Question

Recall that at \(25 \mathrm{rC}, K_{\mathrm{w}}=\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] \times\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-14}\). Calculate the hydronium ion concentration and the hydroxide ion concentration in "pure" water.

Short answer

The concentration of hydronium ions and hydroxide ions in pure water at 25 degrees Celsius is \(1.0 \times 10^{-7}\) mol/L for each.

Step-by-step solution

Understand the given information

The given information is the ionic product of water, \(K_w\), at 25 degrees Celsius which is \(1.0 \times 10^{-14}\). This value represents the product of the molar concentrations of hydrogen ions \([\mathrm{H}_{3}\mathrm{O}^{+}]\) and hydroxide ions \([\mathrm{OH}^{-}]\) in water at this temperature.

Apply the definition of \(K_w\)

In pure water, the concentration of hydronium ions is equal to the concentration of hydroxide ions because water auto-ionizes into equal amounts of these ions. Hence, we get \([\mathrm{H}_{3}\mathrm{O}^{+}]=[\mathrm{OH}^{-}]\), let's name it \(x\). Using this information, we can substitute into the \(K_w\) product: \(K_w = x \times x\).

Solve for x

Solving for \(x\), the equation becomes: \(x = \sqrt{K_w} = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7}\) mol/L.

Interpret the result

Given that both hydronium ion concentration and hydroxide ion concentration are equal (represented by x), they are both \(1.0 \times 10^{-7}\) mol/L in pure water at 25 degrees Celsius.

Key concepts

Hydronium Ion Concentration

Hydronium ion concentration is a term that refers to the number of hydronium ions, represented as \( \text{H}_3\text{O}^+ \), present in a solution. In water, \( \text{H}_3\text{O}^+ \) ions are formed when water molecules gain a hydrogen ion \( \text{(H}^+ \) ion) from another water molecule. Understanding the concentration of hydronium ions is crucial as it directly relates to the nature of the solution—whether it is acidic, basic, or neutral. For instance, in neutral water at 25 degrees Celsius, the concentration of hydronium ions is \( 1.0 \times 10^{-7} \) moles per liter. This value allows us to derive the pH of the solution, which in the case of pure water is 7, reflecting neutral pH.

Hydroxide Ion Concentration

Similarly, the hydroxide ion concentration describes the amount of hydroxide ions \( \text{(OH}^- \) ions) in a solution. They are the counterpart to hydronium ions and are produced during the same process of autoionization in which water molecules lose a hydrogen ion. The balance of these hydroxide ions in solution determines the alkalinity. At 25 degrees Celsius, pure water has a hydroxide ion concentration of \( 1.0 \times 10^{-7} \) moles per liter. This equilibrium between hydronium and hydroxide ions sustains the neutral pH of water.

Equilibrium Constant for Water

The equilibrium constant for water, denoted as \( K_w \), is a fundamental chemical constant that reflects the degree at which water undergoes autoionization. Autoionization is the process where water molecules spontaneously dissociate into hydronium and hydroxide ions. The constant \( K_w \) is the product of the molar concentrations of these two ions. At standard room temperature of 25 degrees Celsius, the value of \( K_w \) is \( 1.0 \times 10^{-14} \). This constant is essential in many areas of chemistry and is an underlying concept in discussions of acidity, basicity, pH, and pOH calculations. It serves as a reference point for determining the relative acidity or basicity of a solution.

Autoionization of Water

Water is a unique solvent because it can naturally undergo autoionization, also known as self-ionization or autoprotolysis. This is where pure water acts both as an acid and a base, with one water molecule donating a proton to another, resulting in the generation of equal amounts of hydronium \( \text{H}_3\text{O}^+ \) and hydroxide \( \text{OH}^- \) ions. This spontaneous process is vital for understanding the intrinsic property that leads to the establishment of the \( K_w \) value and is indicative of the dynamic nature of water molecules. The presence of these ions in pure water forms the basis of acidity and basicity in aqueous solutions.