Problem 12 - Chemistry Matter and Change

Question

Assess Is the following equation balanced? If not, correct the coefficients to balance the equation. $$2 \mathrm{K}_{2} \mathrm{CrO}_{4}(\mathrm{aq})+\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow 2 \mathrm{KNO}_{3}(\mathrm{aq})+\mathrm{Pb} \mathrm{CrO}_{4}(\mathrm{s})$$

Step-by-Step Solution

Answer

The given equation is not balanced. The balanced equation should be: \(K_{2}CrO_{4}(aq) + Pb(NO_3)_{2}(aq) \rightarrow PbCrO_{4}(s) + 2KNO_{3}(aq)\).

Step 1: Identify the reactants and products

In the given equation, the reactants are 2K2CrO4 (aq) and Pb(NO3)2 (aq), while the products are 2KNO3 (aq) and PbCrO4 (s).

Step 2: Count the atoms of each element on both sides of the equation

Count the number of atoms for each element in the reactants and products: Reactants: - K (potassium): 2 × 2 = 4 atoms - Cr (chromium): 2 atoms - O (oxygen): 2 × 4 = 8 atoms - Pb (lead): 1 atom - N (nitrogen): 2 atoms Products: - K (potassium): 2 × 1 = 2 atoms - N (nitrogen): 2 × 1 = 2 atoms - O (oxygen): 2 × 3 + 4 = 10 atoms - Pb (lead): 1 atom - Cr (chromium): 1 atom

Step 3: Identify imbalances

Compare the number of atoms of each element in the reactants and products: - K (potassium): 4 atoms (reactants) ≠ 2 atoms (products) - Cr (chromium): 2 atoms (reactants) = 1 atom (products) - O (oxygen): 8 atoms (reactants) ≠ 10 atoms (products) - Pb (lead): 1 atom (reactants) = 1 atom (products) - N (nitrogen): 2 atoms (reactants) = 2 atoms (products) There are imbalances in potassium, chromium, and oxygen atoms.

Step 4: Balance the equation

Adjust the coefficients to balance the atoms of each element: $$K_{2}CrO_{4}(aq) + Pb(NO_3)_{2}(aq) \rightarrow PbCrO_{4}(s) + 2KNO_{3}(aq)$$ Now, let's count the atoms again: Reactants: - K (potassium): 2 atoms - Cr (chromium): 1 atom - O (oxygen): 4 atoms - Pb (lead): 1 atom - N (nitrogen): 2 atoms Products: - K (potassium): 2 atoms - N (nitrogen): 2 atoms - O (oxygen): 4 + 4 = 8 atoms - Pb (lead): 1 atom - Cr (chromium): 1 atom Now, all the atoms are balanced on both sides of the equation. The balanced equation is: $$K_{2}CrO_{4}(aq) + Pb(NO_3)_{2}(aq) \rightarrow PbCrO_{4}(s) + 2KNO_{3}(aq)$$

Key Concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. It's like the mathematical backbone of chemistry, helping us understand how much of each substance is involved. At its core, stoichiometry relies on the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction.

To balance a chemical equation using stoichiometry, follow these steps:

• Write down the number of atoms of each element present in the reactants and products.
• Adjust the coefficients (the numbers in front of the molecules) to ensure the number of atoms of each element is the same on both sides of the equation.
• Use the smallest whole numbers for coefficients to finalize the balanced equation.

By following these steps, you ensure that the reaction adheres to the law of conservation of mass. This means you'll have the same amount of each element before and after the reaction occurs, which is critical for accurate chemical calculations and predictions.

Chemical Reaction

A chemical reaction is a process where reactants are transformed into products. During this transformation, bonds between atoms in the reactants break and new bonds form to create the products. Understanding chemical reactions is essential for predicting how substances will behave when mixed.

Every chemical reaction involves distinct changes, like energy change, color change, formation of a precipitate, or gas production. In the given exercise, the reaction is:\[2 \text{K}_2\text{CrO}_4(\text{aq}) + \text{Pb(NO}_3\text{)}_2(\text{aq}) \rightarrow \text{2KNO}_3(\text{aq}) + \text{PbCrO}_4(\text{s})\]This represents a double displacement reaction where the ions in two compounds exchange partners, resulting in the formation of a new product. Observing the states of matter (like \(\text{(aq)}\) for aqueous solution and \(\text{(s)}\) for solid) can also provide insight into the nature and conditions of the reaction. Identifying these cues helps chemists predict product formation and reaction conditions.

Reactants and Products

Reactants are substances that start a chemical reaction. Products are the substances formed as a result of the reaction. In any given chemical equation, reactants are shown on the left, while products are on the right.

Let's look at the example equation:\[2 \text{K}_2\text{CrO}_4(\text{aq}) + \text{Pb(NO}_3\text{)}_2(\text{aq}) \rightarrow \text{2KNO}_3(\text{aq}) + \text{PbCrO}_4(\text{s})\]

• Reactants: \(2 \text{K}_2\text{CrO}_4\) and \(\text{Pb(NO}_3\text{)}_2\)
• Products: \(2\text{KNO}_3\) and \(\text{PbCrO}_4\)

Understanding the difference between reactants and products is crucial for balancing equations. You should always ensure the number of atoms for each element is the same on both sides of the equation. This reflects the conservation of mass, which is a basic principle of chemistry. In this exercise, correctly identifying and balancing reactants and products ensures an accurate representation of the reaction underway.