Question

Imagine that you dissolve sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s),\) in water. a. Write a balanced equation for this reversible process. b. In which direction does the process proceed if you place a tiny amount of sugar in a large pot i lled with water? c. In which direction does the process proceed if you allow the water to evaporate from a sugar solution?

Short answer

a. \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(s) \rightleftharpoons \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(aq)\). b. Forward direction (sugar dissolves). c. Backward direction (sugar precipitates).

Step-by-step solution

Understand Dissolution Process

Dissolving sucrose involves breaking the solid sugar into its molecules and distributing them in water. This can be represented by an equation where sucrose (\(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11 (s)}\) ) dissolves to form aqueous sucroseions \(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11 (aq)}\).

Write Balanced Equation

The dissolution process is written as \[\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(s) \rightleftharpoons \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11}(aq)\] This represents the equilibrium between soluble sucrose in water and solid sucrose.

Analyze Sugar Dissolution in Large Water Volume

When a small amount of sugar is added to a large pot of water, the system is far from saturation, and the sugar tends to completely dissolve. The process proceeds in the forward direction, forming more aqueous sucrose.

Analyze Evaporation of Water

When water evaporates from a sugar solution, the solution becomes more concentrated. As a result, the equilibrium shifts towards forming more solid sugar, proceeding in the backward direction.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a fascinating concept where a reversible reaction has both forward and backward processes occurring at the same rate. This doesn't mean the reaction stops. Instead, it reaches a steady state where the amount of reactants and products remains constant over time.
When you dissolve sucrose in water, the process eventually reaches a point where the dissolving of solid sucrose into aqueous sucrose matches the rate of aqueous sucrose depositing back into solid form. This balance constitutes chemical equilibrium: - Forward reaction: Sucrose dissolves in water - Backward reaction: Aqueous sucrose crystallizes back into solid Achieving equilibrium depends greatly on the conditions like temperature and concentration. At equilibrium, no net change is observed, even though the molecules are still in motion.

Balanced Chemical Equation

Writing a balanced chemical equation is essential in representing a chemical process accurately. In the case of sucrose dissolving, the reaction is reversible and can be represented as: - \[\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} (s) \rightleftharpoons \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} (aq)\]Here, we see the use of a double-headed arrow (\( \rightleftharpoons \)) indicating a reversible reaction. Both the reactants and the products (solid sucrose and aqueous sucrose) are balanced, meaning the stoichiometry is maintained. This balance is key because it reflects the conservation of mass where no molecules are lost or gained, just transformed.

Solubility

Solubility is a property that indicates how much of a substance can dissolve in a solvent at a given temperature. For sucrose, solubility is high, meaning a significant amount can dissolve in water. Understanding solubility helps predict the direction of a dissolution process: - If a small amount of sugar is added to a large volume of water (unsaturated solution), the solution can hold more sucrose, and the sucrose will continue to dissolve. - In a highly concentrated solution (saturated), any additional sugar may not dissolve unless conditions like temperature change.

Reversible Reactions

In reversible reactions, products can revert back to reactants under certain conditions. This feature is crucial for understanding processes like the dissolution of sucrose. - When water in a sugar solution eva porates, removing the solvent, the concentration of the solution increases, driving the reaction backwards to form solid sucrose. - Conversely, adding more solvent would shift the equilibrium toward producing more dissolved sucrose. The reversible nature highlights the responsiveness of chemical processes to changes in conditions, and understanding this can aid in controlling and optimizing various chemical reactions in practical applications.