Assume water boils at 100oC in Houston (near sea level), and at 90oC in Cripple Creek, Colorado (near 9500 ft ). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what is Ea for this process?
Using Arrhenium equation
In (k1k2)=(\frac{k_1}{k_2})=(k2k1)= −Ea[1T1−1T2]R-\frac{E_a[\frac{1}{T_1}-\frac{1}{T_2}]}{R}−REa[T11−T21]
k1=14.5k_1=\frac{1}{4.5}k1=4.51
k2=14.8k_2=\frac{1}{4.8}k2=4.81
T1=273+100T_1=273+100T1=273+100
=373K=373K=373K
T2=273+90T_2=273+90T2=273+90
=363K=363K=363K
R=R=R= Gas constant
=8.314Joules/Kelvin.mol=8.314Joules/Kelvin .mol=8.314Joules/Kelvin.mol
In4.84.5=−Ea8.314[1373−1363]In\frac{4.8}{4.5}=\frac{-E_a}{8.314} \begin{bmatrix} \frac{1}{373}&-\frac{1}{363} \end{bmatrix}In4.54.8=8.314−Ea[3731−3631]
0.064539×8.314=Ea×0.0000738560.064539×8.314=E_a×0.0000738560.064539×8.314=Ea×0.000073856
Ea=7265.2Joules/molE_a=7265.2Joules/molEa=7265.2Joules/mol
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