Question

In 1998 , scientists using a special type of electron microscope were able to measure the force needed to break a single chemical bond. If \(2.0 \times 10^{-9} \mathrm{~N}\) was needed to break a \(\mathrm{C}-\mathrm{Si}\) bond, estimate the bond enthalpy in \(\mathrm{kJ} / \mathrm{mol}\). Assume that the bond has to be stretched by a distance of \(2 \AA\) ( \(2 \times 10^{-10} \mathrm{~m}\) ) before it is broken.

Short answer

The bond enthalpy is approximately 240.9 kJ/mol.

Step-by-step solution

Understand the given data

We are given that the force required to break a single C-Si bond is \(2.0 \times 10^{-9} \mathrm{~N}\). The distance over which the bond is stretched (i.e., before it breaks) is \(2 \times 10^{-10} \mathrm{~m}\). We need to calculate the bond enthalpy in \(\mathrm{kJ} / \mathrm{mol}\).

Calculate energy to break a single bond

Work done (energy) to break the bond can be calculated using the formula \( W = F \times d \), where \( F \) is force and \( d \) is distance. Substituting the provided values, \[ W = (2.0 \times 10^{-9} \mathrm{~N}) \times (2 \times 10^{-10} \mathrm{~m}) = 4.0 \times 10^{-19} \mathrm{~J} \].

Convert energy per bond to energy per mole

To find the bond enthalpy in \(\mathrm{kJ}/\mathrm{mol}\), we convert the energy per bond to per mole using Avogadro's number \(6.022 \times 10^{23}\) molecules per mole. \[\text{Energy per mole} = 4.0 \times 10^{-19} \mathrm{~J/bond} \times 6.022 \times 10^{23} \mathrm{~bonds/mol} = 2.409 \times 10^{5} \mathrm{~J/mol} \].

Convert Joules per mole to kilojoules per mole

Finally, convert \(\mathrm{J/mol}\) to \(\mathrm{kJ/mol}\) by dividing by 1000. \[2.409 \times 10^{5} \mathrm{~J/mol} = 240.9 \mathrm{~kJ/mol} \].

Key concepts

The C-Si Bond

The carbon-silicon (C-Si) bond is an essential component in various chemical structures, particularly in materials and organic chemistry. This bond features prominently in silicones, which are versatile compounds used in an array of products from sealants to implants. The strength of a C-Si bond can be described by its bond enthalpy. This metric provides insight into how much energy is required to break the bond between a carbon and a silicon atom. In this context, bond enthalpy is crucial as it determines the stability and reactivity of the compounds containing C-Si bonds. Understanding the bond enthalpy helps predict how these bonds will behave under different conditions.
Scientists use highly specialized equipment to measure the force needed to break such bonds. Once the force and necessary bond extension are known, it becomes possible to calculate the energy required to disrupt a single bond, providing critical insights into the atomic-level interactions in materials.

Understanding Avogadro's Number

Avogadro's number is a fundamental constant in chemistry. It represents the number of molecules, atoms, or particles found in one mole of a substance, which is exactly \(6.022 \times 10^{23}\). This large number bridges the gap between atomic scale measurements and macroscopic quantities we observe. In calculations involving bond enthalpies, Avogadro's number allows us to convert energy from a per-bond basis to a per-mole basis, which is far more practical for laboratory and industrial applications.
Essentially, using Avogadro’s number lets scientists translate the minuscule energies required to break individual bonds into values that are meaningful and comparable for broader experimentation and application across various substances. This conversion is crucial for standardized reporting of data and for comparing the strength of different bonds in various materials.

Calculating Force Required

In physics and chemistry, force calculations are pivotal for understanding how much energy is required to alter physical or chemical states. In the context of the C-Si bond exercise, the given force \(2.0 \times 10^{-9}\) N is simply the amount of push or pull needed to break the bond, measured in newtons (N). The work done or the energy consumed to break the bond is calculated by combining this force with the distance over which it is applied, using the formula \( W = F \times d \), where \( F \) is force and \( d \) is distance.
This form of energy estimation helps identify how much manipulation is necessary to achieve a chemical reaction or change, providing a quantitative approach to analyze interactions at the molecular level. Such calculations are instrumental in engineering materials and reactions that are both efficient and safe.

Energy Conversion for Bond Enthalpy

Energy conversion is a key process in chemistry that allows scientists to interpret the energy requirements of chemical reactions in terms both understandable and actionable. After calculating the energy needed to break a single bond, typically in joules, it's crucial to convert this energy into a form that reflects macroscopic quantities—this is where kilojoules per mole (kJ/mol) come into play. To do so, we first compute the energy for a mole using Avogadro's number which, in turn, requires a linear conversion from joules to kilojoules by dividing by 1000.
This conversion process is essential for accurately representing data. It supports comparison of bond strengths and assists in practical applications like predicting reaction thermodynamics and designing industrial processes. Through such conversions, scientists glean insights into energy efficiency and material performance, guiding development and innovation across numerous scientific fields.