Kinetics law in homogeneous closed systems

However, for ideal mixtures, if is the molar volume of component A, the total volume at time t is  

Moreover in the second part of the speed-concentration relation, we can replace each concentration by using relation [1.30]. We are thus led to a differential expression with a single function the fractional extent and a variable, whose integration time gives the variation of fractional extent with time. It is then possible to return to [1.30] in order to obtain the variation of all the principle components (reactants and products). 

To illustrate this, we apply this method to hydrogen bromide synthesis for which the volumetric speed-concentration relation is relation [7.54], which will be written as follows  

Let us assume that at the initial time the firactional extent is zero. There is no hydrogen bromide and the reactants are in the stoichiometric proportions. Thus  

This is a gas-phase reaction with conservation of the number of moles of gas. The volume therefore remains constant and thus, from [7.82] and [7.87], we obtain  

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