Question

Write equations for the following reversible systems: (a) a closed container of solid and gaseous forms of \(\mathrm{I}_{2}\) (b) solid \(\mathrm{NaNO}_{3}\) in a saturated aqueous solution of \(\mathrm{NaNO}_{3}\)

Short answer

a) \[ \text{I}_2(s) \rightleftharpoons \text{I}_2(g) \] b) \[ \text{NaNO}_3(s) \rightleftharpoons \text{NaNO}_3(aq) \]

Step-by-step solution

Identify the Phases and Components for Part (a)

For part (a), there is a closed container containing solid and gaseous iodine. Denote the solid iodine as \(\text{I}_2(s)\) and the gaseous iodine as \(\text{I}_2(g)\).

Write the Reversible Equation for Part (a)

The reversible system in the closed container can be represented by the following equation: \[ \text{I}_2(s) \rightleftharpoons \text{I}_2(g) \]

Identify the Phases and Components for Part (b)

For part (b), there is solid sodium nitrate, \(\text{NaNO}_3(s)\), in a saturated aqueous solution. Denote the aqueous sodium nitrate as \(\text{NaNO}_3(aq)\).

Write the Reversible Equation for Part (b)

The reversible system in the saturated solution can be represented by the following equation: \[ \text{NaNO}_3(s) \rightleftharpoons \text{NaNO}_3(aq) \]

Key concepts

phase equilibrium

Phase equilibrium occurs when the physical states of a substance are in a balance without changing over time. In a closed system, different phases like solid, liquid, and gas can coexist in equilibrium.
For instance, in part (a), solid iodine \(\text{I}_2(s)\) and gaseous iodine \(\text{I}_2(g)\) are in equilibrium. The system reaches a point where the rate of sublimation (solid to gas) equals the rate of deposition (gas to solid).
Understanding phase equilibrium is essential for predicting the behavior of substances under different conditions. It helps in the study of changes in temperature, pressure, and concentration affecting the phases.
An everyday example of phase equilibrium is the melting of ice into water at 0° Celsius under standard atmospheric pressure. The ice and water are in equilibrium, but both can exist at this temperature.

solid-gas equilibrium

Solid-gas equilibrium happens when a solid directly transitions into a gas (sublimation) or a gas forms a solid (deposition) within a closed system.
Consider part (a) again with iodine. The solid form \(\text{I}_2(s)\) and gaseous form \(\text{I}_2(g)\) are in equilibrium. The reversible equation is \(\text{I}_2(s) \rightleftharpoons \text{I}_2(g)\).
The forward reaction (sublimation) involves iodine molecules gaining energy to transition into the gas phase. The backward reaction (deposition) involves iodine gas molecules losing energy and forming solid.
This equilibrium is crucial in processes like freeze-drying, where materials are dried by sublimation rather than the evaporation of the liquid form.

saturated solution

A saturated solution is one where the maximum amount of solute has dissolved in the solvent at a specific temperature. Beyond this point, any additional solute won't dissolve and will remain in solid form.
In part (b), the system contains solid sodium nitrate \(\text{NaNO}_3(s)\) and its aqueous solution \(\text{NaNO}_3(aq)\) in equilibrium. The reversible equation is \(\text{NaNO}_3(s) \rightleftharpoons \text{NaNO}_3(aq)\).
When additional \(\text{NaNO}_3\) is added to a saturated solution, it won't dissolve, and a dynamic equilibrium is established where the rate of solid \(\text{NaNO}_3\) dissolving equals the rate of \(\text{NaNO}_3\) crystallizing.
Understanding saturation helps in various fields like pharmacology, where the solubility of drugs can impact their effectiveness.

chemical equilibrium expressions

Chemical equilibrium is the state in a reversible reaction where the rates of the forward and reverse reactions are equal, leading to constant concentrations of the reactants and products over time.
For part (a): \(\text{I}_2(s) \rightleftharpoons \text{I}_2(g)\)
For part (b): \(\text{NaNO}_3(s) \rightleftharpoons \text{NaNO}_3(aq)\)
At equilibrium, the ratio of the concentration of products to reactants remains constant, and this ratio is called the equilibrium constant (K).
For gases, we use partial pressures in the equilibrium expression, and for solutions, we use molar concentrations. The expressions help predict the direction of reactions and concentrations of components at equilibrium.
Equilibrium expressions are critical in analytical chemistry and industrial processes, helping optimize reactions for desired outcomes.