Q.If 0.561 g of KOH is dissolved in water to give 200 mL of solution at 298 K. Calculate the concentrations of potassium, hydrogen and hydroxyl ions. What is its pH?

Hydrogen Ion Concentration and pH

Imagine you have a glass of pure water. It looks simple, but inside, a tiny fraction of water molecules are constantly splitting apart and re-forming. This splitting creates two kinds of charged particles: a hydrogen ion ($H^+$) and a hydroxide ion ($OH^-$). In pure water, these two are perfectly balanced — there are exactly as many $H^+$ as $OH^-$.

Now, if you add something like lemon juice (an acid), you increase the number of hydrogen ions. The balance tips: more $H^+$ than $OH^-$. If you add baking soda (a base), you decrease $H^+$ or increase $OH^-$, and the balance tips the other way.

The question is: how do we measure this imbalance in a simple, practical way? The numbers of $H^+$ ions are incredibly tiny — in pure water, only about 1 in every 10 million water molecules is split at any moment. Writing these numbers directly (like $0.0000001$ moles per litre) is clumsy. That's where pH comes in.

The Precise Definition

pH is a mathematical shortcut. It stands for "power of hydrogen" (from the French puissance d'hydrogène).

The logarithm base 10 does two things at once:

• It compresses a huge range of numbers (from $10^{-14}$ to $10^{0}$) into a manageable scale of 0 to 14.
• The negative sign flips the direction: higher $[H^+]$ gives a lower pH, and lower $[H^+]$ gives a higher pH.

What the Numbers Mean

Notice the pattern: each step of 1 in pH means a tenfold change in $[H^+]$. A solution of pH 3 has 10 times more $H^+$ than pH 4, and 100 times more than pH 5.

The Key Insight

pH is not a measure of "how acidic" something is in a vague sense — it is a precise, logarithmic measure of the actual number of hydrogen ions present. The scale runs from 0 (most acidic, highest $[H^+]$) to 14 (most basic, lowest $[H^+]$), with 7 being neutral. …