Final answer:
The pH of a buffer solution that is 0.250 M in HCN and 0.170 M in KCN can be calculated using the equilibrium approach or the Henderson-Hasselbalch equation. The equilibrium approach involves setting up an equilibrium expression using the acid dissociation constant (Ka), while the Henderson-Hasselbalch equation uses concentrations of the acid and its conjugate base along with the pKa value.
Step-by-step explanation:
To calculate the pH of a buffer solution that is 0.250 M in HCN and 0.170 M in KCN, we can use both the equilibrium approach and the Henderson-Hasselbalch equation.
Equilibrium Approach
The dissociation of HCN in water can be represented as follows:
HCN + H2O → H3O+ + CN-
Given that the acid dissociation constant (Ka) is 4.9 x 10−10, we can write the equilibrium expression as:
Ka = [H3O+][CN-] / [HCN]
As the solution is a buffer, we can assume that the concentration of HCN remains nearly the same, and the concentration of CN- comes from KCN, which is fully dissociated. Therefore, [CN-] is 0.170 M, and [HCN] is 0.250 M. As the buffer solution minimizes changes in pH, the concentration of H3O+ (which is equal to [H+]) will be small enough not to affect the concentrations of HCN and CN- significantly. With these assumptions, we can solve for [H+] and calculate the pH.
Henderson-Hasselbalch Equation
Alternatively, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base (CN-), and [HA] is the concentration of the acid (HCN). Substituting the given values:
pH = 9.31 + log(0.170/0.250)
The resulting pH from both approaches should be the same.