Calculate the pH of the solution that results from each mixture. a. 150.0 mL of 0.25 M HF with 225.0 mL of 0.30 M NaF b. 175.0 mL of 0.10 M C2H5NH2 with 275.0 mL of 0.20 M C2H5NH3Cl

Understanding the Henderson-Hasselbalch equation is crucial for calculating the pH of buffer solutions. It is an expression derived from the acid dissociation constant (Ka) that provides insight into the pH of a solution containing a weak acid and its conjugate base, or a weak base and its conjugate acid.

For weak acid and conjugate base systems, the equation is written as:
\[ pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right) \]
where \( pKa \) is the negative logarithm of the acid dissociation constant, \( [A^-] \) is the concentration of the conjugate base, and \( [HA] \) is the concentration of the acid.

For weak base systems, the equation is adapted by converting pKa to pKb (since pKb = 14 - pKa for water at 25 °C) and then calculating pOH instead of pH:
\[ pOH = pKb + \log\left(\frac{[B^+]}{[B]}\right) \]
Finally, the pH is obtained by subtracting pOH from 14:
\[ pH = 14 - pOH \]
The elegance of this equation lies in its simplicity, allowing students to readily determine the pH of a buffer system if they have knowledge of the concentrations and dissociation constants involved.

In buffer solutions, the pair of a weak acid and its conjugate base works in tandem to neutralize added acids or bases. A weak acid (HA) only partially dissociates in solution, releasing hydrogen ions (H+) and conjugate base ions (A-).

Let's break down these components:

• A weak acid is an acid that does not completely dissociate in aqueous solution.
• The conjugate base (A-) is what the acid becomes after donating a hydrogen ion.

Together, this weak acid-conjugate base pair can resist drastic changes in pH. This is because the weak acid can neutralize added bases while the conjugate base can neutralize added acids. The ability to maintain pH makes this combination ideal for buffer systems in various applications, including biological fluids and industrial processes.

Similar to the weak acid-conjugate base, there's also a weak base and its conjugate acid which constitute a buffer system. A weak base (B), like its acid counterpart, does not fully dissociate in water and thus provides buffering action by absorbing excess H+ ions.

The key points to remember are:

• A weak base partially accepts protons (H+), typically forming a partially charged or neutral species.
• The conjugate acid (B+) is the species formed when a base gains a proton.

When an acid is added to such a system, the weak base will neutralize some of the added H+ ions, while the conjugate acid will release H+ ions if a base is added to the system. This interplay allows for the regulation of pH within a narrow range, which is why these pairs are essential components in many biological and chemical buffer solutions.

Buffer systems are the unsung heroes when it comes to maintaining a stable pH environment. They are composed of a mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid. These systems have the remarkable ability to mitigate the effects of acids or bases, thus keeping the pH of a solution relatively constant even when perturbed by external factors.

Some characteristics and uses of buffer systems include:

• Buffer systems are essential in biological processes, maintaining the pH necessary for enzymatic activities within cells.
• They are also used in laboratory settings, where reactions often require a stable pH.
• Industrial applications such as dyeing fabrics, fermentation processes, and pharmaceutical production rely on buffer systems.

By using the principles of how buffer systems function, students and professionals can predict and control the pH of solutions important in both academic and practical applications.