Problem 88 - Chemistry and Chemical Reactivity

Question

A bomb calorimetric experiment was run to determine the enthalpy of combustion of ethanol. The reaction is $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ The bomb had a heat capacity of \(550 \mathrm{J} / \mathrm{K},\) and the calorimeter contained \(650 \mathrm{g}\) of water. Burning \(4.20 \mathrm{g}\) of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)\) resulted in a rise in temperature from \(18.5^{\circ} \mathrm{C}\) to \(22.3^{\circ} \mathrm{C} .\) Calculate the enthalpy of combustion of ethanol, in \(\mathrm{kJ} / \mathrm{mol}\).

Step-by-Step Solution

Answer

The enthalpy of combustion of ethanol is approximately \(-136.3 \, \mathrm{kJ/mol}\).

Step 1: Determine the Temperature Change

First, calculate the temperature change (denoted as \( \Delta T \)). The initial temperature is \( 18.5^{\circ} \mathrm{C} \) and the final temperature is \( 22.3^{\circ} \mathrm{C} \). Thus,\[ \Delta T = 22.3 - 18.5 = 3.8^{\circ} \mathrm{C}. \]

Step 2: Calculate Heat Absorbed by Calorimeter

Calculate the heat absorbed by the calorimeter, using the formula \( q_{\text{cal}} = C_{\text{cal}} \cdot \Delta T \), where \( C_{\text{cal}} \) is the heat capacity of the calorimeter (\( 550 \, \mathrm{J/K} \)). Thus, \[ q_{\text{cal}} = 550 \, \mathrm{J/K} \times 3.8 \, \mathrm{K} = 2090 \, \mathrm{J}. \]

Step 3: Calculate Heat Absorbed by Water

Calculate the heat absorbed by the water using the formula \( q_{\text{water}} = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the water (\( 650 \, \mathrm{g} \)), \( c \) is the specific heat capacity of water (\( 4.18 \, \mathrm{J/gK} \)), and \( \Delta T = 3.8 \, \mathrm{K} \). Hence, \[ q_{\text{water}} = 650 \, \mathrm{g} \times 4.18 \, \mathrm{J/gK} \times 3.8 \, \mathrm{K} = 10331.4 \, \mathrm{J}. \]

Step 4: Calculate Total Heat Released

The total heat released by the combustion of ethanol is the sum of the heat absorbed by both the calorimeter and the water: \[ q_{\text{total}} = q_{\text{cal}} + q_{\text{water}} = 2090 \, \mathrm{J} + 10331.4 \, \mathrm{J} = 12421.4 \, \mathrm{J}. \]

Step 5: Convert Total Heat to Kilojoules

Convert the total heat released to kilojoules since the problem requests the enthalpy change in \( \mathrm{kJ/mol} \): \[ q_{\text{total}} = 12421.4 \, \mathrm{J} = 12.4214 \, \mathrm{kJ}. \]

Step 6: Calculate Moles of Ethanol Burned

Determine the moles of ethanol burned using its molar mass. The molar mass of ethanol (\( \mathrm{C}_2\mathrm{H}_5\mathrm{OH} \)) is \( 46.07 \, \mathrm{g/mol} \). With \( 4.20 \, \mathrm{g} \) of ethanol burned, the moles of ethanol is \[ n = \frac{4.20 \, \mathrm{g}}{46.07 \, \mathrm{g/mol}} = 0.09115 \, \mathrm{mol}. \]

Step 7: Calculate Enthalpy of Combustion

Calculate the enthalpy of combustion per mole of ethanol using the formula \( \Delta H = \frac{q_{\text{total}}}{n} \): \[ \Delta H = \frac{12.4214 \, \mathrm{kJ}}{0.09115 \, \mathrm{mol}} \approx -136.3 \, \mathrm{kJ/mol}. \] The enthalpy is negative because combustion is an exothermic process.

Key Concepts

Understanding Bomb Calorimetry

Bomb calorimetry is a technique used to measure the heat of combustion of a substance. It involves a bomb calorimeter, which is a sealed container that withstands high pressure.
In a bomb calorimeter, a sample (like ethanol) is placed inside and ignited to react with oxygen. This setup ensures that the high-pressure conditions favor complete combustion. As the reaction occurs, the heat generated by the combustion is transferred to the surrounding water and the calorimeter itself.
Here's how bomb calorimetry works:

• The sample is burned completely in a constant-volume environment known as a bomb.
• As the sample burns, it releases heat that changes the temperature of the calorimeter and the water within.
• By measuring the temperature change ( abla T), and knowing the heat capacity of the calorimeter and water, the total heat released by the reaction can be calculated.

This makes bomb calorimetry a reliable method for determining the enthalpy change of combustion, which is particularly useful in experiments involving flammable liquids like ethanol.

Exploring Chemical Thermodynamics

Chemical thermodynamics deals with the direction and extent of chemical reactions. It helps us understand energy changes during chemical processes like combustion.
Enthalpy ( abla H) is a key concept in chemical thermodynamics. It represents the heat content of a system at constant pressure. For reactions occurring in a bomb calorimeter, however, the volume remains constant instead of the pressure.
In this context, we still use enthalpy but make special adjustments since we're measuring in constant volume.

• The enthalpy change ( abla H) of a reaction is related to the heat change ( abla Q) at constant volume.
• For the combustion reaction of ethanol, we calculate how much heat is released per mole, considering the heat absorbed by both the calorimeter and the water.
• The total heat change in the system is then divided by the number of moles of ethanol burned to find abla H, providing the enthalpy of combustion.

Understanding chemical thermodynamics highlights how energy is conserved and transferred, offering crucial insight into the potential energy dynamics in chemical reactions.

Exothermic Reactions Explained

Exothermic reactions are chemical processes that release energy, usually in the form of heat, to the surroundings. Combustion reactions, like that of ethanol, are classic examples of exothermic processes.
During an exothermic reaction, the energy required to break bonds in the reactants is less than the energy released when bonds are formed in the products. This difference in energy is what causes the temperature of the surroundings to increase.
Key points about exothermic reactions include:

• Enthalpy changes are typically negative, indicating that energy is being released rather than absorbed.
• They often result in a noticeable temperature rise, as heat is a product of the reaction.
• These reactions are spontaneous and usually release a considerable amount of energy, making them very important in industrial applications and energy production.

Understanding exothermic reactions helps explain why certain reactions occur naturally and inform how we can harness these reactions for practical uses, such as generating heat and power.