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# 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))##