form hydrogen ions. Conversely, a higher pKa value signifies a weaker acid, which does not dissociate as much.

For the buffer solution involving ammonium hydroxide (NH4OH) and ammonium chloride (NH4Cl), the pKa of the acid component, NH4⁺, is 9.26. This value gives us a starting point to understand how the buffer will behave in an aqueous solution and is pivotal in determining the effective pH range in which the buffer can maintain a relatively stable pH, important for many biological and chemical applications.

Acid-Base Equilibrium

Acid-base equilibrium refers to the state where the rates of the forward and reverse reactions of acid and base dissociation are equal, leading to a stable concentration of acids, bases, and their respective conjugates in a solution. This balance is essential for the functioning of buffer solutions.

At the heart of this concept is the Henderson-Hasselbalch equation which relates pH, pKa, and the ratio of the concentration of the base to that of the acid. It illustrates how buffers work to resist changes in pH by utilizing the equilibrium between weak acids and their conjugate bases. When a small amount of strong acid or base is added to the buffer, the equilibrium shifts to neutralize the added ions, thereby maintaining the pH within a narrow range.

Buffer Capacity

Buffer capacity defines a buffer solution's ability to resist changes in pH upon the addition of acidic or basic components. It is dependent on the concentrations of the acid and its conjugate base within the buffer solution—the greater their concentration, the higher the buffer capacity.

This capacity is especially significant when considering biological systems, such as the human bloodstream, where a stable pH is crucial for proper physiological function. In the case of the NH4OH-NH4Cl buffer, its capacity would be optimal around the pKa value of NH4⁺. However, if an excessive amount of strong acid or base is added, the buffer can become 'overwhelmed', and its capacity to maintain pH diminishes; thus, knowing a buffer's capacity is practical when anticipating its use.

Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry, characterizing a condition where the concentrations of reactants and products remain constant over time because the forwards and reverse reactions occur at the same rate. This state is dynamic, meaning that while the concentrations stay constant, the molecules continue to react.

When discussing buffer solutions, we encounter a specific type of equilibrium involving acid and base reactions. A buffer's components (weak acid and its conjugate base, or vice versa) work together to 'absorb' additions of H⁺ or OH^- ions by shifting the position of the equilibrium. The ability of the buffer to maintain chemical equilibrium under various conditions is what makes it invaluable in many chemical processes and analytical techniques.