A solution of HCl has $\left[ H ^{+}\right]=0.01 M$. What is the pH of this solution? Use $pH = -\log \left[ H _3 O ^{+}\right]$.
The concentration of hydrogen ions in the hydrochloric acid solution is given as \([H^+] = 0.01 \, M\). Since hydrochloric acid is a strong acid, it dissociates completely in water, meaning the concentration of hydronium ions, \([H_3O^+]\), is equal to the concentration of the hydrogen ions provided: \([H_3O^+] = [H^+] = 0.01 \, M\). The pH of a solution is defined by the formula \(pH = -\log[H_3O^+]\). Our goal is to calculate this value.
To calculate the pH, we first express the concentration \([H_3O^+] = 0.01 \, M\) in scientific notation. We observe that \(0.01 = 10^{-2}\). Substituting this value into the pH formula, we have \(pH = -\log(10^{-2})\). Using the logarithmic property \(\log_{10}(10^x) = x\), we simplify the expression: \(-\log(10^{-2}) = -(-2) = 2\). Thus, the pH of the given solution is 2.
Understanding pH is essential in many practical fields. For example, in gardening, many plants prefer slightly acidic or alkaline soil, and gardeners often test the pH of their soil to ensure it is suitable for specific crops like blueberries (which prefer acidic soil) or lavender (which prefers more neutral to alkaline soil). Similarly, in swimming pool maintenance, the pH of the water must be strictly monitored to prevent irritation to swimmers' eyes and skin while ensuring that pool cleaning chemicals remain effective at killing bacteria. Calculating pH helps maintain these healthy environments.