ideal gas

Examples of ideal gas in the following topics:

• Density Calculations

  • A reformulation of the Ideal Gas Equation involving density allows us to evaluate the behaviors of ideal gases of unknown quantity.
  • The Ideal Gas Equation in the form $PV=nRT$ is an excellent tool for understanding the relationship between the pressure, volume, amount, and temperature of an ideal gas in a defined environment that can be controlled for constant volume.
  • We know the Ideal Gas Equation in the form $PV=nRT$.
  • The term $\frac{m}{V}$ appears on the right-hand side of the above rearranged Ideal Gas Law.
  • Atmospheric science offers one plausible real-life application of the density form of the ideal gas equation.

• Equations of State

  • The ideal gas law is the equation of state of a hypothetical ideal gas (in which there is no molecule to molecule interaction).
  • The ideal gas law is the equation of state of a hypothetical ideal gas (an illustration is offered in ).
  • In an ideal gas, there is no molecule-molecule interaction, and only elastic collisions are allowed.
  • Therefore, we derive a microscopic version of the ideal gas law
  • Because the forces between them are quite weak at these distances, they are often described by the ideal gas law.

• Molar Mass of Gas

  • We can derive a form of the Ideal Gas Equation, PV=nRT, that incorporates the molar mass of the gas (M, $g*mol^{-1}$ ).
  • The molar mass of an ideal gas can be determined using yet another derivation of the Ideal Gas Law: $PV=nRT$.
  • We can plug this into the Ideal Gas Equation:
  • This derivation of the Ideal Gas Equation is useful in determining the molar mass of an unknown gas.
  • How to set up and solve ideal gas law problems that involve molar mass and converting between grams and moles.

• The Ideal Gas Equation

  • In real life, there is no such thing as a truly ideal gas, but at high temperatures and low pressures (conditions in which individual particles will be moving very quickly and be very far apart from one another so that their interaction is almost zero), gases behave close to ideally; this is why the Ideal Gas Law is such a useful approximation.
  • R is the ideal gas constant, which takes on different forms depending on which units are in use.
  • The ideal gas equation enables us to examine the relationship between the non-constant properties of ideal gases (n, P, V, T) as long as three of these properties remain fixed.
  • For the ideal gas equation, note that the product PV is directly proportional to T.
  • Discusses the ideal gas law PV = nRT, and how you use the different values for R: 0.0821, 8.31, and 62.4.

• Problem Solving

  • With the ideal gas law we can figure pressure, volume or temperature, and the number of moles of gases under ideal thermodynamic conditions.
  • The Ideal Gas Law is the equation of state of a hypothetical ideal gas.
  • where R is the universal gas constant, and with it we can find values of the pressure P, volume V, temperature T, or number of moles n under a certain ideal thermodynamic condition.
  • Variations of the ideal gas equation may help solving the problem easily.
  • Remember that the general gas equation only applies if the molar quantity of the gas is fixed.

• Overview of Temperature and Kinetic Theory

  • Also, the temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms, as illustrated in .
  • The kinetic theory of gases uses the model of the ideal gas to relate temperature to the average translational kinetic energy of the molecules in a container of gas in thermodynamic equilibrium .
  • In kinetic theory, the temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom Ek via the equation:
  • We will also derive the ideal gas law:
  • (R: ideal gas constant, n: number of moles of gas) from a microscopic theory.

• Van der Waals Equation

  • The van der Waals equation modifies the Ideal Gas Law to correct for the excluded volume of gas particles and intermolecular attractions.
  • The Ideal Gas Law is based on the assumptions that gases are composed of point masses that undergo perfectly elastic collisions. 
  • This leads to fewer collisions with the container and a lower pressure than what is expected from an ideal gas.
  • Notice that the van der Waals equation becomes the Ideal Gas Law as these two correction terms approach zero.
  • Distinguish the van der Waals equation from the Ideal Gas Law.

• The Effect of the Finite Volume

  • Real gases deviate from the ideal gas law due to the finite volume occupied by individual gas particles.
  • The ideal gas law is commonly used to model the behavior of gas-phase reactions.
  • Ideal gases are assumed to be composed of point masses whose interactions are restricted to perfectly elastic collisions; in other words, a gas particles' volume is considered negligible compared to the container's total volume.
  • At high pressures, the deviation from ideal behavior occurs because the finite volume that the gas molecules occupy is significant compared to the total volume of the container.
  • The van der Waals equation modifies the ideal gas law to correct for this excluded volume, and is written as follows:

• Real Gases

  • Equations other than the Ideal Gas Law model the non-ideal behavior of real gases at high pressures and low temperatures.
  • The Ideal Gas Law assumes that a gas is composed of randomly moving, non-interacting point particles.
  • For most applications, the ideal gas approximation is reasonably accurate; the ideal gas model tends to fail at lower temperatures and higher pressures, however, when intermolecular forces and the excluded volume of gas particles become significant.
  • Note that for an ideal gas, PV=nRT, and Z will equal 1; under non-ideal conditions, however, Z deviates from unity.
  • According to the Ideal Gas Equation, PV=nRT, pressure and volume should have an inverse relationship.

• The Effect of Intermolecular Forces

  • At high pressures and low temperatures, intermolecular forces between gas particles can cause significant deviation from ideal behavior.
  • The Ideal Gas Law is a convenient approximation for predicting the behavior of gases at low pressures and high temperatures.
  • The contribution of intermolecular forces creates deviations from ideal behavior at high pressures and low temperatures, and when the gas particles' weight becomes significant.
  • The Ideal Gas Law does not account for these interactions.
  • To correct for intermolecular forces between gas particles, J.D. van der Waals introduced a new term into the Ideal Gas Equation in 1873.