Question

The pH of a solution is 5.70±0.01. What is the concentration of H⁺ in the solution and its absolute uncertainty? Answer should be [H⁺]=2.0x10⁻¹⁰ and absolute uncertainty = 5x10⁻⁸.

Answer 1

To determine the H+ concentration from a pH of 5.70, we use the inverse log function, resulting in [H+] = 2.0x10^-10. To find the absolute uncertainty, we calculate H+ concentrations for pH 5.69 and 5.71, and the difference is the absolute uncertainty, which is 5x10^-8.

Step-by-step explanation:

The question is asking to calculate the concentration of H⁺ ions in a solution with a given pH and to determine the absolute uncertainty of that concentration. To find the concentration of hydrogen ions (H⁺) in the solution, we can use the formula pH = -log[H⁺].

Given that the pH of the solution is 5.70, we can reverse the operation to find the concentration of hydrogen ions by taking the antilog (inverse log) of the negative pH:

[H⁺] = 10⁻⁵.⁷⁰

This gives us a concentration of [H⁺]=2.0x10⁻¹⁰. Considering the error in the pH (±0.01), we can calculate the maximum and minimum pH values that reflect this uncertainty (5.70 - 0.01 = 5.69 and 5.70 + 0.01 = 5.71) and then find the corresponding concentrations for H⁺. The difference between these concentrations will give us the absolute uncertainty, which is 5x10⁻⁸.