Write a balanced chemical equation for the reaction of aqueous sodium carbonate with aqueous copper(II) chloride to form solid copper(II) carbonate and aqueous sodium chloride.

Understanding a chemical reaction involves recognizing how substances, known as reactants, transform into new substances, called products. For instance, when aqueous sodium carbonate (\textsf{Na}_2\textsf{CO}_3) reacts with aqueous copper(II) chloride (\textsf{CuCl}_2), the result is solid copper(II) carbonate (\textsf{CuCO}_3) and aqueous sodium chloride (\textsf{NaCl}).

\[\text{Na}_2\text{CO}_3 (aq) + \text{CuCl}_2 (aq) \rightarrow \text{CuCO}_3 (s) + 2\text{NaCl} (aq)\]
Each chemical species has a state designated by the symbols (s) for solids, (l) for liquids, (g) for gases, and (aq) for aqueous solutions. The state indicates how the substances interact in a chemical process, which is critical for predicting the outcome of the reaction and the properties of the products.

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It ensures that the number of atoms for each element is conserved from the reactants to the products. Balancing the chemical equation is an essential part of stoichiometry. The process involves assigning coefficients to the reactants and products.

For example, in the reaction between \textsf{Na}_2\textsf{CO}_3 and \textsf{CuCl}_2, coefficients ensure that there are equal numbers of each type of atom on both sides of the equation: \[ \text{Na}_2\text{CO}_3 (aq) + \text{CuCl}_2 (aq) \rightarrow \text{CuCO}_3 (s) + 2\text{NaCl} (aq) \]
By learning the correct techniques to balance equations, you not only follow the law of conservation of mass but also gain insights into the proportional relationships between reactants and products which are vital for calculations involving the yield and purity of a reaction.

Aqueous solutions are created when a substance, often a salt, acid, base, or sugar, is dissolved in water. The water is called the solvent, and the dissolved substance is the solute. In our equation, \(\text{Na}_2\textsf{CO}_3\) and \textsf{CuCl}_2 are in aqueous solutions, indicating that they are fully dissolved and uniformly distributed in water before reacting.

The term (aq) next to a chemical formula signifies an aqueous solution, which has implications for the reaction's dynamics. Ions in aqueous solutions are free to move and react, attributing to the overall reactivity. Understanding how solutes behave in solutions is important for areas such as stoichiometry, reaction rates, and equilibrium. The solubility of substances in water and the resulting ionic interactions are crucial elements that dictate the direction and the extent to which a chemical reaction will proceed.