Estimate the equilibrium constant for the weak acid HCN, if a 4.68×10-3 M aqueous solution of HCN has a [H+] 0.00000151 M (make an exact calculation assuming that initial concentration is not equal to the equilibrium concentration).

HCN = CN- + H+

............HCN ==> H^+ + CN^-

I.........4.68E-3....0.....0
C..........-x........x......x
E........4.69E-4-x...x......x

Ka = (H^+)(CN^-)/(HCN)
Ka = (x)(x)/(4.68E-4-x)
You know x = 1.51E-6. Substitute into the above and solve for Ka.

To estimate the equilibrium constant for the weak acid HCN, we can use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation relates the pH of a solution to the concentration of the acid and its conjugate base.

The equation is given as:

pH = pKa + log([A-]/[HA])

Where:
- pH is the negative logarithm of the hydrogen ion concentration ([H+])
- pKa is the negative logarithm of the acid dissociation constant (Ka) for HCN
- [A-] is the concentration of the conjugate base CN-
- [HA] is the concentration of the acid HCN

In this problem, we are given the concentration of [H+] as 0.00000151 M, which is equal to [HA] since HCN is a weak acid. We need to find the value of pKa to estimate the equilibrium constant.

To find the pKa, we rearrange the Henderson-Hasselbalch equation as:

pKa = pH - log([A-]/[HA])

The concentration of CN- ([A-]) can be determined by subtracting the concentration of [H+] from the initial concentration of HCN:

[A-] = initial concentration of HCN - [H+] = 4.68×10-3 M - 0.00000151 M

Now we have all the necessary values to calculate the pKa:

pKa = -log(0.00000151 / (4.68×10-3 - 0.00000151))

Next, we can use the relationship between pKa and Ka:

Ka = 10^(-pKa)

Finally, to estimate the equilibrium constant (K) for the dissociation of HCN, we can use the expression:

K = [CN-][H+] / [HCN]

Since the concentration of CN- ([A-]) is equal to [HCN], we can simplify the equation to:

K = [H+]^2 / [HCN]

Substituting the known values, we can now estimate the equilibrium constant K.