Problem 22 - General Chemistry: Principles and Modern Applications

Question

Given \(125 \mathrm{mL}\) of a solution that is \(0.0500 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{2}\) and \(0.0500 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\) (a) Over what pH range will this solution be an effective buffer? (b) What is the buffer capacity of the solution? That is, how many millimoles of strong acid or strong base can be added to the solution before any significant change in pH occurs?

Step-by-Step Solution

Answer

The effective pH range for this buffer solution is from 9.64 to 11.64. The buffer capacity of this solution is 6.25 mmol of strong acid or base.

Step 1: Determine the pKA

Firstly, calculate the pKa of the weak base, CH3NH2. Looking at a table of Ka values for weak acids, one can find that the Ka value for the conjugate acid CH3NH3+ is 2.29x10^-11. Since pKa= -log(Ka), the pKa is 10.64.

Step 2: Effective Buffer Range

A buffer solution is most effective when the pH value is within 1 unit of pKa, meaning the effective buffer range is from (pKa - 1) to (pKa + 1). So, the effective buffer pH of this solution ranges from 9.64 to 11.64.

Step 3: Buffer Capacity

For part (b), determine the buffer capacity. This solution can handle equal amounts of acid or base because the weak base and its conjugate acid present are at the same concentration. Look at the lesser concentration, which in this case is 0.0500 M (we multiply by 125 ml to convert the concentration to millimoles, giving us 6.25 mmol). So, this (6.25 mmol) is the maximum amount of strong acid or base that can be added before the pH changes significantly.

Step 4: Conclusion

Therefore, the solution can act as an effective buffer within the pH range 9.64 to 11.64 and the buffer capacity equals 6.25 mmol. That is, until 6.25 mmol of strong acid or base are added, the pH of the solution will not change significantly.

Key Concepts

Buffer Capacity

Buffer capacity is a crucial concept when analyzing how well a solution can resist changes in pH, especially when small amounts of acids or bases are added. In simple terms, it tells us how much strong acid or base a buffer can handle before the pH starts to change significantly. In our given exercise, we have a solution with both a weak base, CH₃NH₂, and its conjugate acid, CH₃NH₃⁺, both at a concentration of 0.0500 M. To calculate the buffer capacity, we consider the amount of weak base and acid present. Since they are equal in this solution, multiplying the concentration by the volume helps in finding the millimoles. Here, the solution has a volume of 125 mL, which gives us 6.25 mmol of each component. Therefore, this buffer can absorb up to 6.25 mmol of added acid or base without causing significant pH changes. It's important to remember that a buffer works best when the concentrations of the weak acid and its conjugate base are approximately equal, as this allows for a balanced capacity.

pH Range

Understanding the pH range over which a buffer is effective is essential to control the acidity or basicity in various chemical processes. A buffer solution resists changes in pH by neutralizing small amounts of added acid or base. The most effective pH range of a buffer is typically within one pH unit above and below the pKa of the acid or base used to create the buffer. For the given solution, the pKa of the weak base's conjugate acid CH₃NH₃⁺ is 10.64. Thus, using the effective buffer range formula, we calculate:

• Lower limit: pKa - 1 = 10.64 - 1 = 9.64
• Upper limit: pKa + 1 = 10.64 + 1 = 11.64

Therefore, this solution can effectively buffer over the pH range from 9.64 to 11.64. This means that within this range, the solution will maintain its pH with minimal changes when small amounts of acids or bases are added.

pKa Calculation

The concept of pKa calculation is fundamental to understanding the strength of an acid or base and its buffering potential. The pKa is a measure that helps determine how strongly an acid dissociates to donate protons in a solution, with lower pKa values indicating stronger acids.To find the pKa of the weak base CH₃NH₂ in the exercise, we first consider its conjugate acid, CH₃NH₃⁺. We refer to a table that lists the Ka, or acid dissociation constant, for CH₃NH₃⁺, which is given as 2.29 x 10⁻¹¹. The pKa is then calculated using the formula:\[pKa = -\log(K_a)\]Substituting the given Ka value, we have:\[pKa = -\log(2.29 \times 10^{-11}) = 10.64\]This pKa value is useful for predicting the pH range where the buffering action is most effective, guiding us in formulating buffers for specific pH goals.