Combustion Analysis and Stoichiometry of Sulfur Compounds

Balanced Chemical Equation for the Combustion of Octasulfur

• Reaction Overview: The combustion of sulfur involves the chemical reaction between solid sulfur (in its stable molecular form as $S_8$) and gaseous oxygen ($O_2$) to produce sulfur dioxide ($SO_2$) gas.

• Reactants and Products:     * Reactant 1: Octasulfur solid ($S_8(s)$).     * Reactant 2: Oxygen gas ($O_2(g)$).     * Product: Sulfur dioxide gas ($SO_2(g)$).

• Balancing the Equation:     * The sulfur molecules consist of eight atoms joined in a ring. To balance the sulfur atoms, eight molecules of sulfur dioxide must be produced.     * Since eight molecules of $SO_2$ contain 16 atoms of oxygen, eight molecules of diatomic oxygen ($O_2$) are required as reactants.

• Final Balanced Equation:     * $S_8(s) + 8O_2(g) \rightarrow 8SO_2(g)$

Quantitative Analysis of Oxygen Consumption in Sulfur Combustion

• Problem Statement: Calculate the volume of $O_2(g)$ required to completely combust a $500\,g$ sample of pure $S_8(s)$.

• Given Conditions:     * Mass of Sample: $500\,g$ of $S_8(s)$.     * Pressure ($P$): $1.00\,atm$.     * Temperature ($T$): $298\,K$.

• Step-by-Step Calculation Procedure:

• Step 1: Determine the Molar Mass of $S_8$:     * The atomic mass of Sulfur ($S$) is approximately $32.06\,g\,mol^{-1}$.     * Molar mass of $S_8 = 8 \times 32.06\,g\,mol^{-1} = 256.48\,g\,mol^{-1}$.

• Step 2: Calculate the Total Moles of $S_8$ in the Sample:     * Using the formula: $n = \frac{\text{mass}}{\text{molar mass}}$     * $n_{S_8} = \frac{500\,g}{256.48\,g\,mol^{-1}} \approx 1.949\,mol$

• Step 3: Apply Stoichiometric Ratios to Find Moles of $O_2$:     * According to the balanced equation, the mole ratio of $S_8$ to $O_2$ is $1:8$.     * $n_{O_2} = 1.949\,mol \times 8 = 15.592\,mol$

• Step 4: Calculate the Volume of Oxygen Gas Using the Ideal Gas Law:     * The Ideal Gas Law is defined as: $PV = nRT$     * Rearranging to solve for Volume ($V$): $V = \frac{nRT}{P}$     * Constants and Variables:         * $n = 15.592\,mol$         * $R \text{ (Ideal Gas Constant)} = 0.08206\,L\,atm\,mol^{-1}\,K^{-1}$         * $T = 298\,K$         * $P = 1.00\,atm$     * Calculation:         * $V = \frac{15.592\,mol \times 0.08206\,L\,atm\,mol^{-1}\,K^{-1} \times 298\,K}{1.00\,atm}$         * $V \approx 381.27\,L$

• Final Answer Summary: To completely combust a $500\,g$ sample of solid sulfur ($S_8$) at $1.00\,atm$ and $298\,K$, approximately $381\,L$ of gaseous oxygen ($O_2$) is required.