Question

Balance each chemical equation. (a) \(\mathrm{N}_{2} \mathrm{H}_{4}(l) \longrightarrow \mathrm{NH}_{3}(g)+\mathrm{N}_{2}(g)\) (b) \(\mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{NH}_{3}(g)\) (c) \(\mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{C}(s) \longrightarrow \mathrm{Cu}(s)+\mathrm{CO}(g)\) (d) \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{HCl}(g)\)

Short answer

\( (a) 2N_2H_4 \rightarrow 3NH_3 + 2N_2 \), \( (b) N_2 + 3H_2 \rightarrow 2NH_3 \), \( (c) Cu_2O + C \rightarrow 2Cu + CO \), \( (d) H_2 + Cl_2 \rightarrow 2HCl \).

Step-by-step solution

Balancing Equation (a)

Count the number of atoms of each element on reactant and product sides. There are 2 nitrogen atoms and 4 hydrogen atoms on the reactant side, but 1 nitrogen molecule and 3 hydrogen atoms on the product side. To balance, place a coefficient of '3' in front of NH3 to get 3 nitrogen atoms and 6 hydrogens. Then, put a coefficient of '2' in front of N2, leading to 3 nitrogen molecules in total, matching the number on the products side. Finally, the hydrogens are balanced with a coefficient of '2' in front of NH4, giving 6 hydrogens on both sides. The balanced equation is: \( 2 \text{N}_{2} \text{H}_{4} \rightarrow 3 \text{NH}_{3} + 2 \text{N}_{2} \).

Balancing Equation (b)

Count the atoms. There are 2 hydrogen atoms and 1 nitrogen molecule on the reactant side and 1 nitrogen and 3 hydrogen atoms on the product side. Place a '3' coefficient in front of NH3 to balance nitrogen and hydrogen. Now, we have 2 nitrogen and 6 hydrogen atoms on both sides. Adjust the coefficients for H2 and N2 to 3 and 1, respectively, to get the balance right. The balanced equation is: \( N_2 + 3H_2 \rightarrow 2NH_3 \).

Balancing Equation (c)

Count the atoms. There are 2 copper atoms and 1 oxygen atom on the reactant side, and only 1 carbon atom. The products side needs balancing for copper and carbon oxide. Placing a '2' coefficient in front of Cu and a '1' coefficient in front of CO will balance the equation. The balanced equation is \( Cu_2O + C \rightarrow 2Cu + CO \).

Balancing Equation (d)

Identify the number of atoms present initially. There are 2 hydrogen atoms and 2 chlorine atoms in reactants, but only 1 hydrogen and 1 chlorine in the product. Place a '2' coefficient before HCl to balance the chlorines and hydrogens. The balanced equation is \( H_2 + Cl_2 \rightarrow 2HCl \).

Key concepts

Chemical Reaction

Understanding chemical reactions is essential when exploring the fundamentals of chemistry. A chemical reaction is a process where substances, known as reactants, transform into new substances called products. During a reaction, the chemical bonds in the reactants break, and new bonds form to create the products. It's like a dance where the reacting molecules rearrange themselves into new patterns. The various types of chemical reactions include synthesis, decomposition, single-replacement, double-replacement, and combustion; each kind involves different rearrangements and types of bonds forming and breaking.

For example, when hydrogen gas reacts with nitrogen gas to form ammonia, this is known as a synthesis reaction because multiple reactants combine to form a single product. The balanced form of this reaction, as seen in our exercise, shows the exact stoichiometry required for this transformation to occur, demonstrating the inherent precision of chemical processes.

Stoichiometry

Stoichiometry is a crucial part of chemistry that deals with the measurement of the quantities of reactants and products involved in a chemical reaction. Think of stoichiometry as the recipe for a chemical reaction; it tells you precisely how much of each substance you need and how much you'll produce. This concept is based on the balanced chemical equation, which respects the law of conservation of mass and ensures that the same number of atoms of each element are present on both sides of the equation.

In our exercises, we adjust the coefficients (the numbers in front of the chemical formulas) to balance the equations, essentially using stoichiometry to confirm that we have the correct proportions. Without a balanced equation, predicting the amounts of reactants needed and products formed would be impossible, making stoichiometry a fundamental tool for chemists in both analysis and experimental design.

Chemical Formulas

Chemical formulas represent the composition of substances using symbols and numbers. Each element is denoted by a unique symbol, derived from Latin or English names, and numbers indicate the quantity of each atom present in the smallest unit of the substance – the molecule (for covalent compounds) or the formula unit (for ionic compounds). A formula can tell us at a glance how many atoms of each element a molecule contains.

In the balancing exercises provided, chemical formulas serve as the blueprint for balancing chemical equations. They allow us to count atoms and to determine the necessary coefficients to achieve a balanced equation. Getting familiar with interpreting chemical formulas is a bedrock skill in chemistry because it sets the stage for understanding reactions, stoichiometry, and much more.

Law of Conservation of Mass

The law of conservation of mass is a fundamental principle in chemistry stating that mass cannot be created or destroyed in a chemical reaction. This law is why balancing chemical equations is so important; it ensures that the mass of the reactants equals the mass of the products. In other words, what you start with in terms of atoms is what you must end with – they can only rearrange themselves, not disappear.

When balancing chemical equations, like those provided in the exercise, we apply this law by making sure that the number of atoms for each element is the same on both the reactants' side and the products' side. This careful balancing acts as a confirmation that our reaction adheres to the unbreakable rule of conservation of mass, one of the key pillars of chemistry.