Question

A solution has a pH of 4.20. Using the relationship between pH and pOH, what is the concentration of OH−?

Answer 1

Answer:

E. 1.6 x 10⁻¹⁰ M.

Explanation:

∵ pH = -log[H⁺] = 4.2

∴ [H⁺] = 6.31 x 10⁻⁵.

∵ [H⁺] [OH⁻] = 10⁻¹⁴.

∴ [OH⁻] = 10⁻¹⁴ / [H⁺] = 10⁻¹⁴ / 6.31 x 10⁻⁵ = 1.6 x 10⁻¹⁰ M.

Answer 2

Answer: E. 1.6ₓ10⁻¹⁰ M

Explanation:

The pH is a measure of acidity or alkalinity of a solution. The pH indicates the concentration of hydrogen ions present in certain solutions according to the following equation,

pH = $- log a_{H^{+} }$ where $a_{H^{+} } = y_{i} [H^{+}]$

where $a_{H^{+} }$ is the activity of hydrogen ions and $y_{i }$ is the activity coefficient. The activity is a measure of an "effective concentration" of a species. It arises because the molecules in a non-ideal gas or solution interact with each other.

The above equation is useful for solutions that do not have ideal behavior, that is, undiluted solutions. However, we can simplify the previous expression equalizing the activity with the concentration of hydrogen ions without major loss of accuracy, since in general we work with diluted solutions in practice.

Then, if pH = 4.20,

pH = - log [H⁺] → [H⁺] = $10^{-pH}$ → [H⁺] = $10^{-4.20}$

→ [H⁺] = 6.31ₓ10⁻⁵ M

Water self-ionization is the chemical reaction in which water molecules react to produce an hydrogen ion (H⁺) and a hydroxide ion (OH⁻),

H₂O (l) ⇄ H⁺(ac) + OH⁻(ac)

The ionization equilibrium of water is described by the ionic product of water and is symbolized by Kw. Around 25ºC  Kw = 1.0ₓ10⁻¹⁴, so

Kw = [H⁺] [OH⁻] → [OH⁻] = Kw / [H⁺]  → [OH⁻] = 1.0ₓ10⁻¹⁴ / 6.31ₓ10⁻⁵ M

→ [OH⁻] = 1.59ₓ10⁻¹⁰ M ≈ 1.6ₓ10⁻¹⁰ M

So, when a solution has a pH of 4.20 the concentration of OH− is 1.6ₓ10⁻¹⁰ M