# What is the pH at 25 degrees Celsius of a 0.0064 M solution of a weak base with a Kb of 1.6E-9?

Mar 8, 2018

pH = 8.5

#### Explanation:

A weak base in water steals a proton off water to make hydroxide ion, and from this you can get your pH.

$$          B: + H20 = BH + OH-


I 0.0064M 0 0
C -x +x +x
E 0.0064M +x +x

employ the x<<0.0064M assumption to avoid quadratic, then check at end to make sure it is less than 5%

$K b = 1.6 \times {10}^{-} 9 = \text{[BH][OH]"/"[B:]}$
$K b = 1.6 \times {10}^{-} 9 = \text{[x][x]"/"[0.0064M]}$
$x = 3.2 \times {10}^{-} 6$.....(3.2xx10^-6)/0.064xx100 = 0.05% assumption is ok

$x = 3.2 \times {10}^{-} 6$ pOH = 5.5 pH = 8.5