Problem 43 - Chemistry: Principles and Reactions

Question

A lead storage battery needs sulfuric acid to function. The recommended minimum concentration of sulfuric acid for maximum effectivity is about \(4.8\) M. A 10.0-mL sample of battery acid requires \(66.52\) mL of \(1.325 M\) KOH for its complete neutralization. Does the concentration of battery acid satisfy the minimum requirement? (Note: Two \(\mathrm{H}^{+}\) ions are produced for every mole of \(\mathrm{H}_{2} \mathrm{SO}_{44}\).)

Step-by-Step Solution

Answer

Answer: Yes, the calculated sulfuric acid concentration in the battery is 5.8372 M, which is greater than the recommended minimum concentration of 4.8 M.

Step 1: Write the balanced chemical equation for the reaction

The reaction between sulfuric acid (H2SO4) and potassium hydroxide (KOH) produces potassium sulfate (K2SO4) and water (H2O). The balanced chemical equation of the reaction is: 2 KOH + H2SO4 -> K2SO4 + 2 H2O

Step 2: Convert the volume of KOH to moles

We need to convert the volume of KOH solution that was needed to neutralize the battery acid into the number of moles. We can do this using the relationship: moles of KOH = volume (liters) × concentration (M) moles of KOH = (66.52 mL × (1 L / 1000 mL)) × 1.325 M = 0.088109 L × 1.325 mol/L = 0.116743 mol

Step 3: Determine the moles of sulfuric acid using the stoichiometry of the reaction

From the balanced equation, we can see that the ratio between moles of KOH and moles of H2SO4 is 2:1. Therefore, we can use the stoichiometry of the reaction to determine the moles of sulfuric acid: moles of H2SO4 = (0.116743 mol KOH) × (1 mol H2SO4 / 2 mol KOH) = 0.058372 mol H2SO4

Step 4: Calculate the molar concentration of the sulfuric acid

To determine the molar concentration of H2SO4 in the battery acid, we need to divide the number of moles of H2SO4 by the volume of the sample in liters: H2SO4 concentration = moles / volume (L) = 0.058372 mol / (10.0 mL × (1 L / 1000 mL)) = 0.058372 mol / 0.01 L = 5.8372 M

Step 5: Compare the concentration to the minimum requirement

Finally, we need to compare the calculated concentration of sulfuric acid in the sample to the recommended minimum concentration (4.8 M). Since 5.8372 M > 4.8 M, the concentration of the battery acid satisfies the minimum requirement.

Key Concepts

Understanding Stoichiometry

Stoichiometry is like a recipe for chemists—it tells them how much of each substance is needed to react and what amounts of products will form. Imagine you are baking cookies, and the recipe states that you need one egg for every two cups of flour to make a certain number of cookies. Stoichiometry in chemistry is similar; it involves calculations based on the balanced chemical equations that tell us the proportions of reactants and products involved in a chemical reaction.

For example, in the exercise we have a balanced equation of the reaction between potassium hydroxide (KOH) and sulfuric acid (H₂SO₄). The stoichiometry of the reaction is given by the coefficients in the balanced equation: 2 moles of KOH react with 1 mole of H₂SO₄ to produce 1 mole of potassium sulfate (K₂SO₄) and 2 moles of water (H₂O). This tells us that for every 2 units of KOH, we need 1 unit of H₂SO₄.

Understanding and applying stoichiometry is crucial because it ensures that chemical reactions have the correct proportions of reactants, preventing waste and ensuring that the reaction proceeds as expected.

The Importance of Chemical Reaction Balancing

Balancing chemical reactions is a foundational skill in chemistry. This practice ensures that the law of conservation of mass is followed, meaning that atoms are neither created nor destroyed in a chemical reaction. It is based on the idea that the amount of atoms going into a reaction must be equal to the amount coming out.

In the provided exercise, we can observe the balanced reaction:

• 2 KOH + H₂SO₄ → K₂SO₄ + 2 H₂O

This equation indicates that two potassium ions from KOH combine with one sulfate ion from H₂SO₄ to form potassium sulfate, and the left-over hydroxide ions combine with the hydrogen ions to form water.

Each side has the same number of each type of atom: potassium (K), oxygens (O), sulfurs (S), and hydrogens (H). By balancing a reaction properly like this, we can accurately use it for stoichiometric calculations, which can then allow us to determine various facets of the chemical process, such as the concentration of a reactant in a solution.

Molarity Calculations Deciphered

Molarity is an expression of the concentration of a solution, describing how many moles of a solute are in one liter of solution. It is denoted by M (molar) and is a crucial concept when dealing with solutions in chemistry.

To perform molarity calculations, you need to know two things: the number of moles of the solute and the volume of the solution in liters. The formula to calculate molarity is: \[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \] In our problem, after finding the moles of KOH that reacted, we used the stoichiometry to find the moles of H₂SO₄ and then divided by the volume of the sulfuric acid sample (converted to liters) to get its concentration.

From the exercise, we found that 0.058372 moles of H₂SO₄ was in 10.0 mL of the solution. To find the molarity, we converted 10.0 mL to liters (0.01 L) and used the formula to get a final molarity of 5.8372 M for the sulfuric acid. This value exceeds the minimum concentration requirement for the battery acid (4.8 M), indicating the battery acid is sufficiently concentrated.