3.1.3. pH Calculation for Strong Acids/Bases

For a solution of a strong acid with concentration C, [H plus] = C (assuming negligible contribution from water if C > 10⁻⁶).

When we talk about strong acids, they are substances that dissociate completely in water to give hydrogen ions (H plus). This means that the concentration of hydrogen ions in the solution is equal to the concentration of the acid itself (C). If the concentration of the acid is greater than 10⁻⁶ M, we can fairly ignore the contribution of hydrogen ions from the self-ionization of water, simplifying our calculations.

Imagine you are making lemonade. If you add a specific amount of lemon juice (strong acid), all of that juice mixes into the water (solvent) completely, and the sour taste you experience corresponds directly to how much lemon juice you added. This direct relationship is what occurs in strong acid solutions with respect to pH.

Example 1: A solution is prepared by dissolving 0.250 mol of HCl in 1.00 L of water.

[H plus] = 0.250 M → pH = – log₁₀ (0.250) = 0.60.

In this example, we have dissolved 0.250 mol of hydrochloric acid (HCl) in 1 liter of water. Since it's a strong acid, it completely dissociates to produce 0.250 M of hydrogen ions in solution. To calculate the pH, we use the formula pH = -log₁₀([H plus]). Plugging in 0.250 M, we find that the pH is 0.60, indicating a very acidic solution.

Think of pouring lemon juice (HCl) into a glass of water. If you pour a certain amount into one liter of water, it would be very sour, and the acidity (pH) indicates just how sour it is. A pH of 0.60 means it’s quite sour.

For a solution of a strong base with concentration C, [OH minus] = C (again, ignoring water).

Strong bases also dissociate completely in water, producing hydroxide ions (OH minus). Similar to strong acids, the concentration of hydroxide ions in a strong base solution is equal to the initial concentration of the base. When calculating, we again ignore the contribution from water as long as this concentration is above 10⁻⁶ M.

Imagine washing your hands with soap that contains a strong base like sodium hydroxide (NaOH). When you mix it with water, the soap completely dissolves, increasing the cleanliness (alkalinity) of the water based on how much soap you used. Here, the pH increase indicates how 'slippery' or basic that solution is.

Example 2: A solution is prepared by dissolving 0.0200 mol of Ca(OH)₂ in 500 mL of water. Ca(OH)₂ dissociates into Ca² plus + 2 OH minus.

Moles of Ca(OH)₂ = 0.0200 mol, volume = 0.500 L → 0.0400 M Ca(OH)₂.

[OH minus] = 2 × 0.0400 M = 0.0800 M.

pOH = – log₁₀ (0.0800) = 1.10 → pH = 14.00 – 1.10 = 12.90.

In this case, we dissolved 0.0200 mol of calcium hydroxide (Ca(OH)₂) in 500 mL of water. First, we convert the volume to liters to find the molarity of the solution. Since Ca(OH)₂ produces 2 hydroxide ions for each formula unit, the resulting hydroxide ion concentration is 0.0800 M. To find the pOH, we use pOH = -log₁₀([OH minus]), which gives us 1.10. Finally, using the relationship pH + pOH = 14, we calculate the pH to be 12.90, indicating a very basic solution.

Consider using a strong drain cleaner that contains calcium hydroxide. When you pour it into water, the strong base dissociates fully and makes the water very slippery and basic, similar to how larger amounts of soap would. The pH level reflects how basic that water is, and here at 12.90, it’s quite alkaline.

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