The unimolecular decomposition of urea in aqueous solution is measured at two di
ID: 485630 • Letter: T
Question
The unimolecular decomposition of urea in aqueous solution is measured at two different temperatures, and the following data are observed: Determine the activation energy for this reaction. Express your answer to three significant figures with the appropriate units. Determine the Arrhenius factor for this reaction. Express your answer to one significant figure with the appropriate units. Using the Arrhenius parameters, determine delta H^as described by the equation for trial 1. Express your answer to one significant figure with the appropriate units.Explanation / Answer
The reaction is NH2CONH2+H2O --->CO2(g) +2NH3(g)
From Arhenius Equation, K= Ko E-Ea/RT
lnK= lnK0-Ea/RT
So a plot of 1/T Vs lnK gives a straight line whose slope is -Ea/R and intercept is lnK0 since there are only two points, grpah is not required
l ln(K2/K1)= (Ea/R)*(1/T1-1/T2) T1= 60+273.15= 333.15K and T2= 71.5+273.15=344.65K
ln (4.4/1.2)= (Ea/R)*(1/333.15-1/344.65)
1.299= (Ea/R)*0.0001
Ea/R = 1.299/0.0001=12970
Ea= 12970*8.314=107833 Joules/mole.
Enthalpy change
Ho = [CO2 + (2)NH3] - [CO(NH2)2 + H2O]
= [ -393.5 + (2)-46.19 ] - [ -319.2 - 285.9 ]
= (-485.9 kJ) - (-605.1)
= +119.2 kJ
Entropy change So =213.6+2*192.5- [173.8+69.96) J/mol.K=354.84 J/mol.K =0.354 Kj/mol.K
Gibbs free energy chnage at 60deg.c = 119.2-(60+273.15)*0.354/1000=119.0821 Kj
Gibbs free energy change at 75 deg.c = 119.2.-(71.5+273.15)*0.354=119.078 Kj
Change in enthalpy = Change in internal energy+ nR*T
n= change in number of moles= 3
Change in internal enrgy at 60 deg.c = 119,2- 3*8.314*333.15/1000=110.89 Kj
Change in internal energy at 75.2 deg.c= 119.2- 3*8.314*348.35/1000=110.51Kj
Due to change in temperature, change in internal energy= 110.89-110.51=0.379 Kj
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