Reaction kinetics for the solid - state reaction of ${alpha}-Al_2O_3$with amorphous $SiO_2$to produce mullite ($3Al_2O_3;{cdot};2SiO_2$) was studied in the temperature range of 1450~$1480^{circ}C$. Rate of kinetic reaction were determined by using $SiO_2$- coated $Al_2O_3$ compact containing 28.16 wt.% $SiO_2$and heating the reactant mixtures in MgO at definite temperature for various times. Amount of products and unreacted reactants were determined by X-ray diffractometry. Data from the volume fraction and ratio of peak intensities of mullite indicated that the reaction of ${alpha}-;Al_2O_3$ with $SiO_2$to form $3Al_2O_3;{cdot};2SiO_2$ start between 1450 and $1480^{circ}C$. The activation energy for solid-state reaction was determined by using the Arrhenius equation; The activation energy was 31.9 kJ/mol.