Catalytic Hydrogenation Of Ethene A Stoichiometry Problem

In the realm of organic chemistry, understanding reaction mechanisms and stoichiometry is paramount. Catalytic hydrogenation, a crucial process in various industrial applications, exemplifies these principles. This article delves into a specific scenario involving a gaseous mixture of ethene, ethane, and hydrogen passed over a heated catalyst. We'll dissect the reaction, perform stoichiometric calculations, and determine the final composition of the mixture. So, guys, let's dive in and unravel the intricacies of this chemical transformation. We'll explore the fundamental concepts, step-by-step calculations, and practical implications of this reaction. By the end of this article, you'll have a solid grasp of catalytic hydrogenation and its application in determining the composition of gaseous mixtures. Remember, chemistry is all about understanding the interactions between molecules, and this example provides a perfect illustration of these interactions in action.

Catalytic hydrogenation is a chemical reaction where hydrogen gas (H₂) is added to a molecule, typically an unsaturated compound, in the presence of a catalyst. In this case, the unsaturated compound is ethene (C₂H₄), an alkene containing a carbon-carbon double bond. The catalyst, often a transition metal like platinum, palladium, or nickel, facilitates the reaction by providing a surface for the reactants to adsorb and react. The key to understanding this reaction lies in the breaking of the π-bond in ethene and the formation of new sigma (σ) bonds with hydrogen atoms. This process converts ethene into ethane (C₂H₆), a saturated alkane. This reaction is highly exothermic, meaning it releases heat, and is thermodynamically favorable. The catalyst plays a crucial role in lowering the activation energy of the reaction, thus making it proceed at a reasonable rate. Without the catalyst, the reaction would be extremely slow and impractical. The surface of the catalyst provides active sites where hydrogen molecules dissociate into individual hydrogen atoms. These hydrogen atoms then migrate across the surface and react with the adsorbed ethene molecules. The process is highly selective, meaning that the catalyst preferentially promotes the addition of hydrogen to the double bond, minimizing side reactions. Understanding the mechanism of catalytic hydrogenation is essential for predicting the outcome of the reaction and optimizing the reaction conditions. This reaction is widely used in various industrial processes, including the production of margarine from vegetable oils and the synthesis of various organic compounds.

To accurately determine the composition of the gaseous mixture after the reaction, we must employ stoichiometry, the branch of chemistry dealing with the quantitative relationships between reactants and products in chemical reactions. The balanced chemical equation for the hydrogenation of ethene is:

C₂H₄ (g) + H₂ (g) → C₂H₆ (g)

This equation reveals a crucial 1:1 stoichiometric ratio between ethene and hydrogen. This means that one mole of ethene reacts with one mole of hydrogen to produce one mole of ethane. This ratio is the cornerstone of our calculations. We can use this ratio to determine the amount of hydrogen consumed and the amount of ethane produced during the reaction. Guys, remember that stoichiometric coefficients represent the relative number of moles of each substance involved in the reaction. These coefficients are essential for converting between the amounts of different reactants and products. In this case, the coefficients tell us that for every 1 liter of ethene that reacts, 1 liter of hydrogen is consumed, and 1 liter of ethane is produced. This relationship allows us to track the changes in the volumes of each gas in the mixture. Stoichiometry provides a powerful tool for predicting the outcome of chemical reactions and for designing experiments to optimize the yield of desired products. By understanding the stoichiometric relationships, we can make quantitative predictions about the amounts of reactants needed and the amounts of products formed. This knowledge is crucial in various fields, including chemical synthesis, industrial production, and environmental chemistry. So, let's use this knowledge to solve the problem at hand.

We are given an initial gaseous mixture containing:

• 5 L of ethene (C₂H₄)
• 3 L of ethane (C₂H₆)
• 2 L of hydrogen (H₂)

The total initial volume is 5 L + 3 L + 2 L = 10 L. It's important to note that ethane, being a saturated compound, does not react under the given conditions. Only ethene will undergo hydrogenation. This is a key piece of information that simplifies our calculations. We need to determine the limiting reactant, which is the reactant that is completely consumed in the reaction. The limiting reactant dictates the maximum amount of product that can be formed. To identify the limiting reactant, we compare the mole ratio of reactants to the stoichiometric ratio from the balanced chemical equation. In this case, we have 5 L of ethene and 2 L of hydrogen. Since the stoichiometric ratio is 1:1, we can see that hydrogen is the limiting reactant because we have less hydrogen than ethene. This means that all 2 L of hydrogen will be consumed, and the amount of ethene that reacts will be determined by the amount of hydrogen available. The excess reactant is ethene, meaning that some ethene will remain unreacted after the reaction is complete. Guys, understanding the concept of limiting reactants is crucial for optimizing chemical reactions and maximizing the yield of the desired product. By carefully controlling the amounts of reactants, we can ensure that the limiting reactant is completely consumed, and the excess reactant is used efficiently. This principle is widely applied in industrial chemistry to improve the efficiency and economics of chemical processes.

Since hydrogen is the limiting reactant, all 2 L of H₂ will react. Based on the 1:1 stoichiometry, 2 L of C₂H₄ will also react. This means:

• Ethene consumed: 2 L
• Ethane produced: 2 L

Now, let's calculate the final volumes of each gas:

• Final volume of ethene (C₂H₄): Initial volume - Volume consumed = 5 L - 2 L = 3 L
• Final volume of ethane (C₂H₆): Initial volume + Volume produced = 3 L + 2 L = 5 L
• Final volume of hydrogen (H₂): 2 L - 2 L = 0 L (completely consumed)

Therefore, the final mixture contains 3 L of ethene and 5 L of ethane. There is no hydrogen remaining. Guys, these calculations demonstrate the power of stoichiometry in predicting the outcome of chemical reactions. By carefully considering the stoichiometric ratios and the limiting reactant, we can accurately determine the amounts of reactants and products involved in a reaction. This knowledge is essential for various applications, including chemical synthesis, industrial process design, and environmental monitoring.

Based on our calculations, the composition of the mixture after the reaction is:

• 3 L of ethene (C₂H₄)
• 5 L of ethane (C₂H₆)

This corresponds to answer option A. We have successfully determined the final composition of the gaseous mixture by applying the principles of stoichiometry and understanding the reaction mechanism of catalytic hydrogenation. This example illustrates the importance of a systematic approach to solving chemical problems, involving careful analysis of the given information, identification of the relevant chemical principles, and step-by-step calculations. Guys, remember that practice is key to mastering these concepts. The more problems you solve, the more confident you will become in your ability to apply these principles to different scenarios. Chemistry is a fascinating subject that reveals the intricate workings of the molecular world. By understanding the fundamental concepts and practicing problem-solving techniques, you can unlock the secrets of chemical transformations and make a positive impact on the world around you.

In summary, we've explored the catalytic hydrogenation of ethene, a fundamental reaction in organic chemistry. We've seen how stoichiometry dictates the quantitative relationships between reactants and products, and how the concept of limiting reactants determines the extent of the reaction. By carefully analyzing the given information and applying the principles of stoichiometry, we were able to accurately determine the final composition of the gaseous mixture. This example highlights the importance of a solid understanding of chemical principles in solving practical problems. Catalytic hydrogenation is not just a theoretical concept; it has significant industrial applications, such as in the production of margarine and various organic compounds. The ability to control and manipulate chemical reactions is crucial for developing new materials, designing efficient chemical processes, and addressing global challenges such as energy production and environmental sustainability. Guys, as you continue your journey in chemistry, remember that the principles you learn are not just confined to the classroom. They have the power to transform the world around you. By embracing the challenge of understanding complex chemical processes, you can contribute to innovation and make a positive impact on society.