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# Edexcel A-level Chemistry The pH scale

1. Determining pH
2. Ionic product of water
3. Dissociation constant
4. pH curves

The pH of an aqueous solution and the concentration of hydrogen ions are related by the following equations: pH = –log[H⁺] and 10⁻ᵖᴴ = [H⁺]. [H⁺] and [H₃O⁺] are exchangeable. We can see that the pH scale is logarithmic, meaning that for every unit of change in the pH there is a ten fold change in the concentration. The negative sign indicates an inverse relationship, thus if the pH increases the concentration decreases, and vice versa. The pOH of solutions can also be calculated in the same way, but using [OH⁻] instead of [H⁺]. The following relationship can be used to convert between pH and pOH: pH + pOH = 14.

Water is amphoteric, meaning it can act both as a Bronsted-Lowry base and as an acid. Therefore it can react with itself, one H₂O donating a proton to another. This process is called the autoionization of water. The equilibrium constant of this reaction is called the autoionization constant, Kw. The expression for the autoionization constant is Kw = [H₃O⁺][OH⁻], and at 25 °C is equal to 10⁻¹⁴. This is only true at 25 °C, as a change in temperature changes the value of Kw. The relationship between Kw and pKw is the same as the relationship between [H⁺] and pH, so pKw = – log Kw. We also know that at 25 °C pKw = pH + pOH = 14.

The dissociation constant is the equilibrium constant for reactions where a bigger molecule separates reversibly into smaller molecules. Weak acids and bases do exactly that when dissolved in water. A weak acid, HA, separates reversibly into its conjugate base and hydrogen ions. In this case the dissociation constant is called the acid dissociation constant, Ka. It is defined by Ka = [A⁻][H⁺] / [HA], and it is a quantitive measure of the strength of an acid. The larger Ka is, the stronger the acid. In case of a weak base, which dissociates into its conjugate acid and hydroxide ions, it is called the base dissociation constant, Kb. It is defined by Kb = [BH⁺][OH⁻] / [B]. The larger the value of Kb, the stronger the base. The pH of a solution can be calculated from Ka by rearranging the equation Ka = [A⁻][H⁺] / [HA] to find [H⁺].

A pH curve, or titration curve, is the plot of the pH of the analyte solution versus the volume of the titrant added as a titration progresses. The titration curve can be used to determine the equivalence point, the point at which the amounts of acid and base used in the titration are just sufficient to cause complete neutralization. Acid-base indicators are often used in titrations. If properly selected, these undergo a rapid colour change at the pH corresponding to the equivalence point of the titration. A suitable indicator has a pKᵢ that is within one pH unit of the expected pH at the equivalence point.

# 1

Look at the pH curve and answer the following. What is the strength of the acid/base and their roles in the titration? What is the pH at the equivalence point?

# 2

Calculate Kw, the equilibrium constant for the autoionization of water, using the fact that at 25 °C pure water has pH = 7 = pOH.

# 3

An aqueous solution has a pOH of 9.7 at 25°. Calculate its [H⁺].

# 4

100 ml of solution contains 0.02 moles of hydrogen bromide. This is mixed with 300 ml of sodium hydroxide solution containing 0.1 moles of sodium hydroxide. What is the pH of the resultant mixture?

# 5

We have a solution of hydrochloric acid and a solution of sodium hydroxide. There are 0.25 moles of HCl in 50 ml of solution, and 0.1 moles of NaOH in 20 ml. What is the pH of the mixture of the two?

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