Heavy water, symbolized D2O 1D = 2H2 finds use as a neutron moderator in nuclear reactors. In a mixture with ordinary water, exchange of isotopes occurs according to the following equation: H2O + D2O ∆ 2 HDO Kc = 3.86 at 298 K When 1.00 mol of H2O is combined with 1.00 mol of D2O, what are the equilibrium amounts of H2O, D2O, and HDO (in moles) at 298 K? Assume the density of the mixture is constant at 1.05 g>cm3.

Verified step by step guidance

1. Identify the initial concentrations of the reactants: 1.00 mol of H2O and 1.00 mol of D2O.
2. Set up an ICE (Initial, Change, Equilibrium) table to track the changes in concentrations of H2O, D2O, and HDO as the reaction reaches equilibrium.
3. Define the change in concentration for the reaction: let x be the amount of H2O and D2O that reacts to form HDO. Therefore, the change for H2O and D2O is -x, and for HDO, it is +2x.
4. Write the equilibrium concentrations in terms of x: [H2O] = 1.00 - x, [D2O] = 1.00 - x, [HDO] = 2x.
5. Use the equilibrium constant expression Kc = [HDO]^2 / ([H2O][D2O]) = 3.86 to solve for x, and then calculate the equilibrium concentrations of H2O, D2O, and HDO.

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this context, the equilibrium constant (Kc) quantifies the ratio of product concentrations to reactant concentrations at equilibrium. Understanding this concept is crucial for calculating the amounts of substances present at equilibrium in the given reaction.

Isotope Exchange Reactions

Isotope exchange reactions involve the swapping of isotopes between molecules, which can affect the physical and chemical properties of the substances involved. In the provided reaction, H2O and D2O exchange hydrogen and deuterium atoms to form HDO. Recognizing how isotopes interact and the implications for reaction dynamics is essential for solving the equilibrium problem presented.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on balanced equations. It allows for the determination of the amounts of substances consumed and produced at equilibrium. In this scenario, applying stoichiometric principles to the initial amounts of H2O and D2O will help in finding the equilibrium concentrations of all species involved in the reaction.