Question

(a) Draw the Lewis structure for hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\) . (b) What is the weakest bond in hydrogen peroxide? (c) Hydrogen peroxide is sold commercially as an aqueous solution in brown bottles to protect it from light. Calculate the longest wavelength of light that has sufficient energy to break the weakest bond in hydrogen peroxide.

Short answer

The Lewis structure of hydrogen peroxide (H2O2) is: H - O - O - H : : : : The weakest bond is the O-O bond. To break it, the longest wavelength of light with sufficient energy required is approximately 202 nm.

Step-by-step solution

(a) Lewis Structure for Hydrogen Peroxide (H2O2)

H2O2 has a total of 12 valence electrons: 1 electron from each of the 2 hydrogen atoms and 6 electrons from each of the 2 oxygen atoms. The Lewis structure can be drawn as follows: 1. Connect the two oxygen atoms with a single bond (O-O) using 2 electrons. Now, each oxygen atom has 5 electrons around it. 2. Connect each hydrogen atom to a different oxygen atom using a single bond (H-O) using 2 more electrons for each bond. Now, each oxygen atom is connected to a hydrogen atom and has 6 electrons around it, while the hydrogen atoms have 2 electrons each. 3. Add lone pairs to both oxygen atoms to satisfy their octet needs. Each oxygen atom should have 2 lone pairs, using the remaining 4 valence electrons. The Lewis structure for hydrogen peroxide is: H - O - O - H : : : :

(b) Weakest Bond in Hydrogen Peroxide

In hydrogen peroxide, there are two types of bonds: O-O (oxygen-oxygen) and O-H (oxygen-hydrogen). The O-O bond is weaker than the O-H bond due to the larger size of the oxygen atoms and less effective overlap of their atomic orbitals resulting in lower bond dissociation energy. Therefore, the weakest bond in hydrogen peroxide is the O-O bond.

(c) Calculate the Longest Wavelength of Light to Break the Weakest Bond

To find the longest wavelength of light needed to break the O-O bond in hydrogen peroxide, we will use Planck's equation: \(E = h \cdot c / \lambda\) Where E is the energy required to break the bond, h is Planck's constant \((6.626 \times 10^{-34} Js)\), c is the speed of light \((2.998 \times 10^8 m/s)\), and \( \lambda \) is the wavelength of light. The bond dissociation energy of O-O bond in hydrogen peroxide is approximately 142 kcal/mol or 594 kJ/mol. To find the energy in joules per photon, we need to convert the energy into joules per photon. \(E_{photon} = 594,000 J/mol \times (1 mol/ 6.022 \times 10^{23} photons)\) = 9.869 x 10^{-19} J/photon Now, we plug the energy into the Planck's equation and solve for the wavelength: \( \lambda = h \cdot c / E_{photon}\) \( \lambda = \frac{(6.626 \times 10^{-34} Js)(2.998 \times 10^8 m/s)}{9.869 x 10^{-19} J/photon}\) \( \lambda \approx 2.02 \times 10^{-7}\, m = 202 \,nm\) The longest wavelength of light that has sufficient energy to break the weakest bond in hydrogen peroxide is approximately 202 nm.

Key concepts

Lewis Structure of H2O2

Understanding the Lewis structure of hydrogen peroxide (H₂O₂) is crucial for students who are delving into the world of molecular chemistry. The Lewis structure is a valuable tool that depicts the arrangement of atoms within a molecule and shows how they are bonded together.

The total count of valence electrons for H₂O₂ is determined by adding the electrons from hydrogen atoms to those from oxygen atoms. Each hydrogen atom contributes one electron, while each oxygen atom brings six. Now, the bonds are formed: each oxygen atom is connected to a hydrogen atom with a single bond, and the oxygen atoms themselves are connected by another single bond. After the bonds are set, leftover electrons are placed as lone pairs around the oxygen atoms to complete their octet, satisfying the rule that elements, except hydrogen, tend to fill their outer shell with eight electrons for stability.

It is important to note that the shapes of molecules can also influence the distribution of electrons, and learners should keep in mind that three-dimensional geometries can affect electron pair orientations. By effectively mastering the Lewis structure, students can predict molecular properties like shape, reactivity, and polarity.

Bond Dissociation Energy

Grasping the concept of bond dissociation energy helps to understand the stability of different bonds within a molecule. In hydrogen peroxide, there are two types of bonds: O-H and O-O. The O-O bond is considered the weaker link compared to the more robust O-H bond.

This difference in stability is explained by bond dissociation energy, which is the amount of energy needed to break a bond between two atoms in a molecule. For the O-O bond in hydrogen peroxide, a lower bond dissociation energy implies that it takes less energy to break this bond as compared to breaking the O-H bond. The concept of bond dissociation energy not only gives insights into the chemical reactivity of molecules but also influences how substances are stored. For instance, hydrogen peroxide is kept in dark containers to prevent light-induced breakdown of the fragile O-O bond due to its lower bond dissociation energy.

Students must comprehend that bond stability is a key factor in determining molecular behavior and reactivity, which can be invaluable in predicting reactions and designing new compounds in chemistry.

Wavelength Calculation to Break Chemical Bonds

The interplay between the energy of light and chemical bonds is a fascinating aspect in chemistry, particularly when discussing how light can induce bond cleavage. To understand which light can break a bond, one must learn to calculate the wavelength of light required using the conceptual framework of energy quantization.

To break a chemical bond, the light must provide an amount of energy that meets or exceeds the bond dissociation energy. By using Planck's equation, we can relate the energy of a photon (the smallest unit of light) to its wavelength. The calculation involves Planck's constant and the speed of light to determine that longest wavelength of light capable of breaking the bond. Students can better understand the electromagnetic spectrum and how different wavelengths correspond to different energies. In the case of hydrogen peroxide, the wavelength calculated at approximately 202 nm falls within the ultraviolet range, indicating that UV light is energetic enough to break the O-O bond.

This understanding is not just theoretical but has practical implications in various fields including chemistry, physics, and materials science. Knowing how to calculate wavelengths for bond breakage can aid students in designing experiments and understanding how substances interact with light.