The enzyme-catalyzed hydrolysis of urea(aq) can be represented as follows: CO(NH

Question

The enzyme-catalyzed hydrolysis of urea(aq) can be represented as follows:

CO(NH2)2(aq) + H2O(l) CO2(g) + 2NH3(aq)

The reaction is carried out in an open solution calorimeter with a calorimeter constant C=485 J/K for the dry calorimeter. When 3.0 g urea is dissolved to make 100 g solution (water + enzyme + pH buffer + urea) allowing hydrolysis to go to completion, the temperature changes from changes from 21.05 to 18.23 oC. The specific heat of the solution is 4.25 J/(K.g).

a) Calculate the molar enthalpy of hydrolysis of urea.

b) Using the needed values from the thermodynamic tables, calculate the standard molar entropy change, Smo of the hydrolysis reaction.

c) Again using the needed values from the thermodynamic tables, calculate the standard molar Gibbs energy change, Gmo of the reaction.

Explanation / Answer

For the hydrolysis of urea

a) change in temperature (dT) = 18.23 - 21.05 = -2.82 oC

Total mass of solution (m) = 100 g

mass of urea = 3 g

moles of urea = 3 g/60.06 g/mol = 0.05 moles

specific heat of solution = 4.25 J/g.K

heat capacity of calorimeter = 485 J/K

So,

heat released (q) = mCpdT

                            = 100 x 4.25 x -2.82 + 485 x -2.82

                            = -2566.2 J

molar enthalpy of hydrolysis of urea = 2566.2 J/0.05 moles x 1000 = 51.324 kJ/mol

b)

dSo(rxn) = dSo(products) - dSo(reactants)

               = (213.68 + 2 x 113.39) - (104.60 + 69.91)

               = 265.95 J/K.mol

c) dGo(rxn) = dGo(products) - dGo(reactants)

                   = (-394.38 + 2 x -16.48) - (-196.82 - 237.18)

                   = 6.66 kJ/mol

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