Question

Heavy metal azides, which are salts of hydrazoic acid, HN3, are used as explosive detonators. A solution of 0.20M hydrazoic acid has a pH of 3.21. What is the Ka for hydrazoic acid?

Answer 1

Let α be the dissociation of the weak hydrazoic acid
                            HA <---> H ⁺ + A^-

initial conc.            c               0         0

change                -cα            +cα      +cα

Equb. conc.         c(1-α)          cα    cα

Dissociation constant , K_a = cα x cα / ( c(1-α)

                                         = c α² / (1-α)

In the case of weak acids α is very small so 1-α is taken as 1

So K_a = cα²

==> α = √ ( K_a / c )

Given pH = 3.21

-log[H⁺] = 3.21

[H⁺] = 10^-3.21

cα = 6.16x10^-4 M

          c = concentration = 0.20 M

Plug the values we get α = 3.08 x10^-3

K_a = cα²

= 0.20 x (3.08 x10^-3)²

= 1.90x10^-6