Question

The intermediate \(\mathrm{SiH}_{2}\) is formed in the thermal decomposition of silicon hydrides. Calculate \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{SiH}_{2}\) from the following reactions: \(\mathrm{Si}_{2} \mathrm{H}_{6}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{SiH}_{4}(\mathrm{~g})\) \(\Delta H^{\circ}=-11.7 \mathrm{~kJ} / \mathrm{mol}\) \(\mathrm{SiH}_{4}(\mathrm{~g}) \rightarrow \mathrm{SiH}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\) \(\Delta H^{\circ}=+239.7 \mathrm{~kJ} / \mathrm{mol}\) \(\Delta H_{\mathrm{f}}^{\circ}, \mathrm{Si}_{2} \mathrm{H}_{6}(\mathrm{~g})=+80.3 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (a) \(353 \mathrm{~kJ} / \mathrm{mol}\) (b) \(321 \mathrm{~kJ} / \mathrm{mol}\) (c) \(198 \mathrm{~kJ} / \mathrm{mol}\) (d) \(274 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

\(\Delta H_{f}^\circ\) for SiH2(g) is 274 kJ/mol.

Step-by-step solution

Write down the given reactions with their enthalpies

The first reaction is \[\begin{equation}\text{Si}_2\text{H}_6(g) + \text{H}_2(g) \rightarrow 2 \text{SiH}_4(g) \end{equation}\]with \[\begin{equation}\text{\(\Delta H^\circ = -11.7 \kJ/mol\)}\end{equation}\]The second reaction is \[\begin{equation}\text{SiH}_4(g) \rightarrow \text{SiH}_2(g) + \text{H}_2(g)\end{equation}\]with \[\begin{equation}\text{\(\Delta H^\circ = +239.7 \kJ/mol\)}\end{equation}\]The standard enthalpy of formation for \[\begin{equation}\text{Si}_2\text{H}_6(g)\end{equation}\]is given as \[\begin{equation}\text{\(\Delta H_{f}^\circ\)} = +80.3 \kJ/mol\end{equation}\]

Calculate the enthalpy of formation for SiH4 (g)

From the enthalpy of reaction 1, we can find the enthalpy of formation of SiH4 by dividing the reaction enthalpy by 2 (since 2 moles are formed) and adding it to half of the enthalpy of formation of Si2H6. \[\begin{equation}\Delta H_{f}^\circ(\text{SiH}_4) = \frac{1}{2}\Delta H^\circ_{rxn1} + \frac{1}{2}\Delta H_{f}^\circ(\text{Si}_2\text{H}_6)\end{equation}\]Then, plug in the values: \[\begin{equation}\Delta H_{f}^\circ(\text{SiH}_4) = \frac{1}{2} (-11.7) + \frac{1}{2} (80.3)\end{equation}\]\[\begin{equation}\Delta H_{f}^\circ(\text{SiH}_4) = -5.85 + 40.15\end{equation}\]\[\begin{equation}\Delta H_{f}^\circ(\text{SiH}_4) = 34.3 \kJ/mol\end{equation}\]

Calculate the enthalpy of formation for SiH2 (g)

Now, use the enthalpy of formation of SiH4 calculated in Step 2, and the enthalpy of reaction 2 to find the enthalpy of formation for SiH2. \[\begin{equation}\Delta H_{f}^\circ(\text{SiH}_2) = \Delta H^\circ_{rxn2} + \Delta H_{f}^\circ(\text{SiH}_4) - \Delta H_{f}^\circ(\text{H}_2)\end{equation}\]Since \[\begin{equation}\Delta H_{f}^\circ(\text{H}_2(g)) = 0\end{equation}\](by definition for elements in their standard state), the equation simplifies to: \[\begin{equation}\Delta H_{f}^\circ(\text{SiH}_2) = +239.7 + 34.3\end{equation}\]\[\begin{equation}\Delta H_{f}^\circ(\text{SiH}_2) = 274\end{equation}\]kJ/mol.

Key concepts

Chemical Thermodynamics

Chemical thermodynamics involves the application of thermodynamic principles to chemical reactions and processes. It is integral to understanding how energy is transformed and conserved within chemical systems. The heart of this field lies in the laws of thermodynamics, which describe the transfer of energy, the concept of equilibrium, and the directionality of processes.

For instance, the concept of enthalpy, denoted as \( H \), is a key term in this discipline. It corresponds to the total heat content of a system at constant pressure and is used to assess the heat absorbed or released during chemical reactions. The change in enthalpy, \( \Delta H \), often measured in joules or kilojoules per mole (J/mol or kJ/mol), is particularly significant when analyzing the energetic aspects of reactions, as it helps us to understand whether a process is exothermic (releases energy) or endothermic (absorbs energy).

In the given exercise, for example, the calculation of \( \Delta H_{f}^\circ \) involves determining the change in enthalpy during the formation of a substance from its constituent elements under standard conditions.

Thermal Decomposition

Thermal decomposition is a type of chemical reaction where a compound breaks down into two or more substances when it is heated. This kind of reaction is endothermic, meaning heat is absorbed to break the bonds of the compounds involved. The creation of \( \mathrm{SiH}_{2} \) from \( \mathrm{SiH}_{4} \) is a classic example of thermal decomposition, where diatomic hydrogen is released as a byproduct.

In simplified terms, when you heat certain silicon hydrides like \( \mathrm{SiH}_{4} \) to a high enough temperature, they break apart into smaller molecules. In such scenarios, it's essential to have a firm grasp on the changes in enthalpy (heat content) because they will dictate whether the decomposition can occur spontaneously and the conditions necessary for the reaction to proceed.

Silicon Hydrides

Silicon hydrides, known collectively as silanes, are compounds made up of silicon and hydrogen. They can be regarded as analogs of the alkanes (hydrocarbons) with silicon replacing the carbon atoms. One of the simplest silanes is silane itself (\( \mathrm{SiH}_{4} \)), and the exercise presented involves the decomposition of these kinds of compounds.

In chemistry, understanding the behavior of silicon hydrides under various conditions is important for applications in semiconductor technology and materials science. The thermal stability of these compounds can be studied by analyzing the enthalpies of their formation and decomposition reactions, which provide valuable information on the energy changes associated with their transformations.

Standard Enthalpy Change

The standard enthalpy change, \( \Delta H^\circ \), is an essential quantity in chemical thermodynamics. It's defined as the enthalpy change that occurs when a reaction takes place under standard conditions: a pressure of 1 bar, a stated temperature (usually 298 K), and all substances in their standard states. Standard enthalpy changes enable chemists to predict how much energy will be absorbed or released during chemical reactions.

In the step-by-step solution of our exercise, we extrapolate the standard enthalpy of formation for our products and reactants to ultimately find the enthalpy of formation for \( \mathrm{SiH}_{2} \) (\( \Delta H_{f}^\circ \) of \( \mathrm{SiH}_{2} \)). By understanding these values, we can assess the stability of compounds, predict the feasibility of synthetic routes, and evaluate the energetic favorability of various chemical processes.