Calculate the molar concentrations of \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\) in solutions that have the following \(\mathrm{pOH}\) values. (a) 12.27 (b) 6.14 (c) 10.65 (d) 4.28 (e) 3.76

When exploring the chemistry of acids and bases, two critical measurements for the acidity or basicity of a solution are its pH and pOH. These are interconnected, with the pH quantifying the concentration of hydronium ions (H^+) and the pOH dealing with hydroxide ions (OH^-). The sum of pH and pOH is always equal to about 14 at 25°C, a relationship that is fundamental to solving most acid-base problems.

This relationship means that if you know either the pH or pOH of a solution, you can easily find the other. For example, if a solution has a pH of 3, its pOH would be 14 - 3, which equals 11. This balance is essential for maintaining the neutrality of pure water, where the pH equals pOH at 7, demonstrating its neutral characteristic midway between acidic and basic. Understanding this crucial relationship is the stepping stone to mastering more complex acid-base chemistry.

Calculating the concentration of hydroxide ions (OH^-) is vital when working with basic solutions or neutralizing acids. The concentration is directly related to the solution's pOH, where pOH is defined as the negative base-10 logarithm of the hydroxide ion concentration. Here's how to do the calculation:

If you're given the pOH of a solution, to find the hydroxide ion concentration, you use the formula [OH^-] = 10^{-pOH}. So, given a pOH of 6.14, the concentration of OH^- is 10^{-6.14} M, with M standing for molarity, or moles per liter. This equation serves as a tool to transition between the logarithmic pOH scale and the actual concentration of OH^- ions, providing a quantitative insight into the solution's basicity.

To gauge the acidity of a solution, chemists calculate the concentration of hydronium ions (H^+), which is expressed in terms of pH. The pH is the negative logarithm of the H^+ ion concentration. When only the pOH is known, determining the H^+ concentration involves a two-step process. First, the corresponding pH is calculated using the connection between pH and pOH—subtract the pOH from 14. Then, convert the pH to the hydronium ion concentration using [H^+] = 10^{-pH}.

For example, for a solution with a pOH of 10.65, the pH is 14 - 10.65 = 3.35. Thus, the concentration of H^+ is 10^{-3.35} M. This conversion from pOH to H^+ concentration is fundamental for understanding the solution's acidity and is often applied in neutralization reactions and in predicting the behavior of acid-base equilibria.