The hydroxide ion, represented by the chemical formula \(OH^-\), is a negatively charged particle consisting of one oxygen atom bonded to one hydrogen atom. It is a foundational component of aqueous chemistry, playing a central role in determining the basicity, or alkalinity, of a solution. The concentration of this ion, expressed in moles per liter (molarity, M) and denoted by \([OH^-]\), directly measures how alkaline a water-based substance is. Solutions with a higher concentration of hydroxide ions are classified as basic, possessing a pH greater than 7. Calculating this concentration is fundamental to understanding acid-base balance and chemical equilibrium.
Calculating Hydroxide Ion Concentration from pOH
The most straightforward method for finding the hydroxide ion concentration, \([OH^-]\), uses the \(pOH\) value, a scale designed to measure alkalinity. The \(pOH\) is defined as the negative logarithm (base 10) of the hydroxide ion concentration. To solve for the concentration, the inverse logarithmic relationship is used: \([OH^-] = 10^{-pOH}\). This calculation involves performing the antilogarithm on the negative \(pOH\) value. For instance, if a solution has a \(pOH\) of 2.4, the concentration is found by calculating \(10^{-2.4}\), which results in approximately \(0.0040\) M.
Calculating Hydroxide Ion Concentration from pH
Calculating the hydroxide ion concentration from the \(pH\) of a solution requires an intermediate step, as \(pH\) directly relates to the hydronium ion concentration. The first step is converting the given \(pH\) into the corresponding \(pOH\) value. This conversion relies on the established relationship that, in any aqueous solution at \(25^\circ C\), the sum of \(pH\) and \(pOH\) is always 14. The formula used is \(pOH = 14 – pH\). For example, if the \(pH\) is \(11.6\), the \(pOH\) is \(14.0 – 11.6\), yielding \(2.4\). This two-step approach is particularly useful because \(pH\) meters are the standard instrument for acid-base measurement. This \(pOH\) value is then used in the final step: the direct conversion to \([OH^-]\) using the formula \([OH^-] = 10^{-pOH}\).
Calculating Hydroxide Ion Concentration from Hydronium Ion Concentration
The concentrations of hydronium ions, \([H^+]\), and hydroxide ions, \([OH^-]\), are linked by the autoionization of water. This relationship is quantified by the ion product constant for water, \(K_w\), which is an equilibrium constant defined by the equation \(K_w = [H^+][OH^-]\). At the standard temperature of \(25^\circ C\), the value of \(K_w\) is fixed at \(1.0 \times 10^{-14}\). Since the product of the two concentrations is constant, knowing \([H^+]\) allows for the direct calculation of \([OH^-]\). The formula is \([OH^-] = K_w / [H^+]\). For example, if \([H^+]\) is \(2.0 \times 10^{-6}\) M, the calculation \((1.0 \times 10^{-14}) / (2.0 \times 10^{-6})\) M yields an \([OH^-]\) of \(5.0 \times 10^{-9}\) M.
Calculating Hydroxide Ion Concentration from Base Concentration
The hydroxide ion concentration can be determined directly from the concentration of the dissolved substance, primarily for strong bases. Strong bases are compounds that dissociate completely into their constituent ions when dissolved in water. For a strong base like sodium hydroxide (\(NaOH\)), which releases one hydroxide ion per molecule, the initial concentration of the base equals the final \([OH^-]\) concentration. For example, a \(0.1\) M solution of \(NaOH\) yields an \([OH^-]\) of \(0.1\) M. When dealing with bases that release more than one hydroxide ion, such as calcium hydroxide (\(Ca(OH)_2\)), the calculation must account for stoichiometry. Since these compounds release two hydroxide ions per formula unit, the initial base concentration must be multiplied by two to find the final \([OH^-]\) concentration.