Question

One method proposed for removing \(\mathrm{SO}_{2}\) from the flue gases of power plants involves reaction with aqueous \(\mathrm{H}_{2} \mathrm{~S}\). Elemental sulfur is the product. (a) Write a balanced chemical equation for the reaction. (b) What volume of \(\mathrm{H}_{2} \mathrm{~S}\) at \(27^{\circ} \mathrm{C}\) and 760 torr would be required to remove the \(\mathrm{SO}_{2}\) formed by burning 2.0 tons of coal containing \(3.5 \% \mathrm{~S}\) by mass? (c) What mass of elemental sulfur is produced? Assume that all reactions are \(100 \%\) efficient.

Short answer

(a) The balanced chemical equation for the reaction is: \(\mathrm{SO}_2 + 2\mathrm{H}_2\mathrm{S} \rightarrow 3\mathrm{S} + 2\mathrm{H}_2\mathrm{O}\). (b) The volume of \(\mathrm{H}_2\mathrm{S}\) required to remove the \(\mathrm{SO}_2\) formed by burning 2.0 tons of coal containing 3.5% S by mass at \(27^{\circ}\mathrm{C}\) and 760 torr is 1.32 × \(10^5\) L. (c) The mass of elemental sulfur produced is 2.10 × \(10^5\) g.

Step-by-step solution

Write the balanced chemical equation

: The reaction between sulfur dioxide (\(\mathrm{SO}_2\)) and hydrogen sulfide (\(\mathrm{H}_{2}\mathrm{S}\)) produces elemental sulfur (\(\mathrm{S}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)): \[ \mathrm{SO}_2 + 2\mathrm{H}_2\mathrm{S} \rightarrow 3\mathrm{S} + 2\mathrm{H}_2\mathrm{O} \]

Calculate the moles of sulfur dioxide produced

: First, we need to determine the moles of sulfur dioxide (\(\mathrm{SO}_2\)) produced by burning 2.0 tons of coal with 3.5% sulfur by mass. The mass of sulfur in the coal is: \[ 2.0 \times 10^6\ \text{g} \times 0.035 = 7.0 \times 10^4\ \text{g} \] Now, let's find the moles of sulfur dioxide produced. We can assume each sulfur atom reacts with oxygen to form \(\mathrm{SO}_2\). The molar mass of sulfur (\(\mathrm{S}\)) is 32.07g/mol, and the molar mass of sulfur dioxide (\(\mathrm{SO}_2\)) is 32.07g/mol + 2(16.00g/mol) = 64.07g/mol. Moles of \(\mathrm{SO}_2\) produced: \[ \frac{7.0 \times 10^4\ \text{g}}{32.07\ \text{g/mol}} \times \frac{1\ \text{mol }\mathrm{SO}_2}{1\ \text{mol }\mathrm{S}} = 2.18 \times 10^3\ \text{mol }\mathrm{SO}_2 \]

Determine the moles of hydrogen sulfide required

: From the balanced chemical equation in step 1, we see that 1 mol of \(\mathrm{SO}_2\) reacts with 2 mol of \(\mathrm{H}_2\mathrm{S}\). Thus, the moles of \(\mathrm{H}_2\mathrm{S}\) required would be double the moles of \(\mathrm{SO}_2\) produced: \[ 2.18 \times 10^3\ \text{mol }\mathrm{SO}_2 \times \frac{2\ \text{mol }\mathrm{H}_2\mathrm{S}}{1\ \text{mol }\mathrm{SO}_2} = 4.36 \times 10^3\ \text{mol }\mathrm{H}_2\mathrm{S} \]

Calculate the volume of hydrogen sulfide required

: To find the volume of \(\mathrm{H}_2\mathrm{S}\) required, we can use the ideal gas law, which is given by: \[ PV = nRT \] Where P is the pressure in atm (1 atm = 760 torr), V is the volume in liters, n is the number of moles, R is the gas constant (0.0821 L⋅atm/mol⋅K), and T is the temperature in Kelvin. First, let's convert the temperature from Celsius to Kelvin: \[ T = 27^\circ\mathrm{C} + 273.15 = 300.15\ \mathrm{K} \] Now let's plug the values into the ideal gas law and solve for the volume of \(\mathrm{H}_2\mathrm{S}\). Since the pressure is given in torr, we should convert it to atm: \[ V = \frac{nRT}{P} = \frac{(4.36 \times 10^3\ \text{mol})(0.0821\ \text{L⋅atm/mol⋅K})(300.15\ \mathrm{K})} {760\ \text{torr} \times \frac{1\ \text{atm}}{760\ \text{torr}}} = 1.32 \times 10^5\ \text{L} \] So, the volume of \(\mathrm{H}_2\mathrm{S}\) required is 1.32 x \(10^5\) L.

Calculate the mass of elemental sulfur produced

: From the balanced chemical equation in step 1, we see that 1 mol of \(\mathrm{SO}_2\) reacts to produce 3 mol of elemental sulfur (\(\mathrm{S}\)). Thus, the moles of \(\mathrm{S}\) produced would be triple the moles of \(\mathrm{SO}_2\) produced: \[ 2.18 \times 10^3\ \text{mol }\mathrm{SO}_2 \times \frac{3\ \text{mol }\mathrm{S}}{1\ \text{mol }\mathrm{SO}_2} = 6.54 \times 10^3\ \text{mol }\mathrm{S} \] Finally, let's convert the moles of \(\mathrm{S}\) produced to mass: \[ 6.54 \times 10^3\ \text{mol }\mathrm{S} \times \frac{32.07\ \text{g }\mathrm{S}}{1\ \text{mol }\mathrm{S}} = 2.10 \times 10^5\ \text{g} \] So, the mass of elemental sulfur produced is 2.10 x \(10^5\) g.

Key concepts

Chemical Equation

In chemistry, writing a balanced chemical equation is an essential skill that describes a chemical reaction precisely. Balance in a chemical equation ensures that the number of atoms of each element is the same on both sides, respecting the Law of Conservation of Mass.

In the case of the reaction between sulfur dioxide (\(\mathrm{SO}_2\)) and hydrogen sulfide (\(\mathrm{H}_2\mathrm{S}\)), the products formed are elemental sulfur (\(\mathrm{S}\)) and water (\(\mathrm{H}_2\mathrm{O}\)). The balanced equation is:\[\mathrm{SO}_2 + 2\mathrm{H}_2\mathrm{S} \rightarrow 3\mathrm{S} + 2\mathrm{H}_2\mathrm{O}\]

• Each molecule of \(\mathrm{SO}_2\) reacts with two molecules of \(\mathrm{H}_2\mathrm{S}\).
• This produces three atoms of sulfur and two molecules of water.

Balancing equations like this require careful counting of the atoms involved and sometimes involves trial and error expressed through coefficients in the equation.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry and physics describing the behavior of ideal gases. It connects pressure, volume, temperature, and moles of a gas.\[PV = nRT\]Where:

• \(P\): Pressure of the gas (in atm)
• \(V\): Volume (in liters)
• \(n\): Number of moles
• \(R\): Gas constant (0.0821 L·atm/mol·K)
• \(T\): Temperature (in Kelvin)

In the problem above, we are tasked to find the volume of hydrogen sulfide required at a specific temperature and pressure.

Convert the temperature from Celsius to Kelvin by adding 273.15. For pressure in atm, it’s often stated as 1 atm = 760 torr. Use these conversions to ensure all values are in the correct units before substituting into the equation.

Moles Calculation

Moles are a unit of measurement in chemistry key for understanding the amount of substance in a reaction. To find moles, use the formula:\[n = \frac{\text{mass}}{\text{molar mass}}\]This allows conversion from mass (in grams) to moles, facilitating stoichiometric calculations. Its importance is highlighted in this activity where the moles of \(\mathrm{SO}_2\) formed are determined by burning coal.

For the coal, calculate the amount of sulfur, then convert it to \(\mathrm{SO}_2\) moles. Ensuring you are aware of each compound's molar mass is important to perform this conversion accurately. Once the moles of one reactant are known, the reaction stoichiometry (from the balanced chemical equation) helps predict the moles of other substances involved.