Question

Find the pH and fraction of dissociation (α) of a 0.0900 M solution of a weak acid

HA with Ka = 1.00 x 10-5.

Answer 1

HA <=> H+ & A-

Ka = [H+] [A-] / [HA]

1.00 e-5 = [X] [X] / [0.09]

X2 =0.9 e-6

X = [H+] = 0.94868 e-3

your answer
rounded to 3 sig figs is
pH = - 3.022

if I had thought that the quadratic was needed,  

fraction of dissociation:

HA <=> H+ & A-

Ka = [H+] [A-] / [HA]

1.00 e-5 = [X] [X] / [0.09- X]

1.00 e-5 [0.09- X] = [X] [X]

0.9 e-6 - e-5 X = X2

X2 + e-5 X - 0.9 e-6 = 0

0.0009436964

X = [H+] = 0.0009436964 Molar
pH =3.025

& fraction of dissociation : 0.0009436964 / 0.09 M = 0.01048