Question

The heat of combustion of C₆H₅COOH (benzoic acid) at constant volume is measured in a bomb calorimeter at 300K and is found to be – 3199.76kJ mol^–1. Find the value of enthalpy change. (R = 8.31 JK^–1 mol^–1).

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Solution

The required thermochemical equation is,

bold C subscript bold 6 bold H subscript bold 5 bold COOH bold left parenthesis bold s bold right parenthesis bold space bold plus bold space bold 15 over bold 2 bold O subscript bold 2 bold left parenthesis bold g bold right parenthesis bold space bold rightwards arrow bold space bold 8 bold CO subscript bold 2 bold left parenthesis bold g bold right parenthesis bold space bold plus bold space bold 3 bold H subscript bold 2 bold O bold left parenthesis bold l bold right parenthesis bold Here bold space bold increment bold U bold space bold equals bold space bold minus bold 3199 bold. bold 76 bold space bold kJ bold space bold mol to the power of bold minus bold 1 end exponent bold space bold equals bold space bold minus bold 3199760 bold space bold J bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold R bold space bold equals bold space bold 8 bold. bold 31 bold space bold JK to the power of bold minus bold 1 end exponent bold space bold mol to the power of bold minus bold 1 end exponent bold space bold space bold space bold space bold space bold space bold increment bold n subscript bold g bold space bold equals bold space bold 7 bold minus bold 15 over bold 2 bold space bold equals bold space bold minus bold 1 over bold 2 bold space bold space bold space bold space bold space bold space bold space bold space bold K bold space bold equals bold space bold 300

We know that,

bold increment bold H bold space bold equals bold space bold increment bold U bold space bold plus bold space bold increment bold n subscript bold g bold RT

Substituting the values, we have,

bold increment bold H bold space bold equals bold space bold minus bold 3199760 bold space bold plus bold space open parentheses bold minus bold 1 over bold 2 close parentheses bold space bold left parenthesis bold 8 bold. bold 31 bold right parenthesis bold space bold cross times bold space bold 300

bold equals bold minus bold 3199760 bold minus bold space bold 1246 bold. bold 5 bold space bold equals bold space bold minus bold 3201006 bold. bold 5 bold space bold J bold space bold equals bold space bold minus bold 3201 bold space bold kJ bold space bold mol to the power of bold minus bold 1 end exponent

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