Problem 70 - Chemistry Matter and Change

Question

Car Battery Car batteries use lead, lead(IV) oxide, and a sulfuric acid solution to produce an electric current. The products of the reaction are lead(II) sulfate in solution and water. \begin{equation} \begin{array}{l}{\text { a. Write the balanced equation for the reaction. }} \\\ {\text { b. Determine the mass of lead(II) sulfate produced }} \\ {\text { when } 25.0 \text { g of lead reacts with an excess of lead(IV) }} \\\ {\text { oxide and sulfuric acid. }}\end{array} \end{equation}

Step-by-Step Solution

Answer

The balanced equation is \( \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O} \). 25.0 g of lead produces 36.6 g of PbSO_4.

Step 1: Writing the Skeleton Equation

The reaction involves lead (Pb), lead(IV) oxide (PbO_2), sulfuric acid (H_2SO_4), producing lead(II) sulfate (PbSO_4) and water (H_2O). The unbalanced chemical equation is \( \text{Pb} + \text{PbO}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{PbSO}_4 + \text{H}_2\text{O} \).

Step 2: Balancing the Chemical Equation

To balance the equation, ensure that the number of each type of atom is the same on both sides. The balanced equation is: \[ \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O} \].

Step 3: Finding the Molar Mass of Lead

Lead (Pb) has an atomic mass of 207.2 g/mol. Calculate the molar mass of PbSO_4 by adding the atomic masses: \( \text{Pb} = 207.2 \), \( \text{S} = 32.1 \), \( 4 \times \text{O} = 64.0 \). Thus, \( \text{PbSO}_4 = 303.3 \text{ g/mol} \).

Step 4: Calculating Moles of Lead

Given 25.0 g of lead, we convert this mass to moles: \( \text{moles of Pb} = \frac{25.0 \text{ g}}{207.2 \text{ g/mol}} = 0.1207 \text{ moles} \).

Step 5: Calculating Moles of Lead(II) Sulfate

From the balanced equation, 1 mole of Pb produces 1 mole of PbSO_4. Therefore, 0.1207 moles of Pb will produce 0.1207 moles of PbSO_4.

Step 6: Calculating Mass of Lead(II) Sulfate

Using the molar mass of PbSO_4, calculate the mass produced: \( \text{mass} = \text{moles} \times \text{molar mass} = 0.1207 \text{ moles} \times 303.3 \text{ g/mol} = 36.6 \text{ g} \).

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is an essential part of understanding chemical reactions. It ensures the law of conservation of mass is maintained. This law states that matter cannot be created or destroyed in a chemical reaction. Thus, when balancing chemical equations, the number of each type of atom on the reactant side must be equal to the number on the product side.

Here's how to balance the chemical equation for the given problem involving a lead-acid battery reaction:

• Begin with the skeleton equation, which is a simple unbalanced equation showing the reactants and products: \[ \text{Pb} + \text{PbO}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{PbSO}_4 + \text{H}_2\text{O} \]
• Adjust coefficients to balance each element sequentially, like lead, oxygen, hydrogen, and sulfur.
• The balanced equation becomes: \[ \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O} \]

Balancing equations involves trial and error but becomes easier with practice. It requires accounting for each type of atom and adjusting the numbers accordingly until both sides match.

Lead-Acid Battery

The lead-acid battery is a popular type of rechargeable battery. It has been widely used for several decades, particularly in automotive applications due to its robustness and relatively low cost. The chemical reaction inside the lead-acid battery involves lead, lead(IV) oxide, and sulfuric acid. These react to produce lead(II) sulfate and water while generating an electric current. The balanced chemical equation for this reaction is:

• \[ \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O} \]

This equation demonstrates how the combination of these substances facilitates the discharge process. During discharging, electrons flow through the external circuit, providing power. Proper maintenance and understanding of the chemistry involved in these batteries can lead to extending their lifetime and ensuring efficient energy output. Recognizing the reversible nature of this reaction is key to restoring the battery's charge by reversing the discharge processes.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that refers to the calculation of reactants and products in chemical reactions. It is based on the balanced chemical equation and allows chemists to predict the amounts of substances consumed and produced.

In the lead-acid battery reaction, stoichiometry comes into play in determining how much lead(II) sulfate is produced from a known amount of lead. Here's the step-by-step stoichiometric calculation used in the solution:

• The balanced equation tells us that 1 mole of lead produces 1 mole of lead(II) sulfate.
• Calculate moles of lead given its mass: \[ \text{moles of Pb} = \frac{25.0 \text{ g}}{207.2 \text{ g/mol}} = 0.1207 \text{ moles} \]
• From stoichiometry, the same amount of moles of \( \text{PbSO}_4 \) is produced:

This simple yet crucial step converts the quantities of chemicals in a reaction into a form that can be easily measured and applied in a laboratory or industrial setting.

Molar Mass Calculations

Understanding molar mass is essential when dealing with chemical equations and stoichiometry. Molar mass is the mass of one mole of a given substance and is typically expressed in grams per mole (g/mol). It allows conversion between the mass of a substance and the amount in moles, which is crucial for stoichiometric calculations.

Here's how to calculate the molar mass of substances involved in the lead-acid battery reaction:

• The molar mass of lead (Pb) is 207.2 g/mol, a fundamental parameter due to its frequent participation in reactions and alloys.
• For lead(II) sulfate (\( \text{PbSO}_4 \)), calculate by summing the atomic masses of its constituent elements:
  • Lead contributes 207.2 g/mol.
  • Sulfur adds 32.1 g/mol.
  • Oxygen contributes 16 g/mol per atom; as there are four, that's 64 g/mol in total.
• Thus, the total molar mass of \( \text{PbSO}_4 \) is: \[ 207.2 + 32.1 + 64.0 = 303.3 \text{ g/mol} \]

Calculating molar mass is crucial for determining how much product can be formed from a given amount of reactants, hence ensuring precise and efficient experiment planning and resource use.