Question

The Enthalpy of combustion of C$_6$H$_6$COOH(s) at 25$^\circ$C and 1.0 atm pressure is -2546 kJ/mol. What is the Internal energy change for this reaction?

• A. -2544.8 kJ
• B. -2539.8 kJ
• C. -2560.3 kJ
• D. -2552.2 kJ

Hint:

For combustion reactions, if there is no change in the number of moles of gas, the internal energy change is approximately the same as the enthalpy change.

Answer 1

The Correct Option is A

The relationship between the enthalpy (\(H\)) and internal energy (\(U\)) can be given by the following equation: \[ \Delta H = \Delta U + \Delta nRT \] Where: - \(\Delta H\) is the change in enthalpy (given as -2546 kJ/mol), - \(\Delta n\) is the change in the number of moles of gas in the reaction, 
- \(R\) is the gas constant (\(8.314 \, J \, mol^{-1} \, K^{-1}\)), 
- \(T\) is the temperature in Kelvin (298 K at 25°C). In the case of combustion, the combustion products (carbon dioxide and water) usually result in no change in the number of moles of gas (\(\Delta n = 0\)). 
Therefore, the internal energy change \(\Delta U\) is equal to the enthalpy change \(\Delta H\): \[ \Delta U = \Delta H \] Hence, the internal energy change for the reaction is -2544.8 kJ/mol.