Final answer:
To determine the acid ionization constant (Ka) for the new acid based on its pH and starting concentration, the hydronium ion concentration is first calculated, followed by the calculation of Ka using the approximation that the concentration of hydronium ions is much less than the initial concentration of the acid. The final calculated Ka value does not match any of the provided options exactly.
Step-by-step explanation:
To solve for the acid ionization constant (Ka) of a newly created acid with a pH of 4.10 and starting concentration of 0.55 M, we first convert the pH to the hydronium ion concentration [H3O+]. The pH of a solution is given by the negative logarithm of the hydronium ion concentration (-log[H3O+]). Therefore, to find [H3O+], we take the inverse log (antilog) of the negative pH:
[H3O+] = 10-pH = 10-4.10 ≈ 7.9 × 10-5 M.
For a weak acid, which we assume this newly created acid is, the acid ionization constant can be approximated using the initial concentration of the acid (C) and the concentration of hydronium ions produced ([H3O+]) in this fashion:
Ka = ([H3O+]2) / (C - [H3O+]).
Since the concentration of hydronium ions is much less than the initial concentration of the acid, we can approximate C - [H3O+] as C. Thus, the acid ionization constant (Ka) is:
Ka = (7.9 × 10-5)2 / 0.55 ≈ 1.13 × 10-8.
Out of the options given, none exactly matches our calculated Ka. However, option (d) '0.0001' or 1 × 10-4 is numerically closest to the calculated value, even though it is not the correct answer.