Balance the following equations: (a) CF₄(l) + Br₂(g) → CBr₄(l) + F₂(g) (b) Cu(s) + HNO₃(aq) → Cu(NO₃)₂(aq) + NO2(g) + H₂O(l)

Verified step by step guidance

1. Step 1: Identify the reactants and the products in the chemical equation. The reactants are Cu(s) and HNO3(aq), and the products are Cu(NO3)2(aq), NO2(g), and H2O(l).
2. Step 2: Balance the equation for the atoms that appear in only one reactant and one product first. In this case, start with copper (Cu). There is one Cu atom on the reactant side and one Cu atom on the product side, so Cu is already balanced.
3. Step 3: Next, balance the nitrogen (N) atoms. There is one N atom in HNO3 on the reactant side and there are 2 N atoms on the product side (one in Cu(NO3)2 and one in NO2). Therefore, you need to multiply HNO3 by 2 on the reactant side.
4. Step 4: Now, balance the hydrogen (H) and oxygen (O) atoms. There are 2 H atoms in 2HNO3 on the reactant side and there are 2 H atoms in H2O on the product side, so H is balanced. There are 6 O atoms in 2HNO3 on the reactant side and there are 6 O atoms on the product side (4 in Cu(NO3)2, one in NO2, and one in H2O), so O is also balanced.
5. Step 5: Check your work. The balanced equation should have the same number of each type of atom on the reactant side as on the product side. In this case, the balanced equation is Cu(s) + 2HNO3(aq) → Cu(NO3)2(aq) + NO2(g) + H2O(l).

Key Concepts

Balancing Chemical Equations

Balancing chemical equations involves ensuring that the number of atoms for each element is the same on both sides of the equation. This is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Coefficients are adjusted in front of compounds to achieve balance, while subscripts indicate the number of atoms in a molecule.

Oxidation-Reduction Reactions

Oxidation-reduction (redox) reactions involve the transfer of electrons between substances, leading to changes in oxidation states. In these reactions, one species is oxidized (loses electrons) while another is reduced (gains electrons). Identifying the oxidation states of elements in the reactants and products is crucial for balancing redox equations.

State Symbols in Chemical Reactions

State symbols indicate the physical state of reactants and products in a chemical equation. Common symbols include (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous solutions. Understanding these symbols helps in visualizing the reaction conditions and is essential for accurately balancing equations, especially when dealing with solutions and gases.