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Chapter 16: Problem 17

Calculate the \(\mathrm{pH}\) of the \(0.20 \mathrm{M} \mathrm{NH}_{3} / 0.20 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) buffer. What is the pH of the buffer after the addition of \(10.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{HCl}\) to \(65.0 \mathrm{~mL}\) of the buffer?

Short Answer

Expert verified
The initial pH of the buffer is 9.25. After addition of 10.0 mL of 0.10 M HCl, the pH of the buffer is 9.22.

Step by step solution

01

Calculate the initial pH of the buffer using the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is given by \(pH = pKa + \log{\left(\frac{[NH3]}{[NH4+]}\right)}\). pKa is the negative log of the Ka of the NH4+. Given that the Ka of NH4+ is \(5.56 \times 10^{-10}\), the pKa is -log(Ka) = 9.25. The molarities of NH3 and NH4Cl in the buffer are both 0.20 M. Substituting these values into the equation gives \(pH = 9.25 + \log{\left(\frac{0.20}{0.20}\right)} = 9.25\)
02

Determine the molar concentrations after addition of HCl

When the strong acid HCl is added to the buffer, it reacts with the weak base NH3 to form more NH4+. The reaction can be written as NH3 + HCl -> NH4Cl. The number of moles of NH3 and HCl are needed to know how much NH4+ is produced. This is calculated by multiplying the volume (in liters) by the molarity. The initial number of moles of NH3 is 0.20 M * 0.065 L = 0.013 mol. The number of moles HCl added is 0.10 M * 0.01 L = 0.001 mol. So, 0.001 mol of NH3 reacts with the HCl, leaving 0.012 mol of NH3, and forming an additional 0.001 mol of NH4+.
03

Recalculate the pH after the addition of HCl

The new total volume of the solution after addition of HCl is 0.065 L + 0.01 L = 0.075 L. This means the new molarities of NH3 and NH4+ are 0.012 mol / 0.075 L = 0.16 M for NH3 and (0.20 M * 0.065 L + 0.001 mol) / 0.075 L = 0.176 M for NH4+. The new pH can be calculated using the Henderson-Hasselbalch equation again: \(pH = 9.25 + \log{\left(\frac{0.16}{0.176}\right)} = 9.22\). The pH of the buffer has slightly decreased due to the addition of the strong acid HCl.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Buffer Solution
A buffer solution is a special kind of solution that resists changes in pH when small amounts of an acid or base are added. It contains a weak acid and its conjugate base, or a weak base and its conjugate acid. This dual presence helps balance pH by neutralizing added acids or bases.
  • In the given problem, the buffer is made of ammonia ( H_3 ) and ammonium chloride ( H_4Cl ).
  • Here, H_3 acts as a weak base, while H_4^+ (from H_4Cl ) is its conjugate acid.
This buffer can effectively maintain the pH because when an acid is added, the H_3 can react with the hydronium ions ( H^+ ) from the acid. Conversely, if a base is added, the H_4^+ can donate a proton to neutralize the base. Thus, buffer solutions play a vital role, particularly in biochemical and industrial applications, where consistent pH is crucial.
pH Calculation
The pH of a solution is a measure of its acidity or basicity. Calculating pH in the context of a buffer solution often involves the Henderson-Hasselbalch equation:
\[ pH = pKa + \log{\left( \frac{[\text{base}]}{[\text{acid}]} \right)} \]This formula helps us find the pH of a buffer. It relies on the concentration ratio of the base and its conjugate acid.
  • "pKa" here is the negative logarithm of the Ka, which indicates the dissociation constant of the weak acid in the buffer.
  • In this exercise, Ka for H_4^+ is provided, and the corresponding pKa is 9.25.
This means that initially, when both the base and acid have equal concentrations, the log part (ratio) becomes zero, simplifying our calculation. Understanding this method is essential for managing buffer systems and ensuring solutions don't deviate from desired pH levels.
Acid-Base Reaction
Acid-base reactions are fundamental in chemistry and involve the transfer of hydrogen ions ( H^+ ) from an acid to a base. Such a reaction is key when strong acids or bases interact with buffer systems.
When HCl , a strong acid, is added to the buffer in this problem:
  • The H^+ from HCl pairs with ammonia ( H_3 ), a weak base, forming ammonium ions ( H_4^+ ).
  • This results in a decrease in ammonia and an increase in ammonium ions within the solution.
This type of reaction is pivotal because it showcases a buffer's capacity to neutralize added acids. The balance within the buffer helps partially resist significant changes in pH, demonstrating the importance of understanding acid-base interactions for effective chemical and biological solution management.
Molarity
Molarity is a concentration measurement used typically for solutions, denoted as moles of solute per liter of solution. Understanding molarity helps us accurately gauge how concentrated a solution is, which directly impacts pH calculation.
In this exercise, understanding molarity allows us to determine the changes in concentrations of H_3 and H_4^+ after the addition of HCl.
  • The molarity of H_3 and H_4Cl in the original buffer is both 0.20 M.
  • After adding 0.01 moles of HCl, which reacts with H_3, changes occur: 0.16 M for H_3 and 0.176 M for H_4^+.
    • Changes in molarity arise due to the chemical reaction and increased total solution volume. Accurately using molarity ensures that subsequent pH calculations with the Henderson-Hasselbalch equation remain precise and meaningful.
    HCl Addition
    Adding HCl to a buffer solution introduces a strong acid into the system. Strong acids completely dissociate in water, releasing H^+ ions which can overwhelm unbuffered systems.
    In this scenario:
    • H^+ from HCl reacts with H_3, maintaining the system's buffer capabilities.
    • This leads to more H_4^+ being formed, slightly altering the buffer's pH from 9.25 to 9.22.
    Seeing how the pH only slightly shifts after the addition of HCl reflects the efficiency of a good buffer solution. This minor change is critical, showcasing a buffer's ability to absorb disruptions and maintain near-original pH, a property highly valued in both chemistry labs and natural biological processes.

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