Refining petroleum involves cracking large hydrocar- bon molecule...

Question

Refining petroleum involves cracking large hydrocar- bon 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?

Accepted Answer

Hello. In this problem we are told that hefting a component of gasoline undergoes thermal cracking to produce methane and painting At 700 Kelvin obtain having a pressure of 30 atmospheres is heated in a closed vessel at constant volume. What is the total pressure at equilibrium? And were asked to calculate the percentage of obtain converted to ethane and painting. Let's begin by creating an ice table from there. We can determine then our equilibrium partial pressures of our three gasses. Zoe I have a reaction to obtain and going to form a sane and painting then have initial change in equilibrium. Initially our pressure of captain is 30 atmospheres. We have no ethane or painting are changes minus X plus X plus X equilibrium. We have the initial plus the change so 30 minus X. X. And X. Writing our equilibrium constant expression. Then we have the partial pressure of ethane times of partial pressure of painting all over the partial pressure of obtain. So making use of the values in our ice table. This is the N. X times X. All over 30 -1. Which we're told this is equal to 20. Then this simplifies to X squared and we moved the denominator over to the right hand side. We have 20 times 30 minus X Which works out to 600 -20x. Move everything over to the left hand side. That is equal to zero. So now we're gonna solve our quadratic equation. So X is equal to negative B plus or minus the square root of B squared minus four A. C. All over two. A. Making use of the values in our Equation, then X. is equal to -20. Also minus the square root of 20 squared -4 times one. Times -600. All over two a. so two times one simplifying what's shown in the square root. This works out to the 20 Plus or -2.9. Goodbye. two x 2. So we get to Fruits. So the first one we get 16.458 And the other one is equal to a negative 36.4575. So a negative partial pressure doesn't make sense. So we eliminate that one. So based on our ice table then X is equal to the equilibrium partial pressure of methane and panting. So they're equal to 16.5 atmospheres. And then our equilibrium partial pressure. Captain is equal to 30 minus X. So this then works out to 13.5 atmospheres. So our total pressure Then it defaulted some of the pressure for the three gasses. So ethane and Pantene are both 16.5 atmospheres At equilibrium and that of hip pain is 13. Atmospheres. So our total pressure works out to 46.5 atmospheres. Were also asked to determine the amount of pain that is converted. So looking at the ice table, we see that the amount of time that is converted equal to X. We take that divided by our original pressure 15. So this works out then to 16.5 atmospheres over atmospheres. And then we're gonna multiply this by in a percentage. It works out then to 55 of the 15, then is converted to our products. Thanks for watching. Hope this help.

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