Question

A reaction used to produce the silicon for semiconductors from sand \(\left(\mathrm{SiO}_{2}\right),\) can be broken up into three steps: $$ \begin{aligned} \mathrm{SiO}_{2}(s)+2 \mathrm{C}(s) & \longrightarrow \mathrm{Si}(s)+2 \mathrm{CO}(g) & & \Delta H=689.9 \mathrm{~kJ} \\\ \mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) & \longrightarrow \mathrm{SiCl}_{4}(g) & & \Delta H=-657.0 \mathrm{~kJ} \\ \mathrm{SiCl}_{4}(g)+2 \mathrm{Mg}(s) & \longrightarrow 2 \mathrm{MgCl}_{2}(s)+\mathrm{Si}(s) & \Delta H=-625.6 \mathrm{~kJ} \end{aligned} $$ (a) Write a thermochemical equation for the overall reaction where silicon is obtained from silicon dioxide and \(\mathrm{CO}\) and \(\mathrm{MgCl}_{2}\) are by-products. (b) What is \(\Delta H\) for the formation of one mole of silicon? (c) Is the overall reaction exothermic?

Short answer

Answer: The reaction for the formation of one mole of silicon is endothermic.

Step-by-step solution

Combine Thermochemical Equations

First, let's combine the given thermochemical equations through the following steps: 1. Equation 1 is already in the correct form: \(\mathrm{SiO}_{2}(s)+2 \mathrm{C}(s) \longrightarrow \mathrm{Si}(s)+2 \mathrm{CO}(g)\) 2. Inverse Equation 2: \(-\mathrm{Si}(s)-2 \mathrm{Cl}_{2}(g) \longrightarrow -\mathrm{SiCl}_{4}(g)\) 3. Inverse and multiply Equation 3 by 2 to have the correct number of moles for each reactant and product: \(-2\mathrm{SiCl}_{4}(g)-4 \mathrm{Mg}(s) \longrightarrow -4 \mathrm{MgCl}_{2}(s)-2\mathrm{Si}(s)\) 4. Sum the equations. Notice that some terms in reactants and products side cancel out: $$\mathrm{SiO}_{2}(s) + 2 \mathrm{C}(s) -2\mathrm{Si}(s) -4 \mathrm{Mg}(s) \longrightarrow 2 \mathrm{CO}(g) -2\mathrm{SiCl}_{4}(g) -4\mathrm{MgCl}_{2}(s)$$ The overall reaction will be: $$\mathrm{SiO}_{2}(s) + 2 \mathrm{C}(s) - 2\mathrm{Si}(s) - 4\mathrm{Mg}(s) \longrightarrow 2 \mathrm{CO}(g) - 2\mathrm{SiCl}_{4}(g) - 4\mathrm{MgCl}_{2}(s)$$

Compute the Overall Enthalpy Change

Now, we'll compute the overall enthalpy change for the reaction, which is the sum of the individual enthalpy changes: $$\Delta H_\text{overall} = \Delta H_1 + (-\Delta H_2) + (-2\Delta H_3)$$ $$\Delta H_\text{overall} = 689.9\,\mathrm{kJ} - (-657.0\,\mathrm{kJ}) - 2(-625.6\,\mathrm{kJ})$$ Plug in the given enthalpy change values and perform the calculations to find the overall enthalpy change: $$\Delta H_\text{overall} = 689.9 + 657.0 + 2(625.6)$$ $$\Delta H_\text{overall} = 2598.1\,\mathrm{kJ}$$

Compute \(\Delta H\) for One Mole Formation of Silicon

Now, determine the enthalpy change for the formation of one mole of silicon. Since we have a 2 moles of silicon product being formed in the overall reaction, we need to divide the overall enthalpy change by 2: $$\Delta H_\text{formation} = \frac{\Delta H_\text{overall}}{2}$$ $$\Delta H_\text{formation} = \frac{2598.1}{2}$$ $$\Delta H_\text{formation} = 1299.05\,\mathrm{kJ/mol}$$

Determine if the reaction is exothermic

We can now determine if the reaction is exothermic or endothermic based on the sign of the overall enthalpy change. If the overall enthalpy change is negative, the reaction is exothermic. If the overall enthalpy change is positive, the reaction is endothermic. Since \(\Delta H_\text{overall} = 2598.1\,\mathrm{kJ}\) is positive, the reaction is endothermic.

Key concepts

Enthalpy Change

Understanding the concept of enthalpy change is crucial for students studying thermochemical equations. Enthalpy change, denoted as \( \Delta H \), is the measure of heat energy that is either absorbed or released in a chemical reaction at constant pressure. The value of \( \Delta H \) depends on the nature of the reaction. When a substance reacts, bonds are broken and new ones are formed. Breaking bonds requires energy, while forming bonds releases energy. The overall enthalpy change is the difference between the energy absorbed in breaking the bonds and that released in forming new bonds.

In the given exercise, the overall enthalpy change for the production of silicon is determined by summing the enthalpy changes of each step in the process. This calculation gives us a clear picture of the energy profile of the reaction. A positive value of \( \Delta H \) indicates that the reaction consumes energy, making it endothermic. On the other hand, a negative \( \Delta H \) signifies an exothermic reaction, where energy is released. In educational materials, ensuring students understand these concepts helps them approach problems methodically, looking out for signs that indicate whether energy will be absorbed or released in a reaction.

Exothermic and Endothermic Reactions

Exothermic and endothermic reactions are two categories of chemical reactions defined by the flow of heat. An exothermic reaction releases heat to the surroundings, resulting in a temperature rise in the surrounding environment. Common examples include combustion reactions and many oxidation processes. Conversely, endothermic reactions absorb heat, causing a drop in the temperature of the surroundings, like photosynthesis or the reaction cited in this exercise.

Understanding the Difference

The distinction between these two reaction types is at the heart of thermochemistry. Students often explore activities such as mixing chemicals that dissolve with an observable change in temperature to provide a tactile learning experience of these concepts. The overall reaction in the exercise, which involves the production of silicon from silicon dioxide, is determined to be endothermic since the \( \Delta H \) calculated is positive. By grasping these principles, students can predict the energy requirements of reactions and potential safety measures needed when conducting experiments.

Silicon Semiconductor Production

Silicon semiconductor production is a multi-step chemical and physical process whereby high-purity silicon is obtained for use in electronic devices. The production starts with the extraction of silicon from silica sand. The exercise presented highlights the chemical reactions involved in producing silicon, typically through a method known as the carbothermal reduction, followed by chemical reactions with chlorine to create a volatile silicon compound, which is then reduced with magnesium.

Real-World Application

Understanding the chemistry behind the production of silicon semiconductors is essential for students pursuing careers in materials science, engineering, or electronics. It combines concepts of thermochemistry such as enthalpy change and understanding exothermic and endothermic reactions. The manufacturing process must be carefully controlled to ensure that the silicon is pure enough for semiconductor usage. Students learning the process through theoretical problems, like the one in this exercise, gain insight into practical applications of the chemical concepts they study in textbooks. By studying the enthalpy changes at each step as shown in the solution, students can also learn about the energy efficiencies of industrial processes and the challenges faced during large-scale production.