Problem 79 - Chemistry The Molecular Science

Question

We burn 3.47 g lithium in excess oxygen at constant atmospheric pressure to form \(\mathrm{Li}_{2} \mathrm{O} .\) Then, we bring the reaction mixture back to \(25^{\circ} \mathrm{C}\). In this process \(146 \mathrm{~kJ}\) of heat is given off. Calculate the standard formation enthalpy of \(\mathrm{Li}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The standard enthalpy of formation of \(\text{Li}_2\text{O}\) is -292 kJ/mol.

Step 1: Write the chemical equation

The reaction for burning lithium in oxygen to form lithium oxide is given by the equation: \[ 4 ext{Li} (s) + ext{O}_2 (g) \rightarrow 2 ext{Li}_2 ext{O} (s) \] This equation shows the consumption of 4 moles of lithium to yield 2 moles of lithium oxide.

Step 2: Calculate moles of Lithium used

Determine the moles of lithium that are burned by using its molar mass: Molar mass of Li = 6.94 g/mol Moles of Li = \( \frac{3.47 ext{ g}}{6.94 ext{ g/mol}} \approx 0.500 ext{ mol} \)

Step 3: Relate moles to energy change

According to the stoichiometry of the reaction, 4 moles of Li produce 2 moles of \(\text{Li}_2\text{O}\) with an energy release of 146 kJ calculated for the moles of lithium used. Since 0.5 moles of Li were used, the heat released per 4 moles is: \[ ext{Heat per 4 moles} = \frac{146 ext{ kJ}}{0.5/4} = 584 ext{ kJ} \]

Step 4: Calculate standard formation enthalpy

The standard enthalpy of formation \(\Delta H_f^\circ\) of \(\text{Li}_2\text{O}\) is defined as the heat change for the formation of 1 mole of \(\text{Li}_2\text{O}\) from its elements in their standard states. From the balanced equation, 2 moles of \(\text{Li}_2\text{O}\) are formed with a release of 584 kJ of energy. Thus, the \(\Delta H_f^\circ\) for 1 mole is: \[ \Delta H_f^\circ = \frac{584 ext{ kJ}}{2} = 292 \text{ kJ/mol} \] Therefore, the standard enthalpy of formation of \(\text{Li}_2\text{O}\) is -292 kJ/mol, the negative sign indicates exothermic reaction.

Key Concepts

Chemical Stoichiometry

In the world of chemistry, stoichiometry is your trusty method for determining how much of a chemical substance you need or will get in a reaction. It acts like a recipe in cooking. This "recipe" is guided by balanced chemical equations, which show the ratio in which reactants combine and products form.
Take our exercise involving lithium and oxygen. The balanced equation is: \[ 4 \text{Li} (s) + \text{O}_2 (g) \rightarrow 2 \text{Li}_2 \text{O} (s) \]This equation tells us that:

• 4 moles of lithium (Li) are required.
• These 4 moles combine with 1 mole of oxygen (O_2).
• They produce 2 moles of lithium oxide (Li_2O).

The stoichiometric numbers (the coefficients in the equation) allow us to convert between moles, and subsequently to grams using molar masses. This was crucial in determining how the 3.47 g of lithium corresponded to 0.5 moles in our calculations.

Exothermic Reaction

Exothermic reactions are fascinating because they are all about giving off heat. In simple terms, during an exothermic reaction, energy is released to the surrounding environment, usually in the form of heat or light.
When lithium combines with oxygen to form lithium oxide, the process releases a significant amount of heat. This can be felt as the reaction mixture gets hot, a telltale sign of energy leaving the system. Specifically, in our problem, 146 kJ of heat was released when 0.5 moles of lithium reacted.
This energy release is due to the formation of new bonds in lithium oxide being more energetically favorable than breaking the original bonds in lithium and oxygen atoms. Keep in mind that the negative sign in, say, (-292 kJ/mol) for the enthalpy of formation, isn't negative energy, rather an indicator that the reaction is exothermic and heat is given off.

Lithium Oxide

Lithium oxide is a compound known for its usefulness and unique properties. It’s primarily used in ceramics and glass production thanks to its stability and property-enhancing characteristics.
The substance is formed by reacting lithium metal with oxygen, as shown by the balanced equation of our exercise. Interestingly, lithium oxide formation is not only an exothermic process but also showcases lithium's reactive nature when exposed to oxygen.
In addition to industrial uses, lithium oxide is important in the context of studying the structure and properties of ionic compounds. It consists of lithium ions ( Li^+) and oxide ions ( O^{2-}), which form a crystalline solid with a high melting point. Understanding lithium oxide also gives insight into the broader category of metal oxides, highly relevant in both natural processes and industrial applications.