Problem 13 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For complete combustion of ethanol, $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(l) $$ the amount of heat produced as measured in bomb calorimeter, is \(1364.47\) \(\mathrm{kJ} \mathrm{mol}^{-1}\) at \(25^{\circ} \mathrm{C}\). Assuming ideality the enthalpy of combustion, \(\Delta_{\mathrm{c}} \mathrm{H}\), for the reaction will be: \(\left(\mathrm{R}=8.314 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)\) [Main 2014] (a) \(-1366.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-1361.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-1460.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-1350.50 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

(a) -1366.95 kJ mol^{-1}

Step 1: Understanding the Problem

We are given the heat of reaction (measured in a bomb calorimeter) for the combustion of ethanol and need to find the enthalpy of combustion \(\Delta_{\mathrm{c}} \mathrm{H} \). The formula for enthalpy change in terms of heat released in a bomb calorimeter is needed since the bomb calorimeter ensures constant volume.

Step 2: Formula for Enthalpy Change

For processes at constant volume (like in a bomb calorimeter), the heat \(q_v\) measured is equal to the change in internal energy \(\Delta U\). The relation to find the enthalpy change \(\Delta H\) is \(\Delta H = \Delta U + \Delta n_{\mathrm{gas}}RT\), where \(\Delta n_{\mathrm{gas}}\) is the change in moles of gas.

Step 3: Find Change in Moles of Gas

Compute \(\Delta n_{\mathrm{gas}} = n_{\mathrm{products}} - n_{\mathrm{reactants}}\). Here, the products are \(2 \mathrm{CO}_2(g)\) and the gaseous reactant is \(3 \mathrm{O}_2(g)\), so \(\Delta n_{\mathrm{gas}} = 2 - 3 = -1\).

Step 4: Compute Change in Enthalpy

We apply the formula: \(\Delta H = -1364.47 \mathrm{~kJ} + (-1) \times 8.314 \mathrm{~kJ} \mathrm{~mol}^{-1} \times 298 \mathrm{K}\). Simplifying, \(\Delta H = -1364.47 \mathrm{~kJ} - 2.48 \mathrm{~kJ} = -1366.95 \mathrm{~kJ}\).

Step 5: Compare with Options

The calculated enthalpy of combustion is \(\Delta H = -1366.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Upon examining the options, (a) \(-1366.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) is the correct choice.

Key Concepts

Bomb Calorimeter

A bomb calorimeter is a device used for measuring the heat of combustion of a particular reaction. This tool is pivotal in understanding how much energy is released or absorbed during a chemical reaction. In a bomb calorimeter, the sample is burned in a strong steel container, known as a "bomb," under a constant volume condition.

The process is designed to ensure that no heat escapes, allowing for accurate measurement of the energy changes involved. Unlike reactions that occur at constant pressure, bomb calorimeters work at constant volume, meaning they directly measure the change in internal energy (\(\Delta U\)) of the reaction.

This is important as it helps us understand the relationship between the heat measured (\(q_v\)) and the changes in internal energy. This type of measurement is crucial in determining how fuels such as ethanol behave during combustion, providing insight into their potential energy release in practical applications like engines or heaters.

Ethanol Combustion

Ethanol combustion involves the reaction of ethanol (\(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\)) with oxygen (\(\mathrm{O}_2\)) to produce carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2 \mathrm{O}\)). This reaction is exothermic, meaning it releases energy in the form of heat. The specific reaction for ethanol combustion is clearly defined as:

• \[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(l)\]

The energy released during this process can be measured using a bomb calorimeter, as it provides a constant volume environment ideal for tracking combustion reactions. The heat measured is an indicator of how much energy the fuel can release, which is an important factor in assessing the efficiency of ethanol as a renewable energy source.

Ethanol is often favored as a fuel due to its renewable nature and the cleaner combustion it offers compared to fossil fuels. Understanding the precise energy changes during its combustion helps in optimizing its use in various energy applications.

Heat of Reaction

The heat of reaction, also known as the enthalpy change (\(\Delta H\)), is a measure of the energy absorbed or released during a chemical reaction. It indicates the amount of heat that is transferred between the system and its surroundings at constant pressure. In the context of a bomb calorimeter, however, we're working with constant volume, so we need to relate the internal energy change (\(\Delta U\)) to the enthalpy change.

To calculate the enthalpy of combustion (\(\Delta_{\mathrm{c}} H\)) for ethanol, we start with the measured internal energy change and account for the difference caused by gas volume changes using the formula:

• \[\Delta H = \Delta U + \Delta n_{\mathrm{gas}} RT\]

Here, \(\Delta n_{\mathrm{gas}}\) is the change in moles of gas, and \(R\) is the gas constant. The product of \(\Delta n_{\mathrm{gas}} RT\) accounts for the work done on or by the system due to gas expansions or compressions.

By applying this formula, the enthalpy change (\(\Delta H\)) reflects both the energy measured directly and the adjustments due to pressure changes, allowing for an accurate understanding of the energy dynamics in reactions like ethanol combustion.