Ideal Gas Equation, Kinetic Theory, and Atomic Models

Ideal Gas Equation of State

The general equation of state for ideal gases is:

p · V = n · R · T

Kinetic Theory of Gases

Gases consist of molecules that:

• Occupy no volume.
• Move randomly with a velocity whose mean depends on temperature.
• Collide elastically with each other and the vessel walls, causing pressure.

Boyle's Law

P₁ · V₁ = P₂ · V₂

At constant temperature, the volume occupied by a gas is inversely proportional to the pressure it is under.

Charles's and Gay-Lussac's Law

At constant pressure, the volume occupied by a gas is directly proportional to the absolute temperature at which it is located. At constant volume, the pressure of a gas is directly proportional to the absolute temperature at which it is located.

Dalton's Law

The total pressure of a gas mixture equals the sum of the partial pressures of the constituent gases.

Amagat's Law

The total volume of a gas mixture equals the sum of the partial volumes of the constituent gases.

Experiments in Atomic Theory

Experiments in the late nineteenth and early twentieth centuries provided evidence of the divisibility of the atom. Two types of experiments were crucial:

• Electrical discharge through gases at low pressure.
• Bombardment of particles from radioactive gases and thin sheets of metal or other substances.

Discovery of Subatomic Particles

• 1897: Joseph John Thomson discovers the electron.
• 1911: Ernest Rutherford identifies the nucleus of hydrogen as a proton.
• 1932: James Chadwick discovers the neutron.

Thomson's Atomic Model

Thomson proposed that the atom is a sphere of positive electric charge in which negative electrons are embedded, in a number sufficient to neutralize the positive charge.

Atomic Nucleus

• Atomic Number: Number of protons.
• Mass Number: Number of protons plus the number of neutrons.
• Isotopes: Atoms with the same atomic number and different mass numbers.
• Isobars: Atoms with the same mass number and different atomic numbers.
• Atomic Mass: Weighted average of the masses of the isotopes of an element.

Rutherford's Atomic Model

• The atom has a positive nucleus where almost all the mass is concentrated.
• Negative electrons orbit the nucleus in concentric circular orbits.
• There is a large empty space in the atom, and its nucleus is about 10,000 times smaller than the atomic volume.
• The atom is electrically neutral.