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QUESTION

# Given that Ka for HBrO is 2.8 × 10-9 at 25 °C, what is the value of Kb for BrO– at 25 °C? Given that Kb for (CH3)2NH is 5.4 × 10-4 at 25 °C, what is the value of Ka for (CH3)2NH2 at 25 °C?

For a weak acid, you can determine the value of the base dissociation constant, K_b, of its by using the water dissociation constant, K_W.

Mathematically, the relationship that exists between K_a, K_b, and K_W can be written like this

K_W = K_a * K_b = 10^(-14)

In the case of the hypobromite ion, BrO^(-), the base dissociation constant will be

K_b = 10^(-14)/K_a

K_b = 10^(-14)/(2.8 * 10^(-9)) = color(green)(3.6 * 10^(-6))

The same is tru for dimethylamine, (CH_3)_2NH, and its conjugate acid, the dimethylammonium ion, (CH_3)_2NH_2^(+).

K_a = 10^(-14)/K_b

K_a = 10^(-14)/(5.4 * 10^(-4)) = color(green)(1.9 * 10^(-11))