PSPM 2019/2020 Ethanol, $$ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} $$ is produced from fermentation of sugarcane and widely used as an alternative fuel to replace petrol. A 1.00 g sample of ethanol was burnt in a bomb calorimeter, which has total heat capacity of $$ 11.0 \mathrm{~kJ}{ }^{\circ} \mathrm{C}^{-1} $$. The temperature of the calorimeter and its contents increased from $$ \frac{25.0^{\circ} \mathrm{C}}{\mathrm{T}} $$ to $$ \frac{27.7^{\circ} \mathrm{C} ext {. }}{\mathrm{Tf}} $$ (i) Write a balanced chemical equation for the reaction that takes place in the (ii) Calculate the enthalpy of combustion of ethanol per mole.

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PSPM 2019/2020 Ethanol, $$ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} $$ is produced from fermentation of sugarcane and widely used as an alternative fuel to replace petrol. A 1.00 g sample of ethanol was burnt in a bomb calorimeter, which has total heat capacity of $$ 11.0 \mathrm{~kJ}{ }^{\circ} \mathrm{C}^{-1} $$. The temperature of the calorimeter and its contents increased from $$ \frac{25.0^{\circ} \mathrm{C}}{\mathrm{T}} $$ to $$ \frac{27.7^{\circ} \mathrm{C} 	ext {. }}{\mathrm{Tf}} $$ (i) Write a balanced chemical equation for the reaction that takes place in the (ii) Calculate the enthalpy of combustion of ethanol per mole.

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**Problem:**
Ethanol, $$ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} $$, is produced from the fermentation of sugarcane and is widely used as an alternative fuel to replace petrol. A 1.00 g sample of ethanol was burnt in a bomb calorimeter, which has a total heat capacity of $$ 11.0 \, \mathrm{kJ} \, {}^\circ\mathrm{C}^{-1} $$. The temperature of the calorimeter and its contents increased from $$ 25.0^{\circ} \mathrm{C} $$ to $$ 27.7^{\circ} \mathrm{C} $$.

**(i) Balanced Chemical Equation for the Combustion of Ethanol:**

The combustion of ethanol involves reacting ethanol with oxygen to produce carbon dioxide and water. The balanced chemical equation is:

$$
\boxed{\mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{OH}(l) + 3\, \mathrm{O}_{2}(g) \rightarrow 2\, \mathrm{CO}_{2}(g) + 3\, \mathrm{H}_{2}\mathrm{O}(l)}
$$

**(ii) Calculation of the Enthalpy of Combustion of Ethanol per Mole:**

To calculate the enthalpy of combustion ($$ \Delta H_{\text{comb}} $$) per mole of ethanol, follow these steps:

1. **Determine the Heat Released ($$ q $$):**

The heat absorbed by the calorimeter is given by:
   $$
   q = C \times \Delta T
   $$
   Where:
   - $$ C = 11.0 \, \mathrm{kJ} \, {^\circ\mathrm{C}}^{-1} $$ (heat capacity)
   - $$ \Delta T = 27.7^{\circ}\mathrm{C} - 25.0^{\circ}\mathrm{C} = 2.7^{\circ}\mathrm{C} $$

$$
   q = 11.0 \times 2.7 = 29.7 \, \mathrm{kJ}
   $$

2. **Calculate the Moles of Ethanol Burnt:**

The molecular weight of ethanol ($$ \mathrm{C}_{2}\mathrm{H}_{6}\mathrm{O} $$) is:
   $$
   \text{Molecular Weight} = (2 \times 12.01) + (6 \times 1.008) + 16.00 = 46.07 \, \mathrm{g/mol}
   $$
   
   Moles of ethanol:
   $$
   \text{Moles} = \frac{1.00 \, \mathrm{g}}{46.07 \, \mathrm{g/mol}} \approx 0.0217 \, \mathrm{mol}
   $$

3. **Determine the Enthalpy of Combustion per Mole:**

The enthalpy of combustion per mole is:
   $$
   \Delta H_{\text{comb}} = \frac{q}{\text{moles}} = \frac{29.7 \, \mathrm{kJ}}{0.0217 \, \mathrm{mol}} \approx 1366 \, \mathrm{kJ/mol}
   $$
   
   Since combustion is an exothermic process, the enthalpy change is negative:
   $$
   \Delta H_{\text{comb}} \approx -1.36 \times 10^{3} \, \mathrm{kJ/mol}
   $$

**Final Answer:**

**(i)** The balanced combustion equation is
$$
\mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{OH}(l) + 3\, \mathrm{O}_{2}(g) \rightarrow 2\, \mathrm{CO}_{2}(g) + 3\, \mathrm{H}_{2}\mathrm{O}(l)
$$
**(ii)** The enthalpy of combustion of ethanol is –1.36 × 10³ kJ/mol.
**(i)** The balanced equation for burning ethanol is: $$ \mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{OH}(l) + 3\, \mathrm{O}_{2}(g) \rightarrow 2\, \mathrm{CO}_{2}(g) + 3\, \mathrm{H}_{2}\mathrm{O}(l) $$ **(ii)** The enthalpy of combustion of ethanol is –1.36 × 10³ kJ/mol.

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