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The rate constant for the decomposition of N_(2)O_(5) at various temperature is given below : {:(T//^(@)C,0,20,40,60,80),(10^(5)xxk//s^(-1),0.0787,1.70,25.7,178,2140):} Draw a graph between In k & 1//T , calculate the values of A and E_(a) . Predict the rate constant at 30^(@)& 50^(@)C. |
Answer» Solution :From the GIVEN data, we have `slope =(y_(2)-y_(1))/(x_(2)-x_(1))=(-14.055-(-3.84))/((3.66-2.83)xx10^(-3))=10.215xx10^(3)` From Arrhenius equation , `-(E_(a))/(R)` = slope or , `E_(a)=(-"slope"xxR)` `=-(-10.215xx10^(3)xx8.314)-102.322"kJ.mol"^(-1)` Also, In k `In A-(E_(a))/(RT) " or, ""InA"=Ink+(E_(a))/(RT)` or, `A=ke^(-E_(a)//RT)` At `40^(@)C, A = 25.7xx10^(-5)exp[(102322)/(8.314xx313)]=3.06xx10^(13)s^(-1)` At `30^(@)C, T =303K therefore(1)/(T)=3.3xx10^(-3)K^(-1)` From the plot , Ink`=-9.62 therefore k = 6.64xx10^(-5)s^(-1)` At `50^(@)C, T =323K therefore(1)/(T)=3.1xx10^(-3)K^(-1)` From the plot , Ink = -7.15`therefore k = 7.8xx10^(-4)s^(-1)` |
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