Question

The maximum allowable concentration of \(\mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})\) in air is \(20 \mathrm{mg}\) per kilogram of air (20 ppm by mass). How many grams of FeS would be required to react with hydrochloric acid to produce this concentration at \(1.00\) atm and \(25^{\circ} \mathrm{C}\) in an average room measuring \(12 \mathrm{ft} \times 20 \mathrm{ft} \times 8 \mathrm{ft}\) ? (Under these conditions, the average molar mass of air is \(29.0 \mathrm{~g} / \mathrm{mol}\).)

Short answer

To produce the maximum allowable concentration of H₂S in the room, approximately 3.33 grams of FeS is required.

Step-by-step solution

Convert room dimensions to meters

To work with SI units, we need to convert the dimensions of the room from feet to meters. We have the conversion factor: 1 ft = 0.3048 m. So, the room dimensions are: Length = 12 ft × 0.3048 = 3.658 m Width = 20 ft × 0.3048 = 6.096 m Height = 8 ft × 0.3048 = 2.438 m.

Calculate the volume of the room in cubic meters

The volume of the room can be found by multiplying the length, width, and height. The volume is: \(V = Length \times Width \times Height\) V = 3.658 m × 6.096 m × 2.438 m = 54.215 m³.

Calculate the mass of air in the room

First, we'll need to find the moles of air in the room. We can use the ideal gas law (PV=nRT) to calculate moles (n). Rearranging the formula, we get n = PV/RT, where P = 1 atm, V = 54.215 m³, R = 0.0821 (L atm)/(K mol), and T = 298 K (25°C + 273). Now, convert volume (V) to liters: V = 54,215 L n = (1 atm × 54,215 L) / (0.0821 (L atm)/(K mol) × 298 K) n ≈ 2,230 moles Next, we'll calculate the mass of air by multiplying the moles of air by the average molar mass of air (29.0 g/mol). mass of air = 2,230 moles × 29.0 g/mol ≈ 64,670 g.

Calculate the mass of H2S that corresponds to 20 ppm

The mass of H2S can be calculated using the given concentration: mass of H₂S = (mass of air × 20 ppm) / 1,000,000 ppm mass of H₂S = (64,670 g × 20) / 1,000,000 ≈ 1.293 g.

Determine the stoichiometry of the reaction

The reaction between FeS and hydrochloric acid can be represented as: FeS (s) + 2HCl → FeCl₂ + H₂S (g) From the balanced equation, 1 mole of FeS reacts to produce 1 mole of H₂S.

Calculate the mass of FeS required

Using stoichiometry, now we can find the mass of FeS needed to produce the required amount of H₂S. First, we'll convert the mass of H₂S to moles using its molar mass (34.08 g/mol). moles of H₂S = 1.293 g / 34.08 g/mol ≈ 0.0379 moles Since the ratio between FeS and H₂S is 1:1, we require the same number of moles of FeS: moles of FeS = 0.0379 moles Now, we can convert moles of FeS to grams using its molar mass (87.91 g/mol). mass of FeS = 0.0379 moles × 87.91 g/mol ≈ 3.33 g So, to produce the maximum allowable concentration of H₂S in the room, approximately 3.33 grams of FeS is required.

Key concepts

Ideal Gas Law

When dealing with gases, understanding their behavior under various conditions is crucial. That's where the Ideal Gas Law comes in. This fundamental equation, written as \( PV = nRT \), connects the pressure \( P \), volume \( V \), and temperature \( T \) of a gas, with \( n \) representing the moles of gas and \( R \) being the universal gas constant. The Ideal Gas Law is instrumental when calculating elements such as the volume or the number of moles in gaseous reactions.
For instance, in our exercise, we used the Ideal Gas Law to determine the moles of air inside a room. First, we needed to change the measured volume from meters cubed to liters for compatibility with the gas constant \( R \), typically expressed in terms of liters, atm, and Kelvin.
It's a game-changer in stoichiometry especially when working with gaseous reactions or under controlled laboratory environments.

Chemical Reactions

Chemical reactions represent the processes where substances transform into different entities. These transformations adhere strictly to balanced equations where the number of each type of atom on both sides is equal.
In our exercise, the reaction of Iron(II) sulfide (FeS) and hydrochloric acid (HCl) is a perfect example of a balancing act. The chemical equation:

• FeS (s) + 2HCl → FeCl₂ + H₂S (g)

is balanced to show that one mole of FeS reacts equally with two moles of HCl to produce one mole of hydrogen sulfide (H₂S) gas.
Understanding these balanced reactions is crucial. It allows us to predict how much FeS is needed to produce desired quantities of H₂S, advancing our control over chemical processes and ensuring safety when managing substance concentrations.

Concentration Calculations

Calculating concentration involves understanding how much of a substance is present in a mix. Here, concentration is measured in parts per million (ppm), a unit that quantifies mass per mass, making it invaluable in environmental assessments.
The exercise determined how many grams of iron(II) sulfide (FeS) were needed to produce hydrogen sulfide (H₂S) gas at a concentration of 20 ppm in a room filled with air.
Knowing the total mass of air in the room, we applied the formula:

• mass of H₂S = (mass of air × 20 ppm) / 1,000,000

This method ensures that substances remain within safe concentration levels, providing essential insights for applications ranging from medicine to industrial safety.
Concentration calculations are vital, not just for the current scenario but broadly across scientific disciplines, helping evaluate exposure and risks related to chemical presence.