Identify the type of reaction for each of the following. Then, predict products for the reaction, and balance the equation." reaction occurs, write "no reaction." $$\text{a}. \mathrm{HCl}(a q)+\mathrm{NaOH}(a q) \rightarrow\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$$ $$\text{b}. \mathrm{Mg}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{MgCl}_{2}(a q)+\mathrm{H}_{2}(g)$$ $$\text{c}. \mathrm{CdCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{CO}_{3}(a q) \rightarrow 2 \mathrm{NaCl}(a q)+\mathrm{CdCO}_{3}(s)$$

A double-replacement reaction, also known as a metathesis reaction, involves two ionic compounds that exchange partners to form two new compounds. This typically occurs in aqueous solutions and often produces a precipitate, gas, or water.

Illustrating this with the reaction listed in the exercise \( HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l) \), hydrochloric acid \( HCl \) and sodium hydroxide \( NaOH \) exchange ions to produce sodium chloride \( NaCl \) and water \( H_2O \).

Another example from the exercise \( CdCl_2(aq) + Na_2CO_3(aq) \rightarrow 2 NaCl(aq) + CdCO_3(s) \) shows the exchange occurring between cadmium chloride and sodium carbonate, which results in the formation of sodium chloride and cadmium carbonate, the latter of which precipitates out of the solution.

In a single-replacement reaction, also known as a displacement reaction, one element in a compound is replaced with another element. For these reactions to occur, the single element must be more reactive than the element it is intending to replace.

For example, in the exercise the reaction \( Mg(s) + 2 HCl(aq) \rightarrow MgCl_2(aq) + H_2(g) \), magnesium \( Mg \) displaces hydrogen \( H \) from hydrochloric acid \( HCl \), forming magnesium chloride \( MgCl_2 \) and hydrogen gas \( H_2 \).

This type of reaction is also characterized by a metal generally replacing a metal in a compound or a nonmetal replacing a nonmetal.

Balancing chemical equations is a fundamental aspect of chemistry that adheres to the law of conservation of mass, stating that matter cannot be created or destroyed in a chemical reaction. To balance an equation, the number of atoms of each element must be equal on both the reactant and product sides of the equation.

Consider the earlier reactions like \( HCl + NaOH \rightarrow NaCl + H_2O \) which is already balanced with equal numbers of each type of atom on both sides of the equation. Sometimes, balancing requires introducing coefficients, which are numbers placed in front of compounds in a reaction to ensure the same number of atoms for each element on both sides. For instance, if a reaction has the form \( A + BC \rightarrow AC + B \), and \( B \) is diatomic when free, you would balance it as \( 2A + 2BC \rightarrow 2AC + B_2 \) to ensure the conservation of \( A \) and \( B \) atoms.

Predicting the products of a chemical reaction involves understanding how different types of compounds interact. This requires knowledge of the reactivity series, solubility rules, and the ability to identify reaction types. The solubility rules help us predict if a precipitate will form in a double-replacement reaction, while the reactivity series can influence the outcome in single-replacement reactions.

For instance, in the reaction \( Mg + HCl \rightarrow ? \), knowing that magnesium is more reactive than hydrogen allows us to predict that it will replace hydrogen in acid, forming \( MgCl_2 \) and releasing \( H_2 \). In another exercise example \( CdCl_2 + Na_2CO_3 \rightarrow ? \), solubility rules inform us that carbonate compounds form precipitates with most metals, resulting in the solid \( CdCO_3 \) and soluble \( NaCl \) in the products.

Understanding these rules and applying them to reactant types will allow for accurate prediction of the products of a chemical reaction.