Final answer:
The concentration of hydronium ions (H3O+) in the detergent can be calculated by using the ion product of water (1.0×10^-14 M^2) and dividing it by the given hydroxide ion concentration (OH-), giving us a hydronium ion concentration of 2.0×10^-12 M.
Step-by-step explanation:
The concentration of OH- in a solution of dishwasher detergent is 0.0050 M, and to determine the concentration of H3O+ in the detergent, we use the ion product of water at 25 °C, which is 1.0×10^-14 M2. This relationship implies that [H3O+][OH-] = 1.0×10^-14. We can rearrange this expression to solve for [H3O+] by dividing both sides by [OH-]:
[H3O+] = 1.0×10^-14 / [OH-]
Substituting the given hydroxide ion concentration into this equation:
[H3O+] = 1.0×10^-14 / 0.0050 M
The resulting hydronium ion concentration is 2.0×10^-12 M.