gas constant

(noun)

A universal constant, R, that appears in the ideal gas law, (PV = nRT), derived from two fundamental constants, the Boltzman constant and Avogadro's number, (R = NAk).

Related Terms

Examples of gas constant in the following topics:

  • Constant Pressure

    • Isobaric processis a thermodynamic process in which the pressure stays constant (at constant pressure, work done by a gas is $P \Delta V$).
    • For example, an ideal gas that expands while its temperature is kept constant (called isothermal process) will exist in a different state than a gas that expands while pressure stays constant (called isobaric process).
    • Let's consider a case in which a gas does work on a piston at constant pressure P, referring to Fig 1 as illustration.
    • Specific heat at constant pressure is defined by the following equation:
    • By noting that N=NAn and R = kNA (NA: Avogadro's number, R: universal gas constant), we derive:

  • Specific Heat for an Ideal Gas at Constant Pressure and Volume

    • An ideal gas has different specific heat capacities under constant volume or constant pressure conditions.
    • Specific Heat for an Ideal Gas at Constant Pressure and Volume
    • The heat capacity at constant volume of nR = 1 J·K−1 of any gas, including an ideal gas is:
    • For moderate temperatures, the constant for a monoatomic gas is cv=3/2 while for a diatomic gas it is cv=5/2 (see ).
    • The heat capacity at constant pressure of 1 J·K−1 ideal gas is:

  • 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.
    • Take the general gas-phase reaction:
    • Note that in order for K to be constant, temperature must be constant as well.
    • Therefore, the term RT is a constant in the above expression.

  • Equations of State

    • The ideal gas law is the equation of state of a hypothetical ideal gas (an illustration is offered in ).
    • while Charles' law states that volume of a gas is proportional to the absolute temperature T of the gas at constant pressure
    • where C is a constant which is directly proportional to the amount of gas, n (representing the number of moles).
    • The proportionality factor is the universal gas constant, R, i.e.
    • where k is Boltzmann's constant and N is the number of molecules.

  • Isothermal Processes

    • For an ideal, the product of pressure and volume (PV) is a constant if the gas is kept at isothermal conditions.
    • The value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant.
    • In other words, the ideal gas law PV = nRT applies.
    • In thermodynamics, the work involved when a gas changes from state A to state B is simply
    • It is also worth noting that, for many systems, if the temperature is held constant, the internal energy of the system also is constant, and so $\Delta U = 0$.

  • Overview of Temperature and Kinetic Theory

    • The kinetic theory of gases describes a gas as a large number of small particles (atoms and molecules) in constant, random motion.
    • The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion.
    • (k: Boltzmann's constant).
    • We will also derive the ideal gas law:
    • (R: ideal gas constant, n: number of moles of gas) from a microscopic theory.

  • Constant Pressure and Volume

    • Isobaric process is one in which a gas does work at constant pressure, while an isochoric process is one in which volume is kept constant.
    • A process in which a gas does work on its environment at constant pressure is called an isobaric process, while one in which volume is kept constant is called an isochoric process.
    • Since the pressure is constant, the force exerted is constant and the work done is given as PΔV.
    • If a gas is to expand at a constant pressure, heat should be transferred into the system at a certain rate.
    • An isobaric expansion of a gas requires heat transfer during the expansion to keep the pressure constant.

  • Van der Waals Equation

    • where P is the pressure, V is the volume, R is the universal gas constant, and T is the absolute temperature.
    • Isotherm (plots of pressure versus volume at constant temperature) can be produced using the van der Waals model.
    • The constants a and b have positive values and are specific to each gas.
    • The term involving the constant a corrects for intermolecular attraction.
    • The b term represents the excluded volume of the gas or the volume occupied by the gas particles.

  • 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.
    • 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.
    • If the reaction is kept at constant pressure, they must stay farther apart, and an increase in volume will compensate for the increase in particle collision with the surface of the container.
    • 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 particles of a real gas do, in fact, occupy a finite, measurable volume.
    • 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: