Complete the following statements for the reaction \(6 \mathrm{Li}(\mathrm{s})+\mathrm{N}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Li}_{3} \mathrm{~N}(\mathrm{~s})\). The rate of consumption of \(\mathrm{N}_{2}\) is _______ times the rate of formation of \(\mathrm{Li}_{3} \mathrm{~N}\). (b) The rate of formation of \(\mathrm{Li}_{3} \mathrm{~N}\) is _____times the rate of consumption of Li. (c) The rate of consumption of \(\mathrm{N}_{2}\) is ________ times the rate of consumption of Li.

Understanding the speed at which chemical reactions occur is crucial in various fields including manufacturing, environmental science, and biology. The rate of a chemical reaction indicates how quickly reactants are consumed and products are formed over time. For example, in the reaction \[6\mathrm{Li}(\mathrm{s}) + \mathrm{N}_{2}(\mathrm{g}) \rightarrow 2\mathrm{Li}_{3}\mathrm{N}(\mathrm{s})\],we analyze the reaction rates in terms of the disappearance of reactants (\(\mathrm{N}_{2}\)and \(\mathrm{Li}\)) and the appearance of the product (\(\mathrm{Li}_{3}\mathrm{N}\)).

For a balanced reaction, the rates are inversely proportional to the stoichiometric coefficients—this is known as the rate law. Thus, if \(\mathrm{N}_{2}\) is consumed at a certain rate, \(\mathrm{Li}_{3}\mathrm{N}\) will form at twice that rate because two moles of \(\mathrm{Li}_{3}\mathrm{N}\) form for each mole of \(\mathrm{N}_{2}\) consumed.

Understanding this relationship can help predict how changes in conditions (like temperature or catalysts) will affect the rate, allowing us to control and optimize reactions in industrial processes or even prevent unwanted reactions in the environment.

Balancing a chemical equation is akin to balancing a scale—it ensures that the mass and the number of atoms are conserved in a chemical reaction. When we balance an equation, such as \[6\mathrm{Li}(\mathrm{s}) + \mathrm{N}_{2}(\mathrm{g}) \rightarrow 2\mathrm{Li}_{3}\mathrm{N}(\mathrm{s})\],we are confirming that there are equal numbers of each type of atom on both sides of the reaction.

This balance is fundamental, as it reflects the law of conservation of mass. It also provides the basis for calculations in stoichiometry, as the coefficients (the numbers in front of the chemical formulas) represent the ratios of moles of each reactant and product involved in the reaction. As a result, the balanced equation guides us in predicting the quantities of reactants needed and products formed.

Precise balancing is essential for both laboratory work and industrial chemical production, ensuring that reactions occur completely and resources are not wasted.

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world we live in. A mole is Avogadro’s number (\(6.022 \times 10^{23}\)) of particles, which can be atoms, molecules, ions, or electrons. For instance, when the chemical equation \[6\mathrm{Li}(\mathrm{s}) + \mathrm{N}_{2}(\mathrm{g}) \rightarrow 2\mathrm{Li}_{3}\mathrm{N}(\mathrm{s})\]states that 6 moles of lithium react with 1 mole of nitrogen gas, it tells us that \(6 \times 6.022 \times 10^{23}\) atoms of lithium react with \(6.022 \times 10^{23}\) molecules of nitrogen gas.

The concept helps us quantify chemical reactions, as these mole ratios are used to calculate the mass of reactants and products. By understanding the mole, students can better grasp how macroscopic quantities of substances relate to the underlying chemical equations and reactions.