Question

To produce silicon, used in semiconductors, from sand \(\left(\mathrm{SiO}_{2}\right)\), a reaction is used that can be broken down 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 the thermochemical equation for the overall reaction for the formation of silicon from silicon dioxide; \(\mathrm{CO}\) and \(\mathrm{MgCl}_{2}\) are byproducts. (b) What is \(\Delta H\) for the formation of one mole of silicon? (c) Is the overall reaction exothermic?

Short answer

(a) Overall reaction: SiO2(s) + 2 C(s) + 2 Cl2(g) + 2 Mg(s) -> Si(s) + 2 CO(g) + 2 MgCl2(s) (b) Enthalpy change (∆H): -592.7 kJ (c) The overall reaction is exothermic.

Step-by-step solution

Find the overall reaction

To find the overall reaction, we need to add the given equations in such a way that they will produce a single balanced thermochemical equation with SiO2 as a reactant and Si as a product. Notice that since Si is a product in equation (1) and also a reactant in equation (2), we can cancel it out. Similarly, SiCl4 is a product in equation (2) and a reactant in equation (3), so we can cancel it out, too. Combine the remaining terms and we get the overall reaction: SiO2(s) + 2 C(s) + 2 Cl2(g) + 2 Mg(s) -> Si(s) + 2 CO(g) + 2 MgCl2(s)

Calculate the enthalpy change (∆H) for the overall reaction

To calculate the enthalpy change for the overall reaction, we will add the enthalpy changes given for each of the three steps. The enthalpy change of an overall reaction is the sum of the enthalpy changes for each step. ΔH = ΔH₁ + ΔH₂ + ΔH₃ ΔH = (689.9 kJ) + (-657.0 kJ) + (-625.6 kJ) ΔH = -592.7 kJ So, the enthalpy change for the overall reaction is -592.7 kJ.

Determine if the overall reaction is exothermic

The overall reaction is exothermic if the enthalpy change (∆H) is negative. Since we calculated the enthalpy change to be -592.7 kJ (which is negative), the overall reaction is exothermic.

Answers

(a) The overall reaction for the formation of silicon from silicon dioxide is: SiO2(s) + 2 C(s) + 2 Cl2(g) + 2 Mg(s) -> Si(s) + 2 CO(g) + 2 MgCl2(s) (b) The enthalpy change (∆H) for the formation of one mole of silicon is -592.7 kJ. (c) Yes, the overall reaction is exothermic since the enthalpy change is negative.

Key concepts

Enthalpy Change Calculation

Enthalpy change, denoted as \( \Delta H \), is a measure of the heat energy released or absorbed during a chemical reaction under constant pressure. Calculating enthalpy change requires understanding the concept of thermochemical equations, which link the change in enthalpy to the quantities of reactants and products in a balanced chemical equation.

For a step-by-step process, we add the \( \Delta H \) values of all individual reactions that make up the overall chemical process. If the sum is negative, the reaction releases heat to its surroundings, making it exothermic. In contrast, a positive total indicates that the reaction absorbs heat, which is endothermic. Providing a cumulative energy change figure offers a straightforward way for students to assess the energy dynamics of complex chemical reactions, enhancing their grasp on thermal changes during such processes.

Exothermic Reaction

An exothermic reaction is a type of chemical reaction that releases energy in the form of heat to its surroundings, typically resulting in a temperature increase in the reaction medium. This kind of reaction is characterized by a negative \( \Delta H \) value. A common example is the combustion of fuels, like burning wood or gasoline.

Understanding exothermic reactions is crucial for students because it's not just about the energy release; it also involves how molecular bonds are broken and formed, and the factors that drive these reactions energetically favorable. This concept underlines everyday phenomena such as heating, lighting, and biological processes. By learning about exothermic reactions, students can make sense of energy conservation and better evaluate the implications of chemical reactions in both industrial and environmental contexts.

Chemical Reaction Steps

Breaking down complex reactions into a series of steps is a fundamental technique in chemistry called the reaction mechanism. Each step represents a distinct, simpler reaction that features its own reactants, products, and enthalpy change. When pieced together, these steps reveal the intricacies of the complete reaction from start to finish.

By dissecting reactions into manageable parts, students can delve deeper into the nuances of chemical transformations, analyzing aspects like reaction intermediates, rate-determining steps, and the overall energy profile of the reaction. This step-wise approach not only simplifies problem-solving but also equips learners with the analytical skills to understand how reactions progress at the molecular level, fostering a richer and more holistic appreciation of chemical processes.