How Do You Calculate CO Concentration at Equilibrium in a Gaseous Reaction?

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Discussion Overview

The discussion revolves around calculating the concentration of carbon monoxide (CO) at equilibrium in a gaseous reaction involving CO and oxygen (O2) to produce carbon dioxide (CO2). The context is a homework problem that requires understanding of equilibrium constants and stoichiometry.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant presents the equilibrium expression and attempts to set up the problem using the initial concentrations of CO and O2.
  • Another participant suggests that since the equilibrium constant is large, the reaction will favor the products, indicating that the amount of CO2 will be nearly stoichiometric.
  • A different approach is proposed by starting with CO2 and O2 to simplify the calculations, suggesting that x (the change in moles) will be small.
  • One participant explains that stoichiometry allows for the equivalence of starting with reactants or products, asserting that the equilibrium state will remain unchanged regardless of the starting point.

Areas of Agreement / Disagreement

Participants express different approaches to the problem, with no consensus on the best method to calculate the equilibrium concentration of CO. The discussion remains unresolved regarding the assumptions and calculations needed to arrive at a solution.

Contextual Notes

There are uncertainties regarding the assumptions that should be made in the calculations, particularly how to relate the different starting conditions (reactants vs. products) to the equilibrium concentrations.

zorro
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Homework Statement


At a certain temperature, the equilibrium constant for the gaseous reaction of CO with O2 to produce CO2 is 5000 lit/mole. Calculate [CO] at equilibrium, if 1 mol each of CO and O2 afre placed in a 2 L vessel and allowed to come to equilibrium.


Homework Equations





The Attempt at a Solution



Concentration at equilibrium
CO= 1-x
O2= 1-x/2
CO2=x where x is the no of moles dissociated

Kc=x^2/(1-x)^2(1-x/2)=5000

I don't understand what assumption I should make to solve this.
answer is [CO]= 0.014
 
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I have not tried to solve, so it is possible there will be some more hurdles, but first step is more or less obvious - equilibrium is shifted far to the right, so amount of product is almost stoichiometric.

I have a gut feeling that it will be better to approach the question from the other end - assume you started with 1 mole of CO2 and half mole of oxygen. x will be very small then and approximations will be much more obvious.
 
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As you said I took 1 mole CO2 and half mole O2
and got x value as 0.058 (moles of CO)
But how do we relate this the problem (1 mole CO and 1 mole O2)
 
Through stoichiometry. If total amount of substances present is identical, it doesn't matter if you start with products or reactants, equilibrium is the same.
 
Last edited by a moderator:

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