Question

Consider a buffer made by adding 53.5 g of (CH₃)₂NH₂I to 250.0 mL of 1.42 M (CH₃)₂NH (Kb = 5.4 x 10⁻⁴)

a. What is the pH of this buffer?
b . What is the pH of the buffer after 0.300 mol of H⁺ have been added?
c .What is the pH of the buffer after 0.120 mol of OH⁻ have been added?

Answer 1

To determine the pH of a buffer, calculate the moles of the components, convert Kb to pKa, and apply the Henderson-Hasselbalch equation. The same principle applies when H+ or OH- ions are added to the buffer, with recalculations of concentrations required to determine the new pH.

Step-by-step explanation:

To calculate the pH of a buffer, we need to understand the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the concentration of the acid and its conjugate base. The equation is pH = pKa + log([A-]/[HA]), where A- is the conjugate base and HA is the weak acid.

Part a - Initial pH of the Buffer

The molecular weight of (CH₃)₂NH₂I is calculated, and the moles of (CH₃)₂NH and (CH₃)₂NH₂I are determined. Then we use the Henderson-Hasselbalch equation to calculate pH. The pKa value is needed, which is derived from the given Kb by pKa = 14 - pKb. Once we have pKa, we plug the values into the Henderson-Hasselbalch equation.

Part b - pH after adding H+

When H+ ions are added to the buffer, they will react with the base ((CH₃)₂NH), converting some base to its conjugate acid. We'll calculate the new concentrations of the base and its conjugate acid and reapply the Henderson-Hasselbalch equation to find the new pH.

Part c - pH after adding OH-

Similarly, when OH- ions are added, they will react with the acid part of the buffer, converting it to its conjugate base. Again, we calculate the new concentrations and apply the Henderson-Hasselbalch equation to find the final pH.

Answer 2

To find the pH of the buffer solution, we need to calculate the concentrations of the weak base and salt, and use the Kb expression. When adding H⁺ or OH⁻, the resulting substances will determine the pH.

Step-by-step explanation:

a. To determine the pH of this buffer, we need to calculate the concentration of the (CH₃)₂NH₂ (weak base) and the concentration of the (CH₃)₂NH₂I (salt). First, we calculate the moles of (CH₃)₂NH₂I by dividing the mass by the molar mass. Then, we can find the concentration by dividing the moles by the volume in liters. Next, we can find the initial concentration of the (CH₃)₂NH₂ by subtracting the concentration of the salt [(CH₃)₂NH₂I] from the initial concentration of the weak base [(CH₃)₂NH₂]. Finally, we can find the pOH by using the Kb expression of the weak base and the concentration of the weak base, and then convert the pOH to pH.

b. When 0.300 mol of H⁺ is added, we need to determine if it reacts with the weak base or the salt. If it reacts with the weak base, it forms (CH₃)₂NH₃⁺ (conjugate acid), and if it reacts with the salt, it forms CH₃COOH (acetic acid) and HI (hydroiodic acid). The pH depends on the reaction that occurs and the concentrations of the resulting substances.

c. When 0.120 mol of OH⁻ is added, we can use a similar approach as in part b to determine if it reacts with the weak base or the salt. The resulting substances will determine the pH of the buffer.