At `300K` , the standard enthalpies of formation of `C_(6)H_(5)COOH_((s),CO_(2(g))` and `H_(2)O_((l))` are `-408,-393` and `-286kJ mol^(-1)` respectively. Calculate the heat of combustion of benzoic acid at
`(i)` constant pressure,
`(ii)` constant volume. `(R=8.31J mol^(-1)K^(-1))`

Explanation

To calculate the heat of combustion of benzoic acid (C₆H₅COOH) at both constant pressure and constant volume, we can follow these steps:

### Step 1: Write the combustion reaction
The combustion of benzoic acid can be represented as:
\[ \text{C}_6\text{H}_5\text{COOH}_{(s)} + \frac{13}{2} \text{O}_2_{(g)} \rightarrow 7 \text{CO}_2_{(g)} + 3 \text{H}_2\text{O}_{(l)} \]

### Step 2: Calculate the standard enthalpy change (ΔH) for the reaction
Using the standard enthalpies of formation provided:
...