ideal gas constant

Examples of ideal gas constant in the following topics:

• 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.

• 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.
  • (Isotherms refer to the different curves on the graph, which represent a gas' state at different pressure and volume conditions but at constant temperature; "Iso-" means same and "-therm" means temperature—hence isotherm.)
  • 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.

• 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.

• Charles' and Gay-Lussac's Law: Temperature and Volume

  • Charles' and Gay-Lussac's Law states that at constant pressure, temperature and volume are directly proportional.
  • This law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin); in other words, temperature and volume are directly proportional.
  • A visual expression of Charles' and Gay-Lussac's Law is shown in a graph of the volume of one mole of an ideal gas as a function of its temperature at various constant pressures.
  • This model contains gas molecules on the left side and a barrier that moves when the volume of gas expands or contracts, keeping the pressure constant.
  • A visual expression of the law of Charles and Gay-Lussac; specifically, a chart of the volume of one mole of an ideal gas as a function of its temperature at various constant pressures.

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

  • For gas-phase reactions, the equilibrium constant can be expressed in terms of partial pressures, and is given the designation KP.
  • For gas-specific reactions, however, we can also express the equilibrium constant in terms of the partial pressures of the gases involved.
  • 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:
  • Note that in order for K to be constant, temperature must be constant as well.

• The Effect of Intermolecular Forces

  • The Ideal Gas Law is a convenient approximation for predicting the behavior of gases at low pressures and high temperatures.
  • 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.
  • In the term above, a is a constant specific to each gas and V is the volume. van der Waals also corrected the volume term by subtracting out the excluded volume of the gas.
  • where b is the excluded volume of the gas, R is the universal gas constant, and T is the absolute temperature.

• Kinetic Molecular Theory and Gas Laws

  • The volume occupied by the individual particles of a gas is negligible compared to the volume of the gas itself.
  • The particles of an ideal gas exert no attractive forces on each other or on their surroundings.
  • Gas particles are in a constant state of random motion and move in straight lines until they collide with another body.
  • Charles' Law states that at constant pressure, the volume of a gas increases or decreases by the same factor as its temperature.
  • Boyle's Law states that at constant temperature, the absolute pressure and volume of a given mass of confined gas are inversely proportional.

• 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.
  • The van der Waals equation modifies the ideal gas law to correct for this excluded volume, and is written as follows:
  • The available volume is now represented as $V - nb$, where b is a constant that is specific to each gas.
  • The constant b is defined as:

• 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.
  • This leads to fewer collisions with the container and a lower pressure than what is expected from an ideal gas.
  • where P is the pressure, V is the volume, R is the universal gas constant, and T is the absolute temperature.
  • The constants a and b have positive values and are specific to each gas.
  • Distinguish the van der Waals equation from the Ideal Gas Law.

• 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.
  • 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.
  • The model contains gas molecules under constant pressure.