Question

Chlorine can remove the foul smell of \(\mathrm{H}_{2} \mathrm{~S}\) in water. The reaction is $$ \mathrm{H}_{2} \mathrm{~S}(a q)+\mathrm{Cl}_{2}(a q) \longrightarrow 2 \mathrm{H}^{+}(a q)+2 \mathrm{Cl}^{-}(a q)+\mathrm{S}(s) $$ If the contaminated water has 5.0 ppm hydrogen sulfide by mass, what volume of chlorine gas at STP is required to remove all the \(\mathrm{H}_{2} \mathrm{~S}\) from \(1.00 \times 10^{3}\) gallons of water \((d=1.00 \mathrm{~g} / \mathrm{mL}) ?\) What is the \(\mathrm{pH}\) of the solution after treatment with chlorine?

Short answer

What is the pH of the water after treatment? Answer: (Based on the provided step-by-step solution) The volume of chlorine gas required can be calculated by following Steps 1-4. After determining the moles of Cl₂ required, use the ideal gas law (PV=nRT) at STP to calculate the volume of Cl₂ gas. To find the pH of the water after treatment, follow Steps 5-6 to calculate the concentration of H⁺ ions and then determine the pH using the formula pH = -log10[H⁺].

Step-by-step solution

Find the mass of H₂S in the water

Given that the water contains 5.0 ppm (parts per million) of hydrogen sulfide by mass, we can find the mass of H₂S in the water. $$\text{mass of H}_2 \text{S in the water} = \frac{5.0\,\text{ppm}}{10^6} \cdot 1.00\times10^3\times 3.78541\,\text{Liters} \cdot 1.00\,\frac{\text{g}}{\text{mL}}$$

Determine the number of moles of H₂S

Now, using the molar mass of H₂S, we will convert the mass of H₂S to moles. $$\text{moles of H}_2 \text{S} = \frac{\text{mass of H}_2 \text{S}}{\text{molar mass of H}_2 \text{S}}$$ The molar mass of H₂S is approximately 34.08 g/mol.

Determine the number of moles of Cl₂ required

From the balanced chemical equation, 1 mole of H₂S requires 1 mole of Cl₂ for complete reaction. $$\text{moles of Cl}_2 = \text{moles of H}_2\text{S}$$

Calculate the volume of Cl₂ gas at STP

Using the ideal gas law, PV=nRT, and given that the conditions are at standard temperature and pressure (STP), we can find the volume of chlorine gas required. $$V = \frac{nRT}{P}$$ At STP, the temperature is 273.15 K, and the pressure is 1 atm. The ideal gas constant, R = 0.08206 L atm / (mol K). So we have, $$V = \frac{\text{moles of Cl}_2 \times 0.08206 \times 273.15}{1}$$

Calculate the concentration of H⁺ ions after treatment

After the reaction, hydrogen sulfide produces 2 moles of H⁺ ions for every mole of H₂S reacted. $$[\text{H}^+] = 2 \times \frac{\text{moles of H}_2\text{S}}{\text{volume of water in liters}}$$

Determine the pH of the solution after treatment

Now, we can finally calculate the pH of the water after treatment with chlorine using: $$\text{pH} = -\log_{10} [\text{H}^+]$$

Key concepts

Stoichiometry Calculations

Stoichiometry is the mathematical relationship between the amounts of reactants and products in a chemical reaction. To perform stoichiometry calculations, we follow a series of steps:

• Identify the balanced chemical equation for the reaction.
• Convert all given information into moles, using molar mass as needed.
• Use the mole ratio from the balanced equation to calculate the number of moles of the desired substance.
• Convert moles back to required units, such as mass or volume.

In the exercise involving chlorine treatment, for instance, the stoichiometry calculations help in determining the exact volume of chlorine gas needed at standard temperature and pressure (STP) to completely react with the given amount of hydrogen sulfide in the water.

Mole Concept

The mole concept is essential for stoichiometry calculations as it provides a bridge between the atomic and macroscopic levels. A mole corresponds to Avogadro's number of particles, which is approximately 6.022 x 10^23.

For substances in a chemical reaction, knowing the molar mass (the mass of one mole of a compound) allows us to convert between the mass of a substance and the number of moles. In chlorine treatment, we first convert the mass of hydrogen sulfide to moles using its molar mass. This step is fundamental for all subsequent calculations, as moles are used to measure chemicals in reactions.

Chemical Reaction Balancing

To ensure that a chemical equation obeys the Law of Conservation of Mass, it must be balanced, meaning there must be an equal number of atoms of each element on both sides of the equation.

Chemical reaction balancing involves adjusting the coefficients preceding the reactant and product formulas. For the reaction between hydrogen sulfide and chlorine, the coefficients indicate that one mole of hydrogen sulfide reacts with one mole of chlorine to produce sulfur and hydrogen ions in water.

Understanding this balanced reaction is crucial because it allows us to determine the stoichiometry of the reaction, informing us that we need an equal molar amount of chlorine to treat the hydrogen sulfide in the water.

pH Calculation

The pH calculation is a measure of the acidity or basicity of an aqueous solution. The pH scale ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates acidity, while a pH greater than 7 indicates basicity.

The pH is calculated by taking the negative logarithm (to base 10) of the hydrogen ion concentration, represented as \( \text{pH} = -\log_{10} [\text{H}^+] \). In the context of chlorine treatment, the pH of the water after the addition of chlorine gives us an idea of the new acidic conditions. For each mole of hydrogen sulfide that reacts, two moles of hydrogen ions are produced, affecting the pH of the solution. To find the pH post-treatment, we calculate the hydrogen ion concentration from the number of moles of hydrogen sulfide reacted and then apply the pH formula.