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 x 10^-9 N was needed to break a C-Si bond, estimate the bond enthalpy in kJ/mol. Assume that the bond had to be stretched by a distance of 2Å (2.0x10^-10 m) before it is broken.
To estimate the bond enthalpy in kJ/mol, we need to calculate the energy required to break the C-Si bond using the given force and displacement.
Bond enthalpy is defined as the energy required to break one mole of a specific bond in a molecule. In this case, we are given the force required to break a single C-Si bond and the displacement (stretching distance) at which this force is applied.
First, we need to calculate the work done to stretch the bond using the given force and displacement. The formula for work done is:
Work = Force x Displacement x cos(θ)
Since the force is applied in the same direction as the displacement (straight elongation), the angle (θ) between the force and displacement is 0 degrees, which means cos(θ) = 1.
Work = Force x Displacement x cos(0°)
= Force x Displacement
Now, let's plug in the given values:
Work = (2.0 x 10^-9 N) x (2.0 x 10^-10 m)
= 4.0 x 10^-19 J
Next, we need to convert this energy from joules to kilojoules and then scale it up to the energy required to break one mole of bonds.
To convert joules to kilojoules, divide by 1000:
Energy = 4.0 x 10^-19 J / 1000
= 4.0 x 10^-22 kJ
The energy required to break one C-Si bond is 4.0 x 10^-22 kJ.
However, we need to scale this energy up to represent one mole of C-Si bonds. To do this, we need to know the Avogadro's number (6.022 x 10^23).
Since there is 1 mole of C-Si bonds in Avogadro's number, the bond enthalpy in kJ/mol is:
Bond Enthalpy = Energy x Avogadro's number
= (4.0 x 10^-22 kJ) x (6.022 x 10^23 mol^-1)
≈ 2.41 x 10^2 kJ/mol
Therefore, the estimated bond enthalpy for the C-Si bond is approximately 2.41 x 10^2 kJ/mol.