Final answer:
To estimate pH without a calculator, use the concentration's power of ten as the pH, and adjust according to the first digit for more precision. For inverse calculations, use the pH to estimate the power of ten for H3O+ concentration.
Step-by-step explanation:
To estimate pH without a calculator using the -log equation, you can use approximations based on the pH scale and the properties of logarithms. If you have the concentration of hydrogen ions (H3O+), such as 1 x 10-3 M, you recognize that the power of ten gives the pH directly, resulting in a pH of 3.0. For more complex concentrations like 2.3 x 10-5 M, without a calculator, use the fact that the pH is about the negative of the power of ten, adjusted by the first digit of the concentration (the pH would be close to 5 - log(2.3), so slightly above 5). For inverse calculations, knowing the pH can help you estimate the concentration of H3O+. For instance, a pH of 8.3 suggests a concentration of H3O+ roughly of the order of 10-8.3, which is slightly below 10-8 M, making practical estimations without requiring exact calculations.