How to find equilibrium concentration with the given intial concentrations

If you have given the intial concentration of any one species in a reaction and you need to find the equilibrium concentration of each species then what you need to do in such a case; this is what i am explaining here: 

Suppose you place known amounts of reactants in a vessel and let the mixture come to equilibrium.To obtain the composition of the equilibrium mixture,you need to determine the amount of only one of the substances.The amounts of others can be calculated from the amounts originally placed in the vessel and the equation that represents the reaction.

A simple example can explain this:

Example: Carbon monoxide and hydrogen react according to the following equation ;

                         CO (g) + 3H2 (g) <--------------> CH4 (g) + H2O (g)

When 1.00 mol CO and 3.00 mol H2 are placed in a 10.00 L vessel at 927 degree celcius and allowed to come to equilibrium,the mixture is found to contain 0.387 mol H2O .What is the molar composition of the equilibrium mixture?

Answer: The problem involves or starting amounts of reactants.These amounts change as reaction occurs.Later the reaction comes to equilibrium and you analyze the reaction mixture for the amounts of one of the reactants or products.It is convinient to solve this problem using ICE equations.Like this

Amount                   CO (g) + 3H2 (g) <--------------> CH4 (g) + H2O (g)




You fill in the starting amounts from the values given in the problem  statement.You are not given expilicit values for the cahnges that occur, so you let x be the molar change.That is, each product by x moles coefficients of substances in the balanced equation.Reactants decrease by x moles multiplied by the corresponding coefficiets.The decrease is indicated by a negative sign.Equilibrium values are equal  to starting values plus the changes.


Amount                   CO (g) + 3H2 (g) <--------------> CH4 (g) + H2O (g)

Starting         1.00                        3.00                            0               0

Change            -x                            -x                                +x            +x 

Equilibrium     1.00-x                    3.00-3x                         x               x= 0.387


The problem statement gives the equilibrium amount for H2O.This tells you that x= 0.387 mol.Calculate equilibrium amounts for other substances from the expressions given in the table,using this value of x.

                  Equilibrium amount CO = 1.000 - x ) mol= 1.000 - 0.387 mol

                  Equilibrium amount of H2 = 3.00 - 3x = 3.00 - 3x 0.387 =1.839  mol

                   equilibrium amount of CH4 = x mol = 0.387 mol 


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