a 1.08 - g sample of benzoic acid (c₇h₆o₂) is burned in a constant - volume calorimeter that has a heat…

a 1.08 - g sample of benzoic acid (c₇h₆o₂) is burned in a constant - volume calorimeter that has a heat capacity of 7.97 kj/°c. the temperature increases from 19.6°c to 23.2°c.\na) determine the amount of heat released (in kj).\nb) determine the molar energy of combustion of benzoic acid (in kj/mol).

a 1.08 - g sample of benzoic acid (c₇h₆o₂) is burned in a constant - volume calorimeter that has a heat capacity of 7.97 kj/°c. the temperature increases from 19.6°c to 23.2°c.\na) determine the amount of heat released (in kj).\nb) determine the molar energy of combustion of benzoic acid (in kj/mol).

Answer

Explanation:

Step1: Calculate the temperature change

$\Delta T=T_2 - T_1=23.2^{\circ}C - 19.6^{\circ}C = 3.6^{\circ}C$

Step2: Calculate the heat released by the reaction (using $q = C\Delta T$)

$q = C\Delta T$, where $C = 7.97\ kJ/^{\circ}C$ and $\Delta T=3.6^{\circ}C$. So $q=7.97\ kJ/^{\circ}C\times3.6^{\circ}C = 28.692\ kJ$

Step3: Calculate the molar mass of benzoic acid ($C_7H_6O_2$)

The molar mass of $C$ is $12.01\ g/mol$, $H$ is $1.01\ g/mol$ and $O$ is $16.00\ g/mol$. $M=(7\times12.01 + 6\times1.01+2\times16.00)\ g/mol=(84.07 + 6.06 + 32.00)\ g/mol = 122.13\ g/mol$

Step4: Calculate the number of moles of benzoic acid

$n=\frac{m}{M}$, where $m = 1.08\ g$ and $M = 122.13\ g/mol$. So $n=\frac{1.08\ g}{122.13\ g/mol}\approx0.00884\ mol$

Step5: Calculate the molar energy of combustion

$\Delta E=\frac{q}{n}$, where $q = 28.692\ kJ$ and $n = 0.00884\ mol$. So $\Delta E=\frac{28.692\ kJ}{0.00884\ mol}\approx3246\ kJ/mol$

Answer:

a) $28.692$ b) $3246$