Question

The reaction \(8 \mathrm{H}_{2}(g)+\mathrm{S}_{8}(l) \longrightarrow 8 \mathrm{H}_{2} \mathrm{~S}(g)\) is run at \(125^{\circ} \mathrm{C}\) and a constant pressure of \(12.0 \mathrm{~atm}\). Assuming complete reaction, what mass of \(\mathrm{S}_{8}\) would be required to produce \(5.00 \times 10^{2} \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{~S}\) gas under these conditions?

Short answer

To produce 500 mL of \(\mathrm{H}_2\mathrm{S}\) gas, 5.88 g of \(\mathrm{S}_8\) is required.

Step-by-step solution

Write Balanced Equation

The given reaction is already balanced: \(8 \mathrm{H}_{2}(g) + \mathrm{S}_{8}(l) \longrightarrow 8 \mathrm{H}_{2} \mathrm{~S}(g)\). Each mole of \(\mathrm{S}_{8}\) reacts with 8 moles of \(\mathrm{H}_2\) to produce 8 moles of \(\mathrm{H}_2\mathrm{S}\).

Convert Volume of Gas to Moles

Use the ideal gas law equation to find the moles of \(\mathrm{H}_2\mathrm{S}\). The ideal gas law is \( PV = nRT\), where \(P = 12.0 \, \text{atm}, V = 500 \, \text{mL} = 0.500 \, \text{L}, R = 0.0821 \, \text{L}•\text{atm}/\text{mol}•\text{K}, T = 125^{\circ}\text{C} = 398 \,\text{K}\). Solve for \(n\) (moles of \(\mathrm{H}_2\mathrm{S}\)):\[ n = \frac{PV}{RT} = \frac{12.0 \times 0.500}{0.0821 \times 398} \approx 0.183 \, \text{mol} \]

Calculate Moles of \(\mathrm{S}_8\) Required

From the balanced equation, each mole of \(\mathrm{S}_8\) produces 8 moles of \(\mathrm{H}_2\mathrm{S}\). Therefore:\[ \text{Moles of } \mathrm{S}_8 = \frac{0.183}{8} \approx 0.0229 \, \text{mol} \]

Calculate Mass of \(\mathrm{S}_8\)

Calculate the molar mass of \(\mathrm{S}_8\). Sulfur has an atomic mass of approximately 32.07 g/mol, so the molar mass of \(\mathrm{S}_8\) is \(32.07 \times 8 = 256.56 \text{ g/mol}\). Use this to calculate the mass of \(\mathrm{S}_8\):\[ \text{Mass of } \mathrm{S}_8 = 0.0229 \times 256.56 \approx 5.88 \, \text{g} \]

Summary

To produce \(5.00 \times 10^{2}\text{ mL}\) of \(\mathrm{H}_{2}\mathrm{S}_g\) at \(125^{\circ} \text{C}\) and \(12.0 \, \text{atm}\), approximately \(5.88\, \text{g}\) of \(\mathrm{S}_8\) are required.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that describes the behavior of ideal gases. It is expressed as \( PV = nRT \), where:

• \( P \) is the pressure of the gas in atmospheres (atm).
• \( V \) is the volume of the gas in liters (L).
• \( n \) is the number of moles of the gas.
• \( R \) is the ideal gas constant, with a value of \(0.0821 \text{ L} \cdot \text{atm}/\text{mol} \cdot \text{K}\).
• \( T \) is the temperature in Kelvin (K).

To solve problems using the Ideal Gas Law, you need to rearrange the equation to solve for the unknown variable (in this case, the number of moles \( n \)). For a given problem, always ensure units are consistent, such as converting temperature to Kelvin by adding 273 to the Celsius temperature.
This law assumes there are no interactions between gas molecules and that the volume occupied by the gas molecules themselves is negligible.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. This often involves calculating how much of a substance is needed or produced during a reaction.

• Begin with a balanced chemical equation. It shows the ratio in which compounds react and products form.
• Use the coefficients from the balanced equation to create ratios. For example, in the given exercise, the ratio of \( \text{H}_2 \) to \( \text{H}_2\text{S} \) is 1:1.
• Convert between moles and grams as necessary, using molar masses.
• Use the reaction stoichiometry to determine the moles of reactants needed or products produced, depending on the information given.

Understanding stoichiometry allows chemists to scale reactions up or down, ensuring precise usage of chemicals.

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry that ensures the law of conservation of mass is met. This law states that matter is neither created nor destroyed in a chemical reaction.

• Start by writing down the unbalanced equation. Identify the reactants (starting substances) and products (ending substances).
• Change the coefficients to balance atoms on both sides of the equation. Never alter the subscripts in chemical formulas.
• Balance one element at a time, often starting with the most complex molecule.
• Check your work by counting the number of atoms for each element on both sides of the equation.

In the example from the exercise, the given equation \( 8 \text{H}_2(g) + \text{S}_8(l) \rightarrow 8\text{H}_2\text{S}(g)\) is already balanced, meaning the same number of each type of atom appears on both sides of the equation.

Molar Mass Calculation

Calculating the molar mass of a substance is crucial in determining the mass of a given number of moles. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).

• Identify the chemical formula of the substance. For \( \text{S}_8 \), it consists of eight sulfur atoms.
• Find the atomic mass of each element using the periodic table. Sulfur (S) has an atomic mass of about 32.07 g/mol.
• Multiply the atomic mass by the number of each type of atom in the formula. For \( \text{S}_8 \), it is \(32.07 \times 8 = 256.56\) g/mol.
• Use this calculated molar mass to convert between mass and moles in stoichiometric calculations.

Accurate molar mass calculations are foundational for determining how much of a substance is required or produced in a reaction.