Question

When organic compounds containing sulfur are burned, sulfur dioxide is produced. The amount of \(\mathrm{SO}_{2}\) formed can be determined by 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 \(\mathrm{NaOH}\) solution. A \(1.325-\mathrm{g}\) sample of coal is burned and the \(\mathrm{SO}_{2}\) collected in a solution of hydrogen peroxide. It took \(28.44 \mathrm{~mL}\) of \(0.1000 \mathrm{M} \mathrm{NaOH}\) to neutralize 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 1.727%.

Step-by-step solution

Calculate moles of \(\mathrm{NaOH}\)

First, find the number of moles of \(\mathrm{NaOH}\) used in the titration reaction. We can use the volume and molarity of the \(\mathrm{NaOH}\) solution to calculate this: Moles of \(\mathrm{NaOH} = \text{Volume} \times \text{Molarity}\) \[ \text{Moles of }\mathrm{NaOH} = 0.02844 \, \text{L} \times 0.1000 \mathrm{M} = 2.844 \times 10^{-3} \text{ moles} \]

Calculate moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\)

Next, determine the number of moles of sulfuric acid, \(\mathrm{H}_{2}\mathrm{SO}_{4}\). Sulfuric acid has two acidic hydrogens, which means that in the titration reaction, it reacts with two moles of \(\mathrm{NaOH}\) to form one mole of \(\mathrm{H}_{2}\mathrm{SO}_{4}\). We can use stoichiometry to find the number of moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\): \(\frac{1 \; \text{mole of }\mathrm{H}_{2}\mathrm{SO}_{4}}{2 \; \text{moles of }\mathrm{NaOH}} \times 2.844 \times 10^{-3} \text{ moles of }\mathrm{NaOH} = 1.422 \times 10^{-3} \text{ moles of } \mathrm{H}_{2}\mathrm{SO}_{4}\)

Calculate moles of \(\mathrm{SO}_{2}\)

Since 1 mole of \(\mathrm{SO}_{2}\) reacts with 1 mole of \(\mathrm{H}_{2}\mathrm{SO}_{4}\), the number of moles of \(\mathrm{SO}_{2}\) is equal to the number of moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) calculated in the previous step: Moles of \(\mathrm{SO}_{2} = \text{1.422} \times 10^{-3} \, \text{moles}\)

Calculate mass of sulfur

Now, we'll calculate the mass of sulfur present in the \(\mathrm{SO}_{2}\). The molar mass of \(\mathrm{SO}_{2}\) is 64.06 \(g/mol\) (\(32.06 g/mol\) for sulfur and \(16.00 g/mol\) for each oxygen). The mass fraction of sulfur in \(\mathrm{SO}_{2}\) is: \(\frac{32.06 \, \text{g/mol}}{64.06\, \text{g/mol}} = 0.500\) Multiply the moles of \(\mathrm{SO}_{2}\) by this mass fraction to find the mass of sulfur: \[ \text{Mass of sulfur} = 1.422 \times 10^{-3} \, \text{moles} \times 0.500 \times 64.06 \, \frac{\text{g}}{\text{mol}} = 0.02288 \, \text{g} \]

Find mass percent of sulfur in coal sample

Finally, calculate the mass percent of sulfur in the coal sample: \[ \text{Mass percent of sulfur} = \frac{0.02288 \, \text{g}}{1.325 \, \text{g}} \times 100 = 1.727 \% \] The mass percent of sulfur in the coal sample is approximately 1.727%.

Key concepts

Understanding Titration in Chemistry

Titration is an analytical technique used to determine the concentration of a known reactant in a solution. In the context of the given problem, it involves the reaction of a base, in this case sodium hydroxide (NaOH), with an acid produced (sulfuric acid, H₂SO₄) after burning coal that releases sulfur dioxide (SO₂). The process indicates how much NaOH is needed to neutralize the acid, which is directly related to the amount of sulfur dioxide produced. This relationship is a cornerstone of stoichiometry where reactants and products are quantitatively converted based on balanced chemical equations.
It is crucial for students to understand that the endpoint of a titration is reached when the amount of titrant added is stoichiometrically equivalent to the concentration of the analyte, which signals complete neutralization. By knowing the molarity of the NaOH solution and the volume used, you can calculate the moles of NaOH and subsequently determine the moles of H₂SO₄ based on the balanced reaction stoichiometry.

Molar Mass: The Gateway to Quantitative Chemistry

Molar mass, often confused with molecular weight, is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is the bridge that connects the molecular scale to the measurable world. In the problem at hand, it is used to calculate the mass of sulfur dioxide and then, the mass of elemental sulfur. Knowing that the molar mass of SO₂ is 64.06 g/mol and that sulfur contributes 32.06 g/mol to this mass, we can find the mass of sulfur in the SO₂ by using proportional reasoning.
For students, grasping the concept of molar mass is essential for converting between moles, the chemist's counting unit, and grams, which can be measured on a scale. Remember, molar mass values can be found on the periodic table and must be used with care to ensure they are correct for the specific compound in question.

Sulfur Dioxide in Chemical Reactions

Sulfur dioxide (SO₂) is a significant byproduct produced when organic compounds containing sulfur are burned. It's a gas that plays a key role in the environment, industry, and even in analytical chemistry, as seen in the given problem. In this exercise, SO₂ is generated from burning coal, and its amount can be quantified by the subsequent production of sulfuric acid, which is then titrated. The presence of sulfur dioxide is essential to the problem because the exercise aims to determine the sulfur content in the original coal sample by tracking SO₂ through the chemical reactions.
Understanding the chemical properties and behavior of SO₂ in reactions is central to solving this type of problem. Students should note that one mole of SO₂ will react with hydrogen peroxide (H₂O₂) to yield one mole of H₂SO₄, and this stoichiometric relationship is the basis for the calculations.

Calculating Mass Percent for Composition Analysis

Mass percent calculation is a method to express the concentration of an element in a compound or a component in a mixture. It is calculated by dividing the mass of the component by the total mass of the sample and then multiplying by 100 to get a percentage. In the context of this exercise, mass percent allows us to deduce the composition of the coal sample in terms of its sulfur content. This quantity provides insight into the purity and quality of the coal sample.
Students should be mindful that mass percent is commonly used in the field of chemistry to quantify purity, concentration, and elemental makeup. It is an important concept especially in environmental science, where such percentages can indicate pollutant levels. In practice, the mass of sulfur determined from the titration and stoichiometry steps is divided by the mass of the original coal sample to find the mass percent of sulfur in the coal. The result is an essential indicator of the coal's characteristics and potential environmental impact when used as a fuel.