Question

At 298 K the standard enthalpy of combustion of sucrose is -5645 kJ/mol and the standard reaction Gibbs energy is -5798 kJ/mol. Assume ∆H does not change to estimate the additional non-expansion work that may be obtained by raising the temperature to blood temperature, 37o C. Enter your answer in kJ/mol to two significant figures and do not enter the units.

Answer 1

Explanation:

The given data is as follows.

             T = 298 K,          $\Delta H^{o}$ = -5645 kJ/mol

          $\Delta G^{o}$ = -5798 kJ/mol

Relation between $\Delta H$ and $\Delta G$ are as follows.

          $\Delta G^{o}$ = $\Delta H^{o} - T \Delta S^{o}$    

             -5798 kJ/mol = -5645 kJ/mol - $298 \times \Delta S^{o}$

                       -153 kJ/mol = -$298 \times \Delta S^{o}$

                    $\Delta S^{o}$ = 0.513 kJ/mol K

Now, temperature is $37^{o}C$ = (37 + 273) K = 310 K

Since,        $\Delta G$ = $\Delta H^{o} - T \Delta S^{o}$

                            = $-5645 kJ/mol - 310 K \times 0.513 kJ/mol K$

                            = (-5645 kJ/mol - 159.03 kJ/mol)

                            = -5804.03 kJ/mol

As, change in Gibb's free energy = maximum non-expansion work

            $\Delta G = \Delta G_{310 K} - \Delta G_{298 K}$

                           = -5804.03 kJ/mol - (-5798 kJ/mol)

                           = -6.03 kJ/mol

Therefore, we can conclude that the additional non-expansion work is -6.03 kJ/mol.