Problem 120 - Chemistry An Atoms First Approach

Question

When organic compounds containing sulfur are burned, sulfur dioxide is produced. The amount of \(\mathrm{SO}_{2}\) formed can be determined by the reaction with hydrogen peroxide: $$ \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q) $$ The resulting sulfuric acid is then titrated with a standard NaOH solution. A 1.302 -g sample of coal is burned and the \(\mathrm{SO}_{2}\) is collected in a solution of hydrogen peroxide. It took \(28.44 \mathrm{mL}\) of a \(0.1000-M \mathrm{NaOH}\) solution to titrate the resulting sulfuric acid. Calculate the mass percent of sulfur in the coal sample. Sulfuric acid has two acidic hydrogens.

Step-by-Step Solution

Answer

The mass percent of sulfur in the coal sample is 3.50%.

Step 1: Write the balanced equation for the neutralization reaction

The balanced equation for the neutralization reaction between sulfuric acid (H2SO4) and sodium hydroxide (NaOH) is: \[2 \mathrm{NaOH}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)\]

Step 2: Calculate the number of moles of NaOH

To calculate the number of moles of NaOH used in the reaction, we will use the formula: Moles of NaOH = Molarity × Volume in liters The given molarity is 0.1000 M, and the volume is 28.44 mL, which can be converted to liters by dividing by 1000: Volume in liters = 28.44 mL / 1000 = 0.02844 L Now, we can calculate the number of moles of NaOH: Moles of NaOH = 0.1000 M × 0.02844 L = 0.002844 moles

Step 3: Determine the number of moles of H2SO4

Using the stoichiometry of the balanced equation from Step 1, we can determine that the mole ratio of H2SO4 to NaOH is 1:2. So, the number of moles of H2SO4 is half the number of moles of NaOH: Moles of H2SO4 = 0.002844 moles of NaOH × (1 mole of H2SO4 / 2 moles of NaOH) = 0.001422 moles

Step 4: Calculate the number of moles of sulfur

From the chemical formula of H2SO4, we know that there is one sulfur atom in each molecule of H2SO4. Therefore, the number of moles of sulfur is equal to the number of moles of H2SO4: Moles of sulfur = 0.001422 moles of H2SO4

Step 5: Convert the moles of sulfur to grams of sulfur

Using the molar mass of sulfur (32.06 g/mol), we can convert the moles of sulfur to grams: Grams of sulfur = 0.001422 moles × 32.06 g/mol = 0.0456 g

Step 6: Calculate the mass percent of sulfur in the coal sample

Finally, we can calculate the mass percent of sulfur in the coal sample using the formula: Mass percent = (Mass of sulfur / Mass of coal sample) × 100% The mass of the coal sample is given as 1.302 g. So, the mass percent of sulfur is: Mass percent = (0.0456 g / 1.302 g) × 100% = 3.50% The mass percent of sulfur in the coal sample is 3.50%.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the calculation of reactants and products in chemical reactions. It is a quantitative relationship between the amounts of substances involved in a reaction based on the balanced chemical equation.

For the given exercise, stoichiometry helps us understand the conversion of sulfur dioxide produced when burning coal into sulfuric acid, and subsequently how it reacts with sodium hydroxide during titration. The balanced equation provided in the step-by-step solution represents the stoichiometric relationship between the reactants and products.

Importance in Calculations

In calculations, stoichiometry is used to determine the mole ratio of the reactants and products. This is crucial in figuring out how much of one reactant is needed to completely react with another. In our case, it's imperative to know that two moles of NaOH react with one mole of H2SO4. Without this information, we wouldn't be able to accurately compute the mass percent of sulfur in the coal sample.

Titration

Titration is an analytical method used to determine the concentration of an unknown solution by reacting it with a solution of known concentration, called the titrant. During a titration, the point at which the reaction is complete is often indicated by a color change due to an indicator or by reaching a certain electrical measurement in the case of a potentiometric titration.

In the context of the problem, titration is used to find out how much sulfuric acid is produced by the reaction of sulfur dioxide with hydrogen peroxide. By knowing the concentration of the sodium hydroxide solution and the volume needed to reach the endpoint, we can calculate the amount of sulfuric acid and, subsequently, sulfur present in the sample.

Endpoint and Equivalence Point

An important concept in titration is understanding the difference between the endpoint and the equivalence point. The equivalence point is when the number of moles of acid equals the number of moles of base in a neutralization reaction. The endpoint is the point at which the indicator changes color, which ideally happens at the equivalence point.

Sulfur Dioxide Pollution

Sulfur dioxide (SO2) is a significant air pollutant that results from the burning of sulfur-containing compounds, such as coal or oil. It can have severe effects on human health, the environment, and the climate. Health risks include respiratory problems and aggravation of cardiovascular diseases, while environmentally, SO2 can lead to acid rain, which damages ecosystems and buildings.

In the given exercise, the environmental impact of burning coal is implied in the need to calculate the amount of sulfur dioxide produced. By assessing the mass percent of sulfur in coal, one can gauge the potential for SO2 pollution. Reducing the sulfur content in fuels is one way to minimize such pollution.

Environmental Standards and Regulations

Many regions have strict standards and regulations to control sulfur emissions. The determination of sulfur content in fuel sources, like coal, is critical for complying with these standards and for developing strategies to reduce SO2 emissions, which are pivotal for environmental protection and public health.

Molarity

Molarity refers to the concentration of a solution expressed as the number of moles of solute per liter of solution. It is a fundamental concept in chemistry used not only in stoichiometry and titration but also across a wide range of chemical calculations and reactions.

In our exercise, molarity is the unit of concentration for the sodium hydroxide solution used in the titration process. The volume of the NaOH solution, along with its molarity, lets us calculate the number of moles of NaOH, which is then used to derive the amount of sulfuric acid and thereby the mass percent of sulfur in the coal. Understanding molarity is key to performing accurate chemical reactions and is essential for preparing solutions in labs and industry.

Calculating Molarity

For any solution, molarity can be calculated using the formula: \( \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \). Knowing how to compute molarity is fundamental in quantitative chemistry and aids in ensuring reactions proceed as intended.