Question

Consider the following type of energies and decide the correct order of magnitude. 1\. covalent single bond energy 2\. average translational kinetic energy of gases at room temperature 3\. rotational barrier energy in ethane between eclipsed and staggered forms 4\. ionization energy of hydrogen atom (a) \(4>1>3>2\) (b) \(4>1>2>3\) (c) \(2>1>4>3\) (d) \(4>3>2>1\)

Short answer

The correct order is (a) \(4>1>3>2\).

Step-by-step solution

Covalent single bond energy estimation

The energy of a typical covalent single bond, such as a C-H bond, is in the range of 350 to 450 kJ/mol. This is a relatively large amount of energy since covalent bonds are quite strong.

Translational kinetic energy estimation

The average translational kinetic energy of gases at room temperature is calculated using the formula \( \frac{3}{2} kT \), where \( k \) is the Boltzmann constant \( 1.38 \times 10^{-23} \text{ J/K} \) and \( T \) is the temperature in Kelvin (approximately 298 K at room temperature). This gives an energy order magnitude around \( 10^{-21} \text{ J} \) per particle, which converts to a few kJ/mol (about 2.5 kJ/mol).

Rotational barrier energy in ethane

The rotational barrier energy in ethane, i.e., the energy difference between its eclipsed and staggered forms, is approximately 12 kJ/mol. This is relatively low as it accounts for the weak interactions between hydrogen atoms during rotation around the carbon-carbon bond.

Ionization energy of hydrogen atom estimation

The ionization energy of a hydrogen atom is 1312 kJ/mol. This is significantly higher than the energies associated with bond rotation or average kinetic energies at room temperature.

Compare and order energies

Comparing the calculated orders of these energies: ionization energy of hydrogen (1312 kJ/mol) > covalent single bond energy (350-450 kJ/mol) > rotational barrier in ethane (12 kJ/mol) > translational kinetic energy at room temperature (2.5 kJ/mol). This fits option (a): \(4>1>3>2\).

Key concepts

Covalent Bond Energy

When two atoms come together to share electrons, a covalent bond is formed, which is a type of chemical bond where the bonded atoms share one or more pairs of electrons. This sharing creates a stable combination of atoms, such as in the case of a carbon-hydrogen (C-H) bond. Covalent bonds are characterized by the specific energy required to break the bond, known as the bond energy. This energy is usually expressed in kilojoules per mole (kJ/mol). For a C-H bond, the bond energy is typically between 350 and 450 kJ/mol.

• This means a significant amount of energy is needed to break the bond and separate the atoms, indicating the strength of covalent bonds.
• The strength comes from the mutual sharing of electrons between the atoms, leading to a lower energy state.

Covalent bonds play a crucial role in the stability and formation of molecules, making their energy an essential consideration in chemical reactions.

Translational Kinetic Energy

Translational kinetic energy refers to the energy of motion that molecules possess as they move linearly in space. In gases, this energy is of particular importance as it contributes significantly to the overall energy of gas particles.The average translational kinetic energy can be calculated using the formula \( \frac{3}{2} kT \), where \( k \) is the Boltzmann constant \((1.38 \times 10^{-23} \text{ J/K})\) and \( T \) is the temperature in Kelvin.

• At room temperature, which is approximately 298 K, this energy is around \(10^{-21} \text{ J} \) per particle, translating to about 2.5 kJ/mol.
• Although this energy seems small on a molar basis, it is sufficient to drive the movement of gas molecules, allowing them to exert pressure and collide with container walls.

Translational kinetic energy is a fundamental concept in understanding the behavior of gases and their interactions at various temperatures.

Rotational Barrier Energy

In molecules like ethane, rotational barrier energy refers to the energy required to rotate one part of the molecule relative to another around a bond, in this case, the carbon-carbon bond. This energy difference is observed between the eclipsed and staggered conformations. For ethane, the rotational barrier energy is approximately 12 kJ/mol.

• The staggered conformation is more energetically favorable because the hydrogen atoms are positioned to minimize their electron cloud interactions.
• Contrastingly, the eclipsed conformation places more electron clouds in proximity, raising the potential energy.

Rotational barrier energy is crucial for understanding the dynamic behavior of molecules and their preferred conformations.

Ionization Energy

Ionization energy is the amount of energy required to remove an electron from an atom in its gaseous state. It's a vital concept in understanding atomic structure and reactivity. For the hydrogen atom, the ionization energy is quite high at 1312 kJ/mol. This is because the single electron in a hydrogen atom is close to its nucleus, creating a strong attractive force.

• This significant energy requirement reflects the strength of the interaction between the electron and the nucleus.
• Ionization energy tends to increase as you move across a period in the periodic table due to increasing nuclear charge.

Comprehension of ionization energy is essential for grasping how atoms interact, bond formation, and the periodic trends in chemical properties.