Gas Laws in Stoichiometry: 3 Practical Examples

Understanding Gas Laws in Stoichiometry

Gas laws are critical in stoichiometry as they relate the properties of gases to their behavior during chemical reactions. By understanding these relationships, we can predict how gases will react under different conditions, which is essential in various fields such as chemistry, engineering, and environmental science. Below are three practical examples of using gas laws in stoichiometry that illustrate their applications in real-world scenarios.

Example 1: Calculating the Volume of Gas Produced in a Reaction

In a laboratory experiment, a chemist reacts sodium bicarbonate (NaHCO₃) with hydrochloric acid (HCl) to produce carbon dioxide gas (CO₂), water (H₂O), and sodium chloride (NaCl). The reaction can be represented as follows:

NaHCO₃ (s) + HCl (aq) → CO₂ (g) + H₂O (l) + NaCl (aq)

Context: The chemist needs to determine how much carbon dioxide gas is generated when 50 grams of sodium bicarbonate reacts with an excess of hydrochloric acid.

To find the volume of CO₂ produced, we first need to calculate the moles of sodium bicarbonate:

• Molar mass of NaHCO₃ = 84.01 g/mol
• Moles of NaHCO₃ = 50 g / 84.01 g/mol ≈ 0.595 moles

From the balanced equation, we see that 1 mole of NaHCO₃ produces 1 mole of CO₂. Therefore, 0.595 moles of NaHCO₃ will produce 0.595 moles of CO₂.

Using the Ideal Gas Law (PV = nRT), we can calculate the volume of CO₂ at standard temperature and pressure (STP), where P = 1 atm, T = 273.15 K, and R = 0.0821 L·atm/(K·mol):

• V = nRT/P
• V = (0.595 moles) × (0.0821 L·atm/(K·mol)) × (273.15 K) / (1 atm) ≈ 13.44 L

Notes: At non-STP conditions, the temperature and pressure should be adjusted in the Ideal Gas Law equation.

Example 2: Determining the Amount of Reactants Needed for Gas Generation

Consider the synthesis of ammonia (NH₃) through the Haber process, which can be summarized by the equation:

N₂ (g) + 3H₂ (g) ⇌ 2NH₃ (g)

Context: A chemical engineer wants to produce 10 liters of ammonia gas at standard temperature and pressure (STP) and needs to determine how much nitrogen and hydrogen gas is required.

Using the Ideal Gas Law, we first calculate the moles of NH₃:

• At STP, 1 mole of gas occupies 22.4 liters.
• Moles of NH₃ = 10 L / 22.4 L/mol ≈ 0.446 moles

From the balanced equation, 2 moles of NH₃ require 1 mole of N₂ and 3 moles of H₂. Therefore:

• Moles of N₂ required = 0.446 moles NH₃ × (1 mole N₂ / 2 moles NH₃) ≈ 0.223 moles
• Moles of H₂ required = 0.446 moles NH₃ × (3 moles H₂ / 2 moles NH₃) ≈ 0.669 moles

Next, we can determine the volume of nitrogen and hydrogen needed:

• Volume of N₂ = 0.223 moles × 22.4 L/mol ≈ 5.00 L
• Volume of H₂ = 0.669 moles × 22.4 L/mol ≈ 15.00 L

Notes: The reaction is conducted under conditions that can affect gas volumes; thus, real gases may deviate from ideal behavior.

Example 3: Adjusting Conditions for Gas Reactions

In an industrial setting, the production of ethylene (C₂H₄) from ethane (C₂H₆) via dehydrogenation is represented by the equation:

C₂H₆ (g) ⇌ C₂H₄ (g) + H₂ (g)

Context: An engineer needs to optimize the reaction conditions to increase the yield of ethylene gas. The reaction is exothermic and shifts according to Le Chatelier’s principle, which states that increasing temperature will favor the endothermic direction (product formation).

To analyze this, the engineer considers the effect of changing pressure using the Ideal Gas Law. By manipulating the volume and pressure, the amount of C₂H₄ produced can be maximized. If the system is at the following conditions:

• Initial volume = 10 L
• Initial pressure = 2 atm

When the pressure is reduced to 1 atm (increasing the volume to 20 L), the equilibrium can shift according to the gas law:

• P₁V₁ = P₂V₂ implies that volume increases with decreasing pressure, thereby favoring the production of more moles of C₂H₄ and H₂.

Notes: Continuous monitoring of temperature and pressure is essential for optimizing production and ensuring safety in industrial processes.

By understanding these examples of using gas laws in stoichiometry, students and professionals can better appreciate the intricacies of gas behavior in chemical reactions, leading to more effective experimental designs and industrial applications.