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.

• 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.

• 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.

• Expressing the Equilibrium Constant of a Gas in Terms of Pressure

  • Take the general gas-phase reaction:
  • The reason we are allowed to write a K expression in terms of partial pressures for gases can be found by looking at the ideal gas law.
  • Recall that the ideal gas law is given by:
  • For instance, if a reaction produces three moles of gas, and consumes two moles of gas, then $\Delta n=(3-2)=1$.
  • Write the equilibrium expression, KP, in terms of the partial pressures of a gas-phase reaction

• Avogadro's Law: Volume and Amount

  • The law is named after Amedeo Avogadro who, in 1811, hypothesized that two given samples of an ideal gas—of the same volume and at the same temperature and pressure—contain the same number of molecules; thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas.
  • For example, 1.00 L of N2 gas and 1.00 L of Cl2 gas contain the same number of molecules at Standard Temperature and Pressure (STP).
  • V is the volume of the gas, n is the number of moles of the gas, and k is a proportionality constant.
  • As an example, equal volumes of molecular hydrogen and nitrogen contain the same number of molecules and observe ideal gas behavior when they are at the same temperature and pressure.
  • In practice, real gases show small deviations from the ideal behavior and do not adhere to the law perfectly; the law is still a useful approximation for scientists, however.

• Dalton's Law of Partial Pressure

  • Because it is dependent solely the number of particles and not the identity of the gas, the Ideal Gas Equation applies just as well to mixtures of gases is does to pure gases.
  • A 2.0 L container is pressurized with 0.25 atm of oxygen gas and 0.60 atm of nitrogen gas.
  • We know from Boyle's Law that the total pressure of the mixture depends solely on the number of moles of gas, regardless of the types and amounts of gases in the mixture; the Ideal Gas Law reveals that the pressure exerted by a mole of molecules does not depend on the identity of those particular molecules; Dalton's Law now allows us to calculate the total pressure in a system when we know each gas individual contribution.
  • From the Ideal Gas Law, we can easily calculate the measured pressure of the nitrogen gas to be 0.763 atm.
  • We now define the partial pressure of each gas in the mixture to be the pressure of each gas as if it were the only gas present.