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The water in a pressure cooker boils at a temperature greater than 100 degree C

ID: 537943 • Letter: T

Question

The water in a pressure cooker boils at a temperature greater than 100 degree C because it is under pressure. At this higher temperature, the chemical reactions associated with the cooking of food take place at a greater rate. (a) Some food cooks fully in 6.00 min in a pressure cooker at 120.0 degree C and in 48.0 minutes in an open pot at 100.0 degree C. Calculate the average activation energy for the reactions associated with the cooking of this food. kJ mol^-1 (b) How long will the same food take to cook in an open pot of boiling water at an altitude of 8500 feet, where the boiling point of water is 91.4 degree C? min

Explanation / Answer

(a.) By using the equatin

ln (k2 / k1) = (Ea/R) (1/T1 - /T2)

where T1 = 120 C = 120 + 273 = 393 K

     T2 = 100 + 273 = 373 K

Rate constant is inversely proportional to time.

Therefore, k1 = 1/6min-1 and k2 = 1/48 min-1

R = 8.314 J/mol K

Substituting all these values in the above equation, we get:

            ln(6/48) = Ea/8.314 (1/393 – 1/373)

           -2.07944154 = Ea/8.314 *( -0.000136436)

             Ea = (-2.07944154 *8.314 )/(-0.000136436)

           Ea = 126715.0276 J/mol

           Ea = 126.72 kJ/mol

b) At 8500 feet, water boils at 91.4 oC, T1 = 91.4 +273 K (364.4 K) at t1 = ? min

   At sea level, food boils at 100 oC, T2 = 373 K and time 48 min

Applying the same equation:

              ln (k2 / k1) = (Ea/R) (1/T1 - /T2)

             ln (t1/48) = (126715.02 J/mol)/8.314 J/molK [1/364.4 – 1/373]

ln (t1/48) = 15241.16198* [6.3272 x 10-5]

                 = 0.964338104

        t1/48 = e(0.964338104)

     t1 = 48 *2.623

      t1 = 125.9 min