Molarity is a measure of concentration in chemistry. This measurement, symbolized by ‘M’, provides the starting point for various calculations related to a solution’s properties. One such property is pOH, a scale used to express the basicity of a solution. The pOH value is directly related to the concentration of hydroxide ions (\([OH^-]\)) present in the aqueous mixture. The process of finding pOH from a known molarity involves first determining this ion concentration and then applying a specific mathematical transformation.
Determining Hydroxide Ion Concentration from Molarity
The initial step in this calculation requires converting the molarity of the dissolved compound into the actual concentration of the basic ion, which is the hydroxide ion (\([OH^-]\)). For a strong base, this conversion is straightforward because these compounds dissociate completely when dissolved in water. A strong base like sodium hydroxide (NaOH) dissolves to produce exactly one hydroxide ion for every molecule of the base. If a solution is 0.1 M in NaOH, the concentration of hydroxide ions, \([OH^-]\), is also \(0.1 M\).
The situation changes slightly when the strong base contains more than one hydroxide group per molecule. Consider calcium hydroxide, \(Ca(OH)_2\), which dissociates to release two hydroxide ions for every molecule of base. In this case, the concentration of the hydroxide ions is double the initial molarity of the \(Ca(OH)_2\). Therefore, a \(0.1 M\) solution of \(Ca(OH)_2\) would yield an \([OH^-]\) concentration of \(0.2 M\).
Calculating pOH Directly Using the Log Scale
Once the molar concentration of the hydroxide ions (\([OH^-]\)) has been accurately determined, the next step is to translate this value into the pOH scale. This conversion utilizes the mathematical function of the negative logarithm to the base ten. The formula for this calculation is expressed as \(pOH = -\log[OH^-]\). The reason for using the logarithmic scale is to convert the very wide range of possible ion concentrations into a more manageable set of numbers, typically ranging from 0 to 14.
The negative sign in the formula ensures that as the hydroxide ion concentration increases, the resulting pOH value decreases, which is consistent with the pOH scale where lower numbers indicate higher basicity. For example, if the calculated concentration of hydroxide ions is \(1.0 \times 10^{-4} M\), a calculator is used to find the base-ten logarithm of \(1.0 \times 10^{-4}\), which is \(-4\). Applying the negative sign from the formula, \(pOH = -(-4)\), results in a pOH of 4.0. This calculation directly provides the measure of basicity for the solution.
A change of one unit on the pOH scale represents a tenfold change in the actual concentration of hydroxide ions. Knowing this relationship allows for quick comparison of the relative basicity between different solutions.
Converting from pH if Hydrogen Ion Molarity is Provided
Sometimes, the initial molarity provided is for a strong acid, which releases hydrogen ions (\([H^+]\)) rather than hydroxide ions. To find the pOH in this scenario, an indirect path involving the related pH scale must be followed. A strong acid, such as hydrochloric acid (HCl), fully dissociates, meaning its molarity directly equals the hydrogen ion concentration, \([H^+]\). For example, a \(0.01 M\) HCl solution has an \([H^+]\) of \(0.01 M\).
The first calculation in this indirect route is to find the pH, which is defined by the negative logarithm of the hydrogen ion concentration, \(pH = -\log[H^+]\). Using the \(0.01 M\) example, the pH would be calculated as \(-\log(0.01)\), resulting in a pH of 2.0. This pH value quantifies the acidity of the solution, which is the reciprocal concept to basicity.
The final step relies on the established relationship between the two scales in aqueous solutions. Under standard conditions, the sum of pH and pOH always equals 14, expressed as \(pH + pOH = 14\). Subtracting the calculated pH value from 14 yields the pOH. In the example, \(pOH = 14 – 2.0\), which gives a final pOH of 12.0.