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: $$ \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{SO}_{2}(g) h \mathrm{H}_{2} \mathrm{SO}_{4}(a q) $$ The resulting sulfuric acid is then titrated with a standard \(\mathrm{NaOH}\) 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 \(0.1000 \mathrm{M} \mathrm{NaOH}\) solut ion to titrate the resulting sulfuric acid. Calculate the mass percent of sulfur in the coal sample. Sulfuric acid has two acidic hydrogens.

Short answer

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

Step-by-step solution

Write the balanced reaction equations

First, let's write the balanced reaction equations for the formation of H2SO4 from SO2 with H2O2 and the titration of H2SO4 with NaOH. \(H_2O_2(aq) + SO_2(g) \rightarrow H_2SO_4 (aq)\) (1) \(2NaOH(aq) + H_2SO_4 (aq) \rightarrow Na_2SO_4 (aq) + 2H_2O (l)\) (2)

Determine the moles of NaOH used in the titration

The volume of NaOH solution used in the titration is 28.44 mL, and its concentration is 0.1000 M. We use this information to find the number of moles of NaOH: Moles of NaOH = concentration × volume Moles of NaOH = 0.1000 mol/L × 28.44 mL × (1 L/1000 mL) = 0.002844 mol NaOH

Determine the moles of H2SO4, SO2, and S

From the balanced equation (2), we can see that there is a 2:1 ratio between NaOH and H2SO4. Therefore, we can find the moles of H2SO4: Moles of H₂SO₄ = (0.002844 mol NaOH) × (1 mol H₂SO₄ / 2 mol NaOH) = 0.001422 mol H₂SO₄ Since there is a 1:1 ratio between H2SO4 and SO2 (equation 1), the moles of SO2 produced is equal to the moles of H2SO4: Moles of SO₂ = 0.001422 mol Finally, there is a 1:1 ratio between SO2 and S in the molecule. Therefore, the moles of S are also 0.001422 mol in the coal sample.

Calculate the mass of sulfur in the coal sample

Now we can calculate the mass of sulfur in the coal sample using the molar mass of sulfur (32.06 g/mol): Mass of S = moles of S × molar mass of S Mass of S = 0.001422 mol × 32.06 g/mol = 0.0456 g

Calculate the mass percent of sulfur in the coal sample

Finally, we will calculate the mass percent of sulfur in the coal sample using the given coal sample mass (1.302 g) and the mass of sulfur (0.0456 g) calculated in the previous step: Mass percent of S = (mass of S/mass of coal sample) × 100 Mass percent of S = (0.0456 g / 1.302 g) × 100 = 3.50 % The mass percent of sulfur in the coal sample is approximately 3.50%.

Key concepts

Titration

Titration is a technique in chemistry used to determine the concentration of an unknown solution. In this method, a solution of known concentration, called the titrant, is gradually added to a solution of the substance being analyzed, known as the analyte, until the reaction between the two substances is complete. The point at which the reaction is just complete is known as the endpoint, often determined by a color change.

• Titration allows chemists to quantify the concentration of an acid or base in a solution.
• It requires the use of a balanced chemical equation to understand the stoichiometry involved in the reaction.

In the given exercise, sulfuric acid formed during the reaction is titrated with sodium hydroxide (NaOH). The concentration of the NaOH solution and the volume used provides the necessary information to calculate the amount of sulfur in the coal sample.

Sulfur Dioxide

Sulfur dioxide, or \(\mathrm{SO}_2\), is a chemical compound that results from the burning of sulfur-containing materials, such as coal. This colorless gas is notable for its sharp, irritating smell and serves as a precursor for sulfuric acid.
When released into the atmosphere, sulfur dioxide contributes to acid rain, which can harm ecosystems.

• In the context of the experiment, \(\mathrm{SO}_2\) reacts with hydrogen peroxide to form sulfuric acid.
• This reaction is critical for capturing \(\mathrm{SO}_2\) from burning coal in a liquid form.

The conversion of \(\mathrm{SO}_2\) to \(\mathrm{H}_2\mathrm{SO}_4\) ensures the chemical can be analyzed using titration to determine its quantity in the sample.

Organic Chemistry

Organic chemistry revolves around the study of carbon-containing compounds. These compounds make up a significant portion of chemical substances on Earth, including fuels like coal which contain not just carbon but also elements like sulfur.
In organic chemistry, combustion reactions are common, where an organic compound reacts with oxygen (combustion) to form oxides. In burning coal, sulfur is oxidized to form sulfur dioxide.

• This results in a mixture of chemical reactions involving various elements present in the compound.
• The presence of sulfur makes it necessary to analyze the resulting emissions.

Understanding these reactions is crucial, especially when dealing with environmental pollutants like \(\mathrm{SO}_2\).

Coal Analysis

Coal analysis is essential for understanding the composition of coal, which affects its combustion properties and impact on the environment. This analysis often involves determining the sulfur content, which is crucial for both energy production and environmental protection.

• The sulfur content in coal determines how much sulfur dioxide is emitted when the coal is burned.
• Assessing the mass percent of sulfur helps in strategizing ways to reduce \(\mathrm{SO}_2\) emissions.
• Accurate coal analysis is also important for equitable valuation of coal as an energy resource.

In this exercise, analyzing the sulfur content in the coal sample provides information about the potential environmental impact of using this coal for energy, guiding measures for pollution control.