Deuterium oxide 1D2O, where D is deuterium, the hydrogen-2 isotope) has an ion-product constant, Kw, of 8.9 * 10-16 at 20 °C. Calculate 3D+4 and 3OD-4 for pure (neutral) D2O at this temperature.

Verified step by step guidance

1. Identify the ion-product constant of water (Kw) for D2O, which is given as 8.9 * 10^-16 at 20 °C.
2. Recognize that in pure water, the concentrations of the hydrogen-like ion (D+) and the hydroxide-like ion (OD-) are equal due to the neutrality of the water. Thus, [D+] = [OD-].
3. Set up the equation for the ion-product constant of D2O: Kw = [D+][OD-]. Since [D+] = [OD-], you can rewrite this as Kw = [D+]^2.
4. Solve for [D+] by taking the square root of Kw. This gives [D+] = sqrt(Kw).
5. Calculate the values of 3[D+]^4 and 3[OD-]^4 using the value obtained from the previous step. Since [D+] = [OD-], these values will be the same.

Key Concepts

Ion-Product Constant (Kw)

The ion-product constant, Kw, is the equilibrium constant for the self-ionization of water, defined as Kw = [H+][OH-]. In pure water, this value is typically 1.0 x 10^-14 at 25 °C, but it can vary with temperature and the solvent used. For deuterium oxide (D2O), the ion-product constant is different due to the presence of deuterium, which affects the dissociation of the solvent.

Concentration of Ions in Neutral Solutions

In a neutral solution, the concentrations of hydrogen ions [H+] and hydroxide ions [OH-] are equal. For deuterium oxide, the concentrations of deuterium ions (D+) and deuteroxide ions (OD-) will also be equal in a neutral solution. This means that if Kw is known, the concentration of each ion can be calculated using the equation [D+] = [OD-] = √Kw.

Temperature Effects on Ionization

Temperature influences the ionization of water and its isotopes. As temperature increases, the ion-product constant Kw typically increases, leading to higher concentrations of ions in solution. In the case of D2O at 20 °C, understanding how temperature affects Kw is crucial for accurately calculating the concentrations of D+ and OD- ions in neutral D2O.