Problem 113 - Chemistry: The Central Science

Question

Silicon, the element, is the heart of integrated circuits and computer chips in almost all of our electronic devices. Si has the same structure as diamond; each atom is singly bonded to four neighbors. Unlike diamond, silicon has a tendency to oxidize (to \(\mathrm{SiO}_{2}\), another extended solid) if exposed to air. (a) Estimate the enthalpy of reaction for the conversion of \(1 \mathrm{~cm}^{3}\) of silicon into \(\mathrm{SiO}_{2}\). (b) Unlike carbon, silicon rarely forms multiple bonds. Estimate the bond enthalpy of the \(\mathrm{Si}=\mathrm{Si}\) bond, assuming that the ratio of the \(\mathrm{Si}=\mathrm{Si}\) double bond enthalpy to that of the \(\mathrm{Si}-\mathrm{Si}\) single bond is the same as that for carbon-carbon bonds.

Step-by-Step Solution

Answer

The enthalpy of reaction for the conversion of 1 cm³ of silicon into SiO₂ is approximately -7.0 kJ. The Si=Si bond enthalpy is approximately -386 kJ/mol.

Step 1: Calculate the number of silicon atoms in 1 cm³ of silicon

We know that the density of silicon is \(2.33 \mathrm{~g/cm^3}\). The molar mass of silicon is approximately \(28 \mathrm{~g/mol}\). We can use these values to determine the number of moles of silicon in 1 cm³ and then convert it to the number of atoms. The number of moles of silicon in 1 cm³ can be calculated as follows: Moles of Si = \(\frac{\text{mass of Si}}{\text{molar mass of Si}}\) Moles of Si = \(\frac{2.33 \mathrm{~g}}{28 \mathrm{~g/mol}}\) Now, we can use Avogadro's number \((N_A = 6.022\times10^{23}\text{atoms/mol})\) to find the number of silicon atoms: Number of atoms = Moles of Si × \(N_A\)

Step 2: Find the stoichiometry of the reaction and the moles of Si and SiO₂ involved

Since the balanced reaction of silicon with oxygen is given by: \[ \mathrm{Si} + \mathrm{O_2} \rightarrow \mathrm{SiO_2} \] we can determine the moles of SiO₂ formed by using the stoichiometry of reaction. In this case, the stoichiometry is 1:1, meaning one mole of Si reacts with one mole of O₂ to produce one mole of SiO₂.

Step 3: Use the bond enthalpies to estimate the enthalpy of reaction for the conversion of 1 cm³ of silicon into SiO₂

We need to calculate the enthalpy of reaction for the conversion of 1 cm³ of silicon into SiO₂ using bond enthalpies. ΔH_reaction = Enthalpy of formation of SiO₂ - Enthalpy of formation of Si We know the bond enthalpies for Si-Si is approximately \(-226 \mathrm{~kJ/mol}\), and Si-O is approximately \(-369 \mathrm{~kJ/mol}\). ΔH_reaction = \((1 \,\text{mol})(-2 \times 369 \,\mathrm{kJ/mol}) - (1\, \text{mol})(-226\, \mathrm{~kJ/mol})\) ΔH_reaction = \([-738 \mathrm{~kJ/mol} - (-226 \mathrm{~kJ/mol})\) ΔH_reaction = \[-512 \mathrm{~kJ/mol}\] Now we can calculate the enthalpy of reaction for 1 cm³ of silicon converted into SiO₂: ΔH_reaction = \(\frac{-512 \mathrm{~kJ/mol}}{28\, \mathrm{~g/mol} }\) × 2.33 g

Step 4: Estimate the Si=Si bond enthalpy, assuming the ratio of the Si=Si double bond enthalpy to that of the Si-Si single bond is the same as that for carbon-carbon bonds

We know that the C=C bond enthalpy is about \(612 \mathrm{~kJ/mol}\) and the C-C bond enthalpy is about \(348 \mathrm{~kJ/mol}\). We also know that the Si-Si bond enthalpy is about \(-226 \mathrm{~kJ/mol}\). Let x be the Si=Si bond enthalpy. Then, \(\frac{x}{-226} = \frac{612}{348}\) x = \(\frac{-226 \times 612}{348}\) (Solving for x) x ≈ \(-386 \mathrm{~kJ/mol}\) Thus, the Si=Si bond enthalpy is approximately \(-386 \mathrm{~kJ/mol}\).

Key Concepts

Bond Enthalpy

When discussing chemical reactions, bond enthalpy is a crucial concept. It refers to the amount of energy needed to break one mole of a bond in a molecule, in the gas phase. This is an essential consideration when estimating the heat involved in reactions, as bonds must be broken and formed. For silicon, single bonds (Si-Si) have a bond enthalpy of about \(-226 \ \text{kJ/mol}\). For double bonds, like Si=Si, the bond enthalpy is estimated to be around \(-386 \ \text{kJ/mol}\). Understanding bond enthalpy helps predict reaction behavior and stability. When bonds form, they release energy, while breaking bonds requires energy input. This understanding is vital when calculating the enthalpy of a reaction, as seen in the conversion from silicon to \(\text{SiO}_2\) in this exercise. Keeping in mind these energetic changes allows us to predict whether a reaction will be endothermic (absorbing energy) or exothermic (releasing energy). The estimation of bond enthalpy also helps in understanding why certain chemical structures, like those of silicon, exhibit different properties compared to carbon, despite some structural similarities.

Oxidation Reactions

Oxidation reactions involve the transfer of electrons from one substance to another. In simple terms, it often involves a substance gaining oxygen or losing hydrogen. In the case of silicon, when it oxidizes, it reacts with oxygen from the air, forming \(\text{SiO}_2\). This is a highly exothermic reaction, meaning it releases a significant amount of energy. Silicon's tendency to oxidize helps protect it in environments where it might be exposed to air. The formation of \(\text{SiO}_2\) on silicon surfaces creates a protective barrier, similar to how iron forms rust. Despite its single bond nature, silicon's oxidation makes it a stable and widely used material in technology. It transforms from a pure element into a compound that is both chemically stable and structurally sound. In broader terms, the principles of oxidation reactions are fundamental in various industries, including electronics and metallurgy. Understanding the behavior of elements like silicon during oxidation is key to harnessing their properties effectively.

Molecular Stoichiometry

Molecular stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It’s a crucial framework for understanding reactions visually and mathematically. In the reaction of silicon with oxygen to form \(\text{SiO}_2\), the stoichiometry is 1:1. This means one mole of silicon reacts with one mole of oxygen to produce one mole of silicon dioxide. Breaking it down, stoichiometry provides a step-by-step approach to determining the amounts needed or produced, based on the balanced chemical equation. This allows chemists to predict and measure the outcome of reactions accurately. For silicon’s reaction, knowing the stoichiometry facilitates the calculation of needed reactants and the energy changes involved. Beyond simple calculations, molecular stoichiometry underpins the efficiency and yields of chemical processes. It ensures the optimal use of materials and energy, making it invaluable in research, industrial applications, and everyday chemical problem-solving.