Question

Ground water sometimes contains traces of hydrogen sulfide, which has the odor of rotten eggs. Chlorine gas is used to purify the water for drinking. The resulting sulfur reacts with fluorine gas to give sulfur hexafluoride. The reactions are as follows: $$\begin{aligned}8 \mathrm{H}_{2} \mathrm{~S}(a q)+8 \mathrm{Cl}_{2}(g) & \longrightarrow 16 \mathrm{HCl}(a q)+\mathrm{S}_{8}(s) \\\\\mathrm{S}_{8}(s)+24 \mathrm{~F}_{2}(g) & \longrightarrow 8 \mathrm{SF}_{6}(g)\end{aligned} $$ Starting with \(0.950 \mathrm{~L}\) of \(\mathrm{Cl}_{2}\) (STP) and excess fluorine gas, calculate: (a) the mass of sulfur hexafluoride produced (b) the volume of sulfur hexafluoride produced at STP (c) the volume of aqueous \(0.0265 \mathrm{M} \mathrm{H}_{2} \mathrm{~S}\) that reacted

Short answer

(a) 6.19 g, (b) 0.950 L, (c) 1.60 L.

Step-by-step solution

Understanding the Reaction and Stoichiometry

We have two reactions: (1) converting hydrogen sulfide to sulfur using chlorine, and (2) converting sulfur to sulfur hexafluoride using fluorine. The stoichiometry of reaction 1 is 8 moles of \(\mathrm{Cl}_{2}\) react to produce 1 mole of \(\mathrm{S}_{8}\). For reaction 2, 1 mole of \(\mathrm{S}_{8}\) gives 8 moles of \(\mathrm{SF}_{6}\). We start with 0.950 L of \(\mathrm{Cl}_{2}\) at STP, where 1 mole of any gas occupies 22.4 L at STP.

Calculate Moles of Chlorine

To find out how many moles of \(\mathrm{Cl}_{2}\) we have, we use the Volume-Amount relationship at STP: \[ \text{Moles of } \mathrm{Cl}_{2} = \frac{0.950 \text{ L}}{22.4 \text{ L/mol}} \approx 0.0424 \text{ moles} \]

Determine Moles of Sulfur Hexafluoride

From the stoichiometry of the reactions, 8 moles of \(\mathrm{Cl}_{2}\) produce 1 mole of \(\mathrm{S}_{8}\), and 1 mole of \(\mathrm{S}_{8}\) produces 8 moles of \(\mathrm{SF}_{6}\). Therefore, 8 moles of \(\mathrm{Cl}_{2}\) indirectly yield 8 moles of \(\mathrm{SF}_{6}\), so \(0.0424\) moles of \(\mathrm{Cl}_{2}\) will yield: \[ 0.0424 \text{ moles } \mathrm{Cl}_{2} \cdot \frac{8 \text{ moles } \mathrm{SF}_{6}}{8 \text{ moles } \mathrm{Cl}_{2}} = 0.0424 \text{ moles } \mathrm{SF}_{6} \].

Calculate Mass of Sulfur Hexafluoride

The molar mass of \(\mathrm{SF}_{6}\) is calculated as: \(S = 32.07 \text{ g/mol} + 6 \times 18.998 \text{ g/mol} = 146.07 \text{ g/mol}\). Thus, the mass of \(\mathrm{SF}_{6}\) is: \[ 0.0424 \text{ moles} \times 146.07 \text{ g/mol} \approx 6.19 \text{ g} \]

Calculate Volume of Sulfur Hexafluoride at STP

At STP, one mole of a gas occupies 22.4 L. Therefore, the volume of \(\mathrm{SF}_{6}\) produced is: \[ 0.0424 \text{ moles} \times 22.4 \text{ L/mol} \approx 0.950 \text{ L} \]

Determine Volume of Aqueous \(\mathrm{H}_{2} \mathrm{~S}\) Solution

From the reaction stoichiometry, 8 moles of \(\mathrm{H}_{2} \mathrm{~S}\) react with 8 moles of \(\mathrm{Cl}_{2}\), so \(0.0424 \text{ moles } \mathrm{Cl}_{2}\) require \(0.0424 \text{ moles } \mathrm{H}_{2} \mathrm{~S}\). Using the molarity \(0.0265 \text{ M}\), we find the volume as: \[ \text{Volume} = \frac{0.0424 \text{ moles}}{0.0265 \text{ moles/L}} \approx 1.60 \text{ L} \]

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, called reactants, are transformed into different substances, called products. In this exercise, there are two particular chemical reactions that take place sequentially: the transformation of hydrogen sulfide (\(\mathrm{H}_2\mathrm{S}\)) into elemental sulfur (\(\mathrm{S}_8\)), and the subsequent reaction of elemental sulfur with fluorine gas (\(\mathrm{F}_2\)) to produce sulfur hexafluoride (\(\mathrm{SF}_6\)). These reactions make use of chlorine (\(\mathrm{Cl}_2\)) and fluorine as reactants and involve both solid and gaseous states.

• First Reaction: Hydrogen sulfide reacts with chlorine to form hydrochloric acid and elemental sulfur.
• Second Reaction: Elemental sulfur, produced in solid form in the first reaction, is treated with fluorine gas to form sulfur hexafluoride gas.

Understanding these reactions involves knowing the stoichiometry, which details how reactants are combined in a fixed ratio to produce products. Stoichiometry is key to balancing chemical equations and calculating the quantities of reactants and products.

Mole Calculations

Moles are a fundamental unit in chemistry used to measure the amount of a substance. One mole contains\(6.022 \times 10^{23}\)avogadro numbers of particles, making it extremely useful for conversion between atoms/molecules and grams. In the exercise, we calculate moles of chlorine gas starting from its volume under standard temperature and pressure (STP). At STP, one mole of any gas occupies\(22.4 \, \mathrm{L}\). With the given volume of\(0.950 \, \mathrm{L}\)of chlorine gas, we use the formula:\[ \text{Moles of } \mathrm{Cl}_2 = \frac{0.950 \, \mathrm{L}}{22.4 \, \mathrm{L/mol}} \approx 0.0424 \, \text{moles} \]This step is crucial, as moles allow us to make further calculations on other substances involved in the reactions due to stoichiometric relationships. These relationships tell us how moles of one reactant are related to moles of products or other reactants.

Gas Laws

Gas laws describe the behavior of gases with respect to pressure, volume, temperature, and amount. In the exercise, the concept of volume at standard temperature and pressure (STP) is crucial, as it allows conversion from the volume of a gas to the amount in moles.

• STP Conditions: Standard Temperature and Pressure is defined as a temperature of\(0^\circ\mathrm{C}\)and a pressure of\(1 \, \mathrm{atm}\).At these conditions, one mole of any ideal gas occupies\(22.4 \, \mathrm{L}\).

For instance, after finding the moles of chlorine gas, the reactions' stoichiometry tells us how much sulfur hexafluoride gas is produced. Knowing the moles of a gas, we again use the volume-moles relationship under STP:\[ \text{Volume of } \mathrm{SF}_6 = 0.0424 \, \text{moles} \times 22.4 \, \mathrm{L/mol} = 0.950 \, \mathrm{L} \]These calculations are based on the Ideal Gas Law principles, which assume gases behave ideally under given conditions.

Sulfur Hexafluoride

Sulfur hexafluoride (\(\mathrm{SF}_6\)) is a non-toxic, inert gas commonly used in the electrical industry as an insulator in high-voltage applications. In this exercise, \(\mathrm{SF}_6\) is produced from elemental sulfur and fluorine gas.

• Molar Mass Calculation: The molar mass of \(\mathrm{SF}_6\)is calculated by adding the atomic masses of sulfur and six fluorine atoms:\(32.07 \, \text{g/mol} + 6 \times 18.998 \, \text{g/mol} = 146.07 \, \text{g/mol}\).
• Stoichiometry: In the final reaction, 1 mole of \(\mathrm{S}_8\)gives 8 moles of\(\mathrm{SF}_6\).This ratio helps us convert moles of reactants to moles of \(\mathrm{SF}_6\).

Sulfur hexafluoride's production and its quantity in grams are directly derivable from the stoichiometry of the reactions and its molar mass, emphasizing the interplay of chemical discipline and calculation accuracy.

Molarity

Molarity (\(M\)) is the concentration of a solution expressed as moles of solute per liter of solution. In the context of this problem, it is used to find the initial volume of the hydrogen sulfide solution. The molarity of hydrogen sulfide is given as\(0.0265 \, M\). Using the stoichiometry of the reactions, we know that\(0.0424 \, \text{moles}\)of\(\mathrm{Cl}_2\)require the same moles of\(\mathrm{H}_2\mathrm{S}\).Hence, calculating the volume based on molarity:\[ \text{Volume} = \frac{0.0424 \, \text{moles}}{0.0265 \, \text{moles/L}} \approx 1.60 \, \mathrm{L} \]This step ensures that the volume of the solution needed for the reaction is accurate, thus demonstrating the utility of molarity in determining how much solute is present in a particular volume of solvent.