Refining petroleum involves cracking large hydrocarbon molecules into smaller, more volatile pieces. A simple example of hydrocarbon cracking is the gas-phase thermal decomposition of butane to give ethane and ethylene: (c) A sample of butane having a pressure of 50 atm is heated at 500 °C in a closed container at constant volume. When equilibrium is reached, what percentage of the butane has been converted to ethane and ethylene? What is the total pressure at equilibrium?

Verified step by step guidance

1. Write the balanced chemical equation for the decomposition of butane: \[ \text{C}_4\text{H}_{10(g)} \rightarrow \text{C}_2\text{H}_{6(g)} + \text{C}_2\text{H}_{4(g)} \]
2. Define the initial conditions: Initial pressure of butane is 50 atm, and the initial pressures of ethane and ethylene are 0 atm.
3. Set up an ICE (Initial, Change, Equilibrium) table to track the changes in pressure for each species. Let 'x' be the change in pressure for butane that decomposes.
4. Express the equilibrium pressures in terms of 'x': \[ P_{\text{C}_4\text{H}_{10}} = 50 - x \], \[ P_{\text{C}_2\text{H}_6} = x \], \[ P_{\text{C}_2\text{H}_4} = x \].
5. Calculate the total pressure at equilibrium: \[ P_{\text{total}} = (50 - x) + x + x = 50 + x \].

Key Concepts

Hydrocarbon Cracking

Hydrocarbon cracking is a chemical process that breaks down large hydrocarbon molecules into smaller, more useful ones, typically through heat or catalysts. This process is essential in petroleum refining, as it increases the yield of lighter hydrocarbons like ethane and ethylene, which are valuable for fuel and chemical production. Understanding the mechanisms and products of cracking is crucial for predicting the outcomes of reactions involving hydrocarbons.

Equilibrium in Chemical Reactions

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products over time. In the context of the butane cracking reaction, reaching equilibrium means that the amounts of butane, ethane, and ethylene will stabilize, allowing for the calculation of conversion percentages and total pressure. The concept of equilibrium is fundamental in predicting the behavior of reactions under specific conditions.

Gas Laws and Pressure Calculations

Gas laws describe the relationships between pressure, volume, temperature, and the number of moles of a gas. In this scenario, the ideal gas law (PV=nRT) can be applied to determine the total pressure at equilibrium after the reaction. Understanding how to manipulate these variables is essential for calculating the changes in pressure and volume that occur during the cracking process, especially in a closed system.