Balance with respect to solid carbon

The reaction rate (carbon consumption) at the interface is equal to the reactant A molar flow that reaches the interface  

Substituting this rate expression into Equation 19.19  

The time for complete solid consumption (r) is reached when R = 0. Substituting this condition into Equation 19.22, we obtain  

Then we can rearrange Equation 19.22 in order to obtain the following expression for the reaction time (solid consumption)  

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