Derive a relation between pH and pOH.

To derive the relation between pH and pOH, we first need to understand what pH and pOH represent. pH is a measure of the acidity or basicity of a solution, while pOH is a measure of its hydroxide ion (OH-) concentration. Both are logarithmic scales and are related to the concentration of hydrogen ions (H+) and hydroxide ions (OH-) in a solution, respectively.

The pH scale is defined as:

pH = -log[H+]

where [H+] represents the concentration of hydrogen ions in moles per liter.

The pOH scale is defined as:

pOH = -log[OH-]

where [OH-] represents the concentration of hydroxide ions in moles per liter.

Now, in a neutral solution, the concentration of hydrogen ions [H+] is equal to the concentration of hydroxide ions [OH-], which means:

[H+] = [OH-]

Taking the logarithm of both sides:

log[H+] = log[OH-]

Now, using the relationship that pH + pOH = 14 (valid at 25°C for water), we can rewrite the above equation as:

-log[H+] + -log[OH-] = 14

or

-pH - pOH = 14

Rearranging the equation to solve for pOH:

pOH = -pH + 14

This is the relation between pH and pOH. If you know the pH of a solution, you can calculate the pOH using this equation, and vice versa. Keep in mind that this relationship holds for aqueous solutions at 25°C and when the solution is neither too acidic nor too basic.