Question

The heat capacity of a bomb calorimeter is found to be 5.25 kJ/degree C. When a 1.94 g sample of glucose (C_6H_12O_6, MM = 180.l6) is burned in the calorimeter, the final temperature recorded was 36.0 degree C. What is the quantity of heat (in kJ) release or absorbed by the reaction if the heat of combustion for glucose is -2.81 times 10^3 kJ/mole. (please include the proper sign in your numerical answer) What is the initial temperature (in degree C) of the calorimeter?

Answer 1

Ans. Given, heat of combustion of glucose = - 2.81 x 10³ kJ/mol. The -ve sign indicates that heat is being released during combustion.

Moles of glucose combusted in bomb calorimeter = Mass of glucose sample / Molar mass of glucose

                                    = 1.94 g / 180.16 g mol^-1

                                    = 0.01076821 moles

Amount of heat produced from combustion of 0.01076821 moles glucose =

                        Molar heat of combustion of glucose x moles of glucose

                        = - 2.81 x 10³ kJ/mol x 0.01076821 moles

                        = - 0.0303 x 10³ kJ

                        = - 30.3 kJ

Thus, combustion of given glucose sample releases 30.3 kJ heat

#1. Heat absorbed by calorimeter.

In calorimeter, the heat released by combustion of a sample (here, glucose) is absorbed by the calorimeter to increase its temperature.

Thus, heat absorbed by calorimeter = + 30.3 kJ. The +ve sign indicates that heat is being absorbed by the calorimeter.

#2. Let the initial temperature of calorimeter = T

Now,    q = C x dT        - equation 2

            where, q = heat gained by calorimeter = 30.3 kJ

C = heat capacity of calorimeter system = 5.25 kJ/⁰C

                        dT = Final – initial temperature = 36.0⁰C – T

Putting the values in above equation-

            30.3 kJ = 5.25 kJ/⁰C x (36.0⁰C – T)

            Or, 36.0⁰C – T = 30.3 kJ / (5.25 kJ/⁰C) = 5.77⁰C

            Or, -T = 5.77⁰C - 36.0⁰C = -30.23

            So, T = 30.23⁰C

Thus, initial temperature of calorimeter = 30.23⁰C