how to calculate the heat of combustion at 300 kelvin , when the standard enthalpies are given of benzoic acid, carbon dioxide and water at constant pressure and volume

To calculate the heat of combustion at 300 Kelvin using the standard enthalpies of benzoic acid, carbon dioxide, and water, you need to follow these steps:

1. Write the balanced chemical equation for the combustion reaction. In this case, the balanced equation for the combustion of benzoic acid is:

C6H5COOH + 15/2O2 → 7CO2 + 3H2O

2. Determine the stoichiometric coefficients. In the balanced equation, the stoichiometric coefficients tell you the number of moles of each substance involved in the reaction. In this case, the stoichiometric coefficients are 1 for benzoic acid, 15/2 for oxygen (O2), 7 for carbon dioxide (CO2), and 3 for water (H2O).

3. Look up the standard enthalpies of formation (ΔH°f) for benzoic acid (C6H5COOH), carbon dioxide (CO2), and water (H2O) at constant pressure and volume. The standard enthalpies of formation represent the heat released or absorbed when 1 mole of a substance is formed from its constituent elements. Make sure the ΔH°f values you are using are given at the same temperature (usually at 298 K or 25°C) and in the same units.

4. Calculate the ΔH° for the reaction using the standard enthalpies of formation. The ΔH° is the difference between the sum of the standard enthalpies of formation of the products and the sum of the standard enthalpies of formation of the reactants, multiplied by their respective stoichiometric coefficients. Using the balanced equation and the standard enthalpies of formation, you can set up the equation as follows:

ΔH° = (7 × ΔH°f(CO2) + 3 × ΔH°f(H2O)) - (ΔH°f(C6H5COOH) + 15/2 × ΔH°f(O2))

5. Plug in the values for the standard enthalpies of formation from your reference source and calculate the ΔH°. Make sure to convert any units if necessary. For example, if the standard enthalpies of formation are given in kJ/mol, make sure you convert the stoichiometric coefficients to moles if they are in a different unit.

6. Finally, apply the temperature correction to account for the combustion occurring at 300 Kelvin instead of the standard temperature (298 K). The standard enthalpies of formation are given at a specific temperature, so you need to adjust for the change in temperature using the equation:

ΔH = ΔH° + (Tfinal - Tinitial) × Cp

where ΔH is the actual enthalpy change, ΔH° is the standard enthalpy change, Tinitial is the initial temperature (usually the standard temperature 298 K), Tfinal is the final temperature (300 K in this case), and Cp is the heat capacity of the system.

Remember to account for the signs of the ΔH values. A negative value indicates an exothermic reaction (heat is released), while a positive value indicates an endothermic reaction (heat is absorbed).

By following these steps and utilizing the provided standard enthalpy values, you should be able to calculate the heat of combustion of benzoic acid at 300 Kelvin.