Write a balanced chemical equation for the synthesis reaction of \(\mathrm{Cl}_{2}(g)\) with each metal. (a) \(\operatorname{Zn}(s)\) (b) \(G a(s)\) (c) \(\mathrm{Rb}(s)\) (d) \(\operatorname{Mg}(s)\)

A synthesis reaction is a type of chemical reaction in which two or more simple substances combine to form a more complex product. This is the basic form of a synthesis reaction:

\( A + B \rightarrow AB \)

In the context of our exercise, chlorine gas (\( Cl_2 \)) is reacting with metals such as zinc (\( Zn \)), gallium (\( Ga \)), rubidium (\( Rb \)), and magnesium (\( Mg \)) to form metal chlorides. These are all examples of synthesis reactions because we are combining a nonmetal with a metal to form a binary compound, specifically a metal chloride in this case.

Chemical valency refers to the combining capacity of an element, which dictates how many atoms of another element it can combine with. It's based on the number of electrons an atom can lose, gain, or share to become stable. For instance, chlorine has a valency of -1, meaning it tends to gain one electron to reach a stable electronic configuration. In our problem, understanding the valency of chlorine helps in predicting the formulas of the chlorides that will be formed. For example, zinc has a valency of +2, therefore it pairs with two chlorine atoms with a valency of -1 each to form zinc chloride (\( ZnCl_2 \)).

An unbalanced equation, also known as a skeletal chemical equation, does not show the same number of each type of atom on both sides of the reaction. This is important because the law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction. Therefore, we need to balance the equation to reflect this law. In step 2 of our solution, we wrote the initial unbalanced reactions for each metal reacting with chlorine. For gallium, the unbalanced reaction is \( Ga + Cl_2 \rightarrow GaCl_3 \), because gallium forms a trivalent chloride, reflecting that gallium has a +3 valency.

To balance an equation, we adjust the coefficients, which are the numbers placed before reactants and products in a chemical equation to show the relative amounts of each substance. These adjustments ensure that the same number of atoms of each element appears on both sides of the equation, satisfying the law of conservation of mass. In our problem, coefficient adjustments are particularly evident in reaction (b), where we balance gallium and chlorine to form gallium(III) chloride:

\( 2 Ga + 3 Cl_2 \rightarrow 2 GaCl_3 \)

Here, two atoms of gallium will react with three molecules of chlorine to produce two molecules of gallium(III) chloride, ensuring the number of gallium and chlorine atoms are balanced.