Final answer:
The hydronium ion concentration in a solution with pH 10 is 1,000 times greater than in a solution with pH 13, because the pH scale is logarithmic and a change of 3 pH units means a 1,000-fold difference.
Step-by-step explanation:
The hydronium ion concentration in a solution with pH 10 is 1,000 times greater than the hydronium ion concentration in a solution with pH 13. This is because the pH scale is logarithmic, meaning that a change in pH value by 1 corresponds to a 10-fold change in hydronium ion concentration. Since the pH difference between the two solutions is 3 (from pH 13 to pH 10), we have a 10^3 or 1,000 times difference in the concentration of hydronium ions. Therefore, the correct answer is c. 1,000 times greater.