Problem 23 - Chemistry Matter and Change

Question

Calculate Determine the differences in electronegativity, ionic radius, atomic radius, and first ionization energy for oxygen and beryllium.

Step-by-Step Solution

Answer

The differences between oxygen and beryllium are: 1. Electronegativity: Difference = \(1.87\) 2. Ionic Radius: Difference = \(95 pm\) 3. Atomic Radius: Difference = \(23 pm\) 4. First Ionization Energy: Difference = \(415 kJ/mol\)

Step 1: Electronegativity

Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons. The electronegativity values for the elements can be found on the Pauling Electronegativity Scale. For oxygen, the electronegativity is 3.44, and for beryllium, it is 1.57. To find the difference in electronegativity between oxygen and beryllium, subtract the value for beryllium from the value for oxygen: Difference in electronegativity = \(3.44 - 1.57 = 1.87\)

Step 2: Ionic Radius

Ionic radius refers to the size of an ion. In general, when an atom forms an ion, its size changes. To find the ionic radius, you can refer to an ionic radius table. For oxygen, the ionic radius is 140 pm, and for beryllium, it is 45 pm. To find the difference in ionic radius between oxygen and beryllium, subtract the value for beryllium from the value for oxygen: Difference in ionic radius = \(140 - 45 = 95 pm\)

Step 3: Atomic Radius

Atomic radius is the distance from the center of an atom's nucleus to its outermost electron shell. To find the atomic radius, you can refer to an atomic radius table. For oxygen, the atomic radius is 66 pm, and for beryllium, it is 89 pm. To find the difference in atomic radius between oxygen and beryllium, subtract the value for oxygen from the value for beryllium: Difference in atomic radius = \(89 - 66 = 23 pm\)

Step 4: First Ionization Energy

First ionization energy is the energy required to remove an electron from a neutral atom in its gaseous state. To find the first ionization energy, you can refer to an ionization energy table. For oxygen, the first ionization energy is 1314 kJ/mol, and for beryllium, it is 899 kJ/mol. To find the difference in first ionization energy between oxygen and beryllium, subtract the value for beryllium from the value for oxygen: Difference in first ionization energy = \(1314 - 899 = 415 kJ/mol\) In conclusion, the differences between oxygen and beryllium are: ELECTRONEGATIVITY: Difference = 1.87 IONIC RADIUS: Difference = 95 pm ATOMIC RADIUS: Difference = 23 pm FIRST IONIZATION ENERGY: Difference = 415 kJ/mol

Key Concepts

Electronegativity

Electronegativity is a crucial concept in chemistry, especially when discussing the bond formation between atoms. It is defined as an atom's ability to attract and hold onto electrons within a chemical bond. Higher electronegativity means an atom has a stronger pull on electrons.

Oxygen, with an electronegativity of 3.44, pulls electrons towards itself more strongly than beryllium, which has an electronegativity of 1.57. This large difference of 1.87 suggests that in a bond, oxygen will exert a much greater influence on the electrons compared to beryllium. This can lead to the formation of polar bonds where the negatively charged electrons are more likely to be found closer to oxygen, creating a partial negative charge around the oxygen atom.

Ionic Radius

The ionic radius reflects the size of an atom's ion in a crystal lattice. It's the measure from the center of the nucleus to the outer edge of the electron cloud of an ion. When an atom loses electrons and becomes a cation, its ionic radius decreases; conversely, an anion, having gained electrons, will increase in size.

Comparatively, oxygen's ionic radius is much larger at 140 picometers (pm) than that of beryllium at 45 pm. The substantial difference of 95 pm is attributed to oxygen typically forming anions (O^2-) by gaining electrons, increasing its electronic repulsion and, therefore, its size. In contrast, beryllium forms cations (Be²⁺) by losing electrons, resulting in a decreased radius due to reduced electron-electron repulsion.

Atomic Radius

Atomic radius is a vital concept when comparing elements. It represents half the distance between the nuclei of two atoms of the same element when they are joined by a covalent bond. Generally, the atomic radius decreases across a period because of the increasing positive charge in the nucleus, pulling electrons closer.

For beryllium, the atomic radius stands at 89 picometers, while for oxygen, it's 66 picometers. Oxygen's smaller atomic radius is explained by the higher number of protons in its nucleus, exerting a greater pull on its electrons. The difference between the two, which is 23 picometers, indicates how much more compact oxygen's electron cloud is compared to beryllium's.

First Ionization Energy

First ionization energy is the amount of energy required to remove the most loosely bound electron from a neutral atom in its gaseous state. It's a significant indicator of an element's reactivity. As you move across the periodic table, the ionization energy tends to increase because of the greater nuclear charge.

Oxygen's first ionization energy is quite high at 1314 kJ/mol, compared to beryllium's 899 kJ/mol. The difference, 415 kJ/mol, is indicative of oxygen's tighter hold on its electrons due to its relatively large number of protons. This signifies that more energy is required to remove an electron from oxygen than from beryllium, which is consistent with oxygen's higher electronegativity.