Question

Consider a solution that contains both C6H5NH2 and C6H5NH3+. Calculate the ratio [C6H5NH2]/[C6H5NH3+] if the solution has the following pH values. (Assume that the solution is at 25°C.)

Answer 1

The question has incomplete information. The pH values are not discriminated. Let's do, as an example, to pH = 4.69.

Answer:

For pH = 4.69, [C₆H₅NH₂]/[C₆H₅NH₃⁺] = 0.708

Explanation:

C₆H₅NH₂ is a base, and, when in aqueous solution, forms a conjugate acid, which is C₆H₅NH₃⁺. The equilibrium between these two species makes a buffer, a solution that prevents the change in pH by the addition of base or acid.

The pH of a buffer can be calculated by the equation of Handerson-Halsebach:

pH = pKa + log[conjugate base]/[acid]

Where pKa = -logKa, and Ka is the equilibrium constant of the acid. For the base, the equilibrium constant, Kb, is equal to 7x10⁻¹⁰, and

Ka*Kb = Kw

Where Kw is the equilibrium constant for water 1.00x10⁻¹⁴, so Ka for the conjugate acid is:

Ka = 1.00x10⁻¹⁴/7.00x10⁻¹⁰

Ka = 1.43x10⁻⁵

pKa = 4.84

pH = 4.84 + log [C₆H₅NH₂]/[C₆H₅NH₃⁺] (By this step, the pH values given by the question must be substituted)

4.69 = 4.84 + log[C₆H₅NH₂]/[C₆H₅NH₃⁺]

log[C₆H₅NH₂]/[C₆H₅NH₃⁺] = - 0.15

[C₆H₅NH₂]/[C₆H₅NH₃⁺] = $10^{-0.15}$

[C₆H₅NH₂]/[C₆H₅NH₃⁺] = 0.708