Properties and Laws of Gases

Posted on May 15, 2024 in Chemistry

Gases

These particles, which can be very small atoms or molecules, are in continuous motion and constantly collide.

Features

  • Expands to fill the container that contains them spontaneously (the volume of gas is equal to that of the recipient).
  • Are compressible.
  • Gases form homogeneous mixtures with each other regardless of the identities or related properties of the gases.
  • The molecules of gases are relatively far apart.
  • They can be modeled with repeated molecular arrangements.
  • Each particle is completely separated from the others.

Properties Easier to Measure

  • Temperature
  • Pressure
  • Volume

Pressure

Pressure is a property exhibited by all gases confined in a container and is understood as the force (F) that acts on a given area (A).

Pressure = p = F / A = force / area

Gas Laws

Gas laws show the relationships between the properties of gases.

  • Boyle’s Law
  • Charles’ Law
  • Avogadro’s Law

The ideal gas law combines all of these laws.

Boyle’s Law (The Relationship Between Volume and Pressure)

The volume of a fixed amount of gas kept at a constant temperature is inversely proportional to the pressure.

Numerically, it is described as follows: P1V1 = P2V2

Robert Boyle

  • Studied the relationship between the pressure exerted on a gas and the resulting volume.
  • Used a J-shaped tube and employed mercury to apply pressure on the gas.

Charles’ Law (Relationship Between Temperature and Volume)

The volume of a fixed amount of gas at constant pressure increases linearly with temperature. This is described as follows: V1/T1 = V2/T2

Avogadro’s Law (Relationship Between the Amount of Gas and Volume)

The volume of gas at constant temperature and pressure is directly proportional to the number of moles of gas.

This is described numerically as follows: V1/n1 = V2/n2

Ideal Gas Law

The ideal gas law is the combination of Boyle’s Law, Charles’ Law, and Avogadro’s Law.

The three gas laws derived from the relations between two physical properties of a gas while keeping the remaining two constant are:

  • Boyle’s Law: V ∝ 1/P (n, T constant)
  • Charles’ Law: V ∝ T (n, P constant)
  • Avogadro’s Law: V ∝ n (P and T constant)

By combining these, a single, more general gas law relationship is obtained:

V ∝ nT/P

If the proportionality constant is called R, we obtain:

V = R(nT/P)

Rearranging the equation, we get:

PV = nRT

Ideal Gas

An ideal gas is one whose physical behavior is accurately described by the ideal gas equation.

Dalton’s Law (1766-1844) of Partial Pressures

“The total pressure of a gas mixture equals the sum of the pressures that each gas would exert if it were alone.”

Pt = P1 + P2 + P3…

Standard Atmospheric Pressure

Standard atmospheric pressure or normal pressure corresponds to the typical pressure at sea level. It is the pressure necessary to support a column of mercury 760 mm high.

Relations Between the Most Common Pressure Units

1 atm = 760 mmHg = 760 torr = 1.01325 x 105 Pa = 101.135 kPa

(1 torr = 1 mmHg)

Molar Mass Determination

If you know the volume occupied by a gas at a certain temperature (T) and pressure (P), you can solve the ideal gas equation for the amount of gas in moles. As the number of moles of gas is equal to the mass of gas divided by the molar mass, if you know the mass and number of moles of gas, you can solve the expression n = m/M for the molar mass, M. Another alternative is to make the substitution n = m/M directly in the ideal gas equation: PV = mRT/M.

Densities of Gases

To determine the density of a gas, you can begin with the equation for density: d = m/V. Express the mass of gas as the product of the number of moles of gas by its molar mass: m = n x M. This gives you d = m/V = n x M/V = (n/V) x M.

The gas densities differ from the densities of solids and liquids in two important ways:

  1. The gas densities vary greatly with pressure (P) and temperature (T), increasing with increasing gas pressure and decreasing with increasing temperature. The densities of solids and liquids also change slightly with changes in temperature, but they change very little with pressure.
  2. The density of a gas is directly proportional to its molar mass. There is no simple relationship between density and the molar mass of solids and liquids.

Atmospheric Pressure and the Barometer

Due to gravity, the atmosphere exerts a downward force and therefore a pressure on the surface of the Earth.

Atmospheric Pressure Measurement

Atmospheric pressure is measured with a barometer, which is described below:

  • A glass tube with a length somewhat greater than 760 mm is closed at one end and filled with mercury.
  • The filled tube is inverted and placed in a dish of mercury, so that no air enters the tube.
  • Some of the mercury flows out of the tube, but the height of the mercury column remains the same. The headspace of the tube is essentially empty.
  • If the dish is open to the atmosphere, the pressure fluctuates, changing the height of the mercury column in the tube.

Pressure Gauges and the Pressure of an Enclosed Gas

Pressure gauges are used to measure the pressure of a gas in a container. They operate much like the barometer and are normally made with mercury.

To define the state or condition of a gas, only four variables are needed:

  • Temperature (T)
  • Pressure (P)
  • Volume (V)
  • Quantity of matter, i.e., the number of moles (n)