Question

When organic compounds containing sulfur are bumed, 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.

Short answer

The mass percent of sulfur in the coal sample is approximately 3.58%.

Step-by-step solution

Write the balanced chemical equation for the titration of sulfuric acid with sodium hydroxide.

The balanced chemical equation for the reaction between sulfuric acid and sodium hydroxide is: $$\mathrm{H}_{2}\mathrm{SO}_{4}(a q) +2\mathrm{NaOH}(a q)\longrightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}(a q) + 2\mathrm{H}_{2}\mathrm{O}(l)$$ In this equation, one mole of sulfuric acid reacts with two moles of sodium hydroxide to produce one mole of sodium sulfate and two moles of water.

Identify stoichiometric relationships and calculate moles of sulfuric acid produced.

It took 28.44 mL of a 0.1000-M NaOH solution to titrate the resulting sulfuric acid. First, calculate the moles of NaOH used: $$moles \,of\, NaOH = Molarity \times Volume$$ where volume is converted from mL to L. $$moles \,of\, NaOH = 0.1000 \frac{moles}{L} \times 0.02844 L = 0.002844 \,moles \,of\, NaOH$$ From the stoichiometry of the balanced chemical equation, two moles of NaOH react with one mole of sulfuric acid. We use this information to determine the moles of sulfuric acid produced: $$moles \,of \,H_{2}SO_{4} = \frac{1}{2} \times moles \,of\, NaOH = \frac{1}{2} \times 0.002844 = 0.001422 \,moles \,of \,H_{2}SO_{4}$$

Calculate the mass of sulfur in the coal sample and find mass percent of sulfur.

The molar mass of sulfuric acid (H2SO4) is 98 g/mol, and the molar mass of sulfur (S) is 32 g/mol. To determine the mass of sulfur in sulfuric acid, we can set up the following relationship: $$\frac{mass \,of\, S}{mass \,of\, H_{2}SO_{4}} = \frac{molar \,mass \,of \,S}{molar \,mass \,of \,H_{2}SO_{4}}$$ Solve for the mass of S: $$mass \,of\, S =\frac{molar \,mass\, of\, S}{molar \,mass\, of\, H_{2}SO_{4}} \times moles \,of\, H_{2}SO_{4} \times molar\, mass\, of\, H_{2}SO_{4}$$ $$mass\, of\, S =\frac{32 g/mol}{98 g/mol} \times 0.001422 moles \times 98 g/mol = 0.0466 \,g \,of \,S$$ Finally, calculate the mass percent of sulfur: $$Mass \,percent\, of\, S = \frac{mass \,of \,S}{mass\, of\, coal \,sample} \times 100$$ $$Mass\, percent \,of\, S = \frac{0.0466 \,g}{1.302 \,g} \times 100 = 3.58 \%$$ The mass percent of sulfur in the coal sample is approximately 3.58%.

Key concepts

Titration Process

Titration is a laboratory method used to determine the concentration of a substance in a solution. In this exercise, titration is used to find out how much sulfuric acid was produced after burning coal. This sulfuric acid forms when sulfur dioxide from burned coal reacts with hydrogen peroxide. To understand the titration process better, let’s explore its basic components and steps:

• **Indicator**: A chemical used in the titration to signal the end of the reaction. It changes color when the titration is complete.
• **Titrant**: The solution of known concentration (in this case, NaOH) is added until the reaction reaches its endpoint.
• **Analyte**: The solution of unknown concentration (sulfuric acid in this context) being tested.

During the titration, NaOH is gradually added to the sulfuric acid solution. Upon reaching the equivalence point, all the sulfuric acid has reacted. Knowing the volume of NaOH used helps us calculate the amount of sulfuric acid, using stoichiometry, which will be discussed next.

Chemical Stoichiometry

Chemical stoichiometry is at the heart of calculating reactants and products in a chemical reaction. For the sulfur in coal, we first look at the stoichiometry of the reactions involved. This involves the combustion of coal to form sulfur dioxide, its conversion to sulfuric acid, and finally, the reaction of sulfuric acid with NaOH. The balanced chemical equation is crucial in this process:
\[ \text{H}_2\text{SO}_4(aq) + 2\text{NaOH}(aq) \rightarrow \text{Na}_2\text{SO}_4(aq) + 2\text{H}_2\text{O}(l) \]
This shows that one mole of sulfuric acid reacts with two moles of NaOH. From the titration, we can calculate the moles of NaOH used, and using this stoichiometry, we find the moles of sulfuric acid. This stoichiometric relation helps us convert our laboratory measurements into an understandable form, providing the bridge to calculating the quantity of sulfur in coal.

Mass Percent Calculation

Mass percent is a simple calculation expressing the concentration of a component over the total mass of the mixture. Here, it helps us understand the composition of sulfur in coal. Using stoichiometry, we determined the moles of sulfuric acid, and from that, calculated the mass of sulfur:

• First, determine the amount of sulfur in one mole of sulfuric acid: 32 g of sulfur per 98 g of sulfuric acid.
• Multiply the moles of sulfuric acid by this ratio to find the mass of sulfur produced:

\[ \frac{32}{98} \times 0.001422 \times 98 \text{ g/mol} = 0.0466 \text{ g} \text{ of S} \]
Finally, calculate the mass percent by dividing the mass of sulfur by the initial coal sample and multiplying by 100:
\[ \text{Mass percent of S} = \frac{0.0466 \text{ g}}{1.302 \text{ g}} \times 100 = 3.58\% \]
This calculation gives us the mass percent of sulfur in the coal sample, making it easier to assess the sulfur content and its potential environmental impact.