The hydrogen ion concentration of a 10-8 M, HCl aqueous solution at 298 K (Kw = 10-14) is
- 1.0 10-8 M
- 1.0 10-6 M
- 1.0512 10-7 M
- 9.512 10-8 M
Answer
(3) 1.0512 10-7 M
Solution
The acid is so dilute that the H+ ions from water cannot be neglected.
Let x be the concentration of H+ (and OH-) from water, so [H+] = 10-8 + x and [OH-] = x. Then
Kw = (10-8 + x) x = 10-14
x2 + 10-8x - 10-14 = 0
x = -10-8 + 10-16 + 4 10-142
= -1 10-8 + 2.0025 10-72
= 9.512 10-8 M
∴ [H+] = 1 10-8 + 9.512 10-8 = 1.0512 10-7 M
Answer: (3)