Deuterium oxide, D2 O, ionizes like water. At 20 ^∘ C its Kw or ion product constant, analogous

step 1 Here in this problem, KW for D2O is given at 20 degrees centigrade. Here, D2O, ironizes like wat

Deuterium oxide, D2 O, ionizes like water. At 20 ^∘ C its Kw...

Deuterium oxide, $\mathrm{D}_{2} \mathrm{O}$, ionizes like water. At $20{ }^{\circ} \mathrm{C}$ its $K_{\mathrm{w}}$ or ion product constant, analogous to that of water, is $8.9 \times 10^{-16} \cdot$ Calculate $\left[\mathrm{D}^{+}\right]$ and $\left[\mathrm{OD}^{-}\right]$ in deuterium oxide at $20^{\circ} \mathrm{C}$. Calculate also the $\mathrm{pD}$ and the $\mathrm{pOD}$.

Key Concepts

Ion Product Constant (Kw)

The ion product constant (Kw) represents the equilibrium constant for the self-ionization (or autoprotolysis) of a solvent, typically water. It is defined as the product of the molar concentrations of the two ions formed (e.g., H+ and OH– in water, or D+ and OD– in deuterium oxide) at equilibrium. This constant is temperature-dependent and provides a quantitative measure of how much the solvent ionizes under a given set of conditions.

Autoprotolysis

Autoprotolysis is the process in which a solvent spontaneously reacts with itself to produce ions. For water, this results in the formation of hydronium (or hydrogen) ions and hydroxide ions, while in deuterium oxide, it produces deuterium ions and deuterated hydroxide ions. This concept is essential in understanding self-ionization equilibria and how they determine the pH or analogous pD scale of the solvent.

Equilibrium Concentration Calculations

At equilibrium in a pure solvent that undergoes autoprotolysis, the concentrations of the two types of ions are equal. The individual ionic concentration can be calculated by taking the square root of the ion product constant (Kw). This method of calculation is grounded in the stoichiometry of the self-ionization reaction and provides a basis for further quantitative analysis of the system.

Logarithmic pH Scale (and its Analogues such as pD and pOD)

The pH scale is a logarithmic measure of the hydrogen ion concentration in a solution, scaled as the negative logarithm to base ten. In similar fashion, for systems like deuterium oxide, corresponding scales such as pD (or pOD) are used to measure the acidity based on D+ or OD– concentrations. These scales enable comparison across orders of magnitude and simplify the representation of very small ion concentrations.

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