Question

The hydroxyl ion concentration of sodium hydroxide having a \(\mathrm{pH}\) value of 12 , at \(25^{\circ} \mathrm{C}\) is

Short answer

Answer: The hydroxyl ion concentration of the sodium hydroxide solution is 0.01 M.

Step-by-step solution

Find the pOH from the pH value

We know that the pH of the solution is 12. The relationship between pH and pOH is as follows: pH + pOH = 14 Given the pH, we can find the pOH: pOH = 14 - pH

Calculate the pOH value

Substitute the pH value to find the pOH: pOH = 14 - 12 pOH = 2 So, the pOH of the solution is 2.

Calculate the hydroxyl ion concentration

Now that we have the pOH, we can find the hydroxyl ion concentration using the formula: \(\mathrm{[OH^{-}]} = 10^{-\mathrm{pOH}}\) Substitute the calculated pOH value: \(\mathrm{[OH^{-}]} = 10^{-2}\)

Find the hydroxyl ion concentration

Evaluate the expression to find the hydroxyl ion concentration: \(\mathrm{[OH^{-}]} = 0.01\, \mathrm{M}\) So, the hydroxyl ion concentration of the sodium hydroxide solution with pH 12 at 25°C is 0.01 M.

Key concepts

pH calculation

Understanding the concept of pH is fundamental in acid-base chemistry. pH is a measure of the acidity or basicity of a solution. It is defined as the negative logarithm (base 10) of the hydrogen ion concentration. Specifically, the pH formula is given as:
\[\text{pH} = -\log_{10}[\text{H}^+]\]
In this context, \([\text{H}^+]\) represents the concentration of hydrogen ions in moles per liter (Molarity). The pH scale generally ranges from 0 to 14, where a pH less than 7 indicates acidity, 7 is neutral, and greater than 7 signifies basicity. For the problem in discussion, the pH value of 12 suggests a highly basic solution, which leads us to finding the hydroxyl ion concentration.

pOH

The concept of pOH is closely related to pH and is equally vital in understanding the properties of solutions. Like pH, pOH is also a logarithmic measure but of the hydroxyl ion (\(\text{OH}^-\)) concentration. The pOH of a solution can be calculated using the formula:
\[\text{pOH} = -\log_{10}[\text{OH}^-]\]
For a balanced aqueous solution at 25°C, the sum of the pH and pOH always equals 14, which is a key tenet of the pH-pOH relationship used to solve our original exercise. Knowing either the pH or pOH of a solution allows us to calculate the other, thus enabling us to determine the corresponding ionic concentrations.

acid-base chemistry

Acid-base chemistry is a cornerstone of chemical sciences that deals with the properties and reactions of acids and bases. Acids are substances that increase the concentration of hydrogen ions (\(\text{H}^+\)), while bases increase the concentration of hydroxyl ions (\(\text{OH}^-\)) when dissolved in water.
Acid-base reactions typically involve the transfer of a proton (\(\text{H}^+\)) from an acid to a base. In our example, sodium hydroxide (\(\text{NaOH}\)) is a strong base that completely dissociates in water to increase the \(\text{OH}^-\) concentration, thereby increasing the solution's pH. The exercise leverages this understanding to calculate the corresponding hydroxyl ion concentration from the given pH.

stoichiometry

Stoichiometry is the section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is based on the conservation of mass and the concept of moles, where reactions are described in terms of balanced equations with stoichiometric coefficients representing the proportional relationship between reactants and products.
In acid-base reactions, stoichiometry can be used to predict the outcome of reactions and calculate concentrations. In our exercise, the stoichiometry of the dissociation of sodium hydroxide (\(\text{NaOH}\)) into sodium (\(\text{Na}^+\)) and hydroxyl (\(\text{OH}^-\)) ions applies. Since \(\text{NaOH}\) is a strong base that dissociates completely, the molarity of \(\text{OH}^-\) ions in solution initially equals that of the original \(\text{NaOH}\).