Problem 114 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard heat of combustion of \(\mathrm{Al}\) is \(-837.8 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\) at \(25^{\circ} \mathrm{C}\). If \(\mathrm{Al}\) reacts with \(\mathrm{O}_{2}\) at \(25^{\circ} \mathrm{C}\), which of the following releases \(250 \mathrm{kcal}\) of heat? (a) the reaction of \(0.312 \mathrm{~mol}\) of \(\mathrm{Al}\) (b) the formation of \(0.624 \mathrm{~mol}\) of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) (c) the reaction of \(0.712 \mathrm{~mol}\) of \(\mathrm{Al}\) (d) the formation of \(0.615 \mathrm{~mol}\) of \(\mathrm{Al}_{2} \mathrm{O}\).

Step-by-Step Solution

Answer

Option (b) releases approximately 1046 kJ.

Step 1: Convert kcal to kJ

First, we need to convert the heat release from kcal to kJ because the standard heat of combustion is given in kJ. The conversion factor is 1 kcal = 4.184 kJ.\[250 \text{ kcal} \times 4.184 \frac{\text{kJ}}{\text{kcal}} = 1046 \text{ kJ}\]So, 250 kcal equals 1046 kJ.

Step 2: Calculate heat release per option

Using the given standard heat of combustion of Aluminum, -837.8 kJ/mol, calculate the heat release for each option:**(a) For 0.312 mol of Al:**\[0.312 \text{ mol} \times -837.8 \frac{\text{kJ}}{\text{mol}} = -261.3936 \text{ kJ}\]**(b) For 0.624 mol of Al (assuming goes to Al₂O₃):** As 4 mol of Al produces 2 mol of Al₂O₃, the heat release is doubled per mol of Al₂O₃.\[0.624 \text{ mol Al}_2\text{O}_3 \times \left(2 \times -837.8 \right) \frac{\text{kJ}}{\text{mol Al}_2\text{O}_3} = -1046.3616 \text{ kJ}\]**(c) For 0.712 mol of Al:**\[0.712 \text{ mol} \times -837.8 \frac{\text{kJ}}{\text{mol}} = -596.3696 \text{ kJ}\]**(d) Formation of 0.615 mol of Al₂O:** Not relevant here as we don't have the combustion value for forming Al₂O.

Step 3: Compare calculations to 1046 kJ

Now, compare the calculated heat releases to the desired 1046 kJ: - **(a)** releases -261.39 kJ - **(b)** releases -1046.36 kJ - **(c)** releases -596.37 kJ - **(d)** not calculated due to lack of information Among them, option (b) approximately releases the desired 1046 kJ.

Key Concepts

Thermochemistry

The field of thermochemistry involves the study of heat energy exchanges in chemical reactions. This area of chemistry focuses on understanding how energy in the form of heat is absorbed or released when substances interact. In thermochemistry, processes are often classified as either endothermic or exothermic. In an endothermic process, the system absorbs energy from the surroundings, whereas in an exothermic process, energy is released into the surroundings.

When examining the heat of combustion, a specific type of exothermic process, we're interested in the energy change that occurs when a substance reacts completely with oxygen to form combustion products. The heat of combustion provides insight into the energy potential of fuels and materials, highlighting how much energy can be extracted from them through burning. It's particularly useful in applications where thermal energy efficiency is critical, such as in energy production and engine design.

Enthalpy Change Calculations

Enthalpy, often denoted as H, is a measure of the total energy of a system, including internal energy plus the product of pressure and volume. The change in enthalpy (\( \Delta H \)) often reflects heat changes occurring at constant pressure during chemical reactions.

To calculate enthalpy changes, it's crucial to understand the relationship between reaction stoichiometry and the heat absorbed or released. Given a known enthalpy change for a specified reaction amount, calculations can be done to find the heat released or absorbed under different conditions or quantities of reactants. For example, if we know the standard enthalpy of combustion of a substance, we can calculate the heat change for a different quantity by scaling it according to the reaction stoichiometry.

It's important to consistently convert units to ensure accuracy, as seen in the exercise where kcal was converted to kJ. This standardizes the measurement, making it easier to compare energy changes across different reactions and conditions.

Chemical Reaction Stoichiometry

Chemical stoichiometry provides a quantitative basis for understanding the proportions of reactants and products in chemical reactions. It ensures that mass is conserved during a reaction by relating the moles of reactants and products through balanced chemical equations.

For combustion reactions like that of aluminum, stoichiometry helps us determine how much heat is released based on the number of moles of reactants used. Specifically, knowing the balanced equation allows for accurate predictions of product amounts and aligns with enthalpy calculations to deduce energy changes.

The balance and mole ratios derived from stoichiometry are fundamental for calculating reactions' thermal output. They dictate how much of each reactant is necessary to completely react, guiding optimization of energy yield and ensuring efficient resource utilization in industrial processes and conservation efforts.