Problem 81 - General Chemistry: Principles and Modern Applications

Question

A sample of battery acid is to be analyzed for its sulfuric acid content. A \(1.00 \mathrm{mL}\) sample weighs \(1.239 \mathrm{g}\). This \(1.00 \mathrm{mL}\) sample is diluted to \(250.0 \mathrm{mL}\), and \(10.00 \mathrm{mL}\) of this diluted acid requires \(32.44 \mathrm{mL}\) of \(0.00498 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) for its titration. What is the mass percent of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in the battery acid? (Assume that complete ionization and neutralization of the \(\mathrm{H}_{2} \mathrm{SO}_{4}\) occurs.)

Step-by-Step Solution

Answer

The mass percent of \(H_2SO_4\) in the battery acid is 0.1282%.

Step 1: Calculate moles of \(Ba(OH)_2\)

First, calculate moles of \(Ba(OH)_2\) used in the reaction. The number of moles (n) can be calculated using the molarity (M) and volume (V), in liter, as n=M*V. Given, M =0.00498M and V=32.44mL =0.03244L, so n=0.00498 * 0.03244 = 0.000162 moles.

Step 2: Calculate moles of \(H_2SO_4\)

Second, we calculate moles of \(H_2SO_4\). According to balanced chemical reaction - \(H_2SO_4 + Ba(OH)_2 -> BaSO_4 + 2H_2O\), 1 mole of \(H_2SO_4\) reacts with 1 mole of \(Ba(OH)_2\), so moles of \(H_2SO_4\) = moles of \(Ba(OH)_2\) = 0.000162 moles. This is moles of \(H_2SO_4\) in 10mL of diluted solution.

Step 3: Calculate moles of \(H_2SO_4\) in 1mL diluted solution

Now, we calculate moles of \(H_2SO_4\) present in 1mL of the diluted solution. If 10mL diluted solution contains 0.000162 moles of \(H_2SO_4\), then 1mL will contain = 0.0000162 moles of \(H_2SO_4\).

Step 4: Calculate mass of \(H_2SO_4\)

The molar mass of \(H_2SO_4\) is 98 g/mol, so the mass of \(H_2SO_4\) in 1mL sample = moles of \(H_2SO_4\) in 1mL * molar mass of \(H_2SO_4\)= 0.0000162 * 98 = 0.0015876 g. This is the mass of \(H_2SO_4\) in 1mL = 1.239g sample of battery acid.

Step 5: Calculate mass percent of \(H_2SO_4\)

Finally, calculate the mass percent of \(H_2SO_4\) in the sample as (mass of \(H_2SO_4\) / mass of sample) * 100 = (0.0015876 / 1.239) * 100 = 0.1282 %. So, the mass percent of \(H_2SO_4\) in the battery acid is 0.1282%.

Key Concepts

Sulfuric Acid Analysis

Analyzing sulfuric acid in a solution is a key activity in chemistry, especially when dealing with substances like battery acid. The analysis helps determine how much sulfuric acid is present, providing vital information on the concentration which is crucial for both their effectiveness and safety. This process often involves titration, where a solution of known concentration (titrant) is added to a sample until the reaction reaches completion. In the case of sulfuric acid, it is commonly tested against a base such as barium hydroxide, resulting in a reaction that forms a salt and water. This process allows for the precise calculation of the sulfuric acid concentration in the sample.
Understanding sulfuric acid analysis requires a grasp of chemical reactions and how substances react with each other. For example, the titration process uses the reaction of sulfuric acid ( H_{2}SO_{4} ) and barium hydroxide ( Ba(OH)_{2} ) to produce barium sulfate ( BaSO_{4} ) and water ( H_{2}O ). It relies on the stoichiometric relationship between the acid and the base to determine the amount of acid present. This information is used to calculate concentrations and the overall effectiveness of the solution.

Molarity and Dilution

Molarity, a measure of the concentration of a solution, is expressed in moles of solute per liter of solution. In the context of acid-base titration, molarity is essential for determining how much reactant is present in a given volume. This measure helps chemists understand the potency of the solution they are analyzing. For example, the barium hydroxide ( Ba(OH)_{2} ) used in the titration has a known molarity which enables the calculation of how many reactants will interact with the sulfuric acid.
Dilution is a process of reducing the concentration of a solute in a solution, usually by adding more solvent. In the battery acid exercise, the initial 1.00 mL sample is diluted to 250.0 mL. This step is critical in ensuring that the solution is at an optimal concentration for a successful titration. It balances the solution to a level where it can react appropriately with the titrant, and it also ensures that measurements remain manageable and precise. The diluted solution subsequently allows us to deduce the concentration of sulfuric acid accurately, leading to further calculations such as the mass percent in the original solution.

Chemical Stoichiometry

Chemical stoichiometry is the science of calculating the relative quantities of reactants and products in chemical reactions. It is a foundational pillar in chemistry that allows us to understand how different compounds react quantitatively. In the titration process, stoichiometry is applied when evaluating the reaction between sulfuric acid ( H_{2}SO_{4} ) and barium hydroxide ( Ba(OH)_{2} ). This reaction follows a one-to-one stoichiometric ratio, meaning one mole of sulfuric acid reacts with one mole of barium hydroxide.
Understanding stoichiometry is crucial as it provides the basis for converting moles of one substance to moles of another. For instance, when you know the amount of Ba(OH)_{2} in the solution and use it to calculate the corresponding amount of H_{2}SO_{4} that reacted. This principle allows for precise determinations needed to calculate the mass percentage of sulfuric acid in a sample. Mastering stoichiometry enables scientists and students alike to predict how a chemical system will respond under different conditions, making it an indispensable tool in chemistry.