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The figure has two plots of Pressure, p, on the vertical axis as a function of volume, V, on the horizontal axis, at several different temperatures. Figure a shows six isotherms labeled, from the bottom to top, T 1, T 2, T C, T 3, T 4 and T 5. A note on the graph tells us that these temperatures are also in increasing order. The graphs show that pressure generally decreases with increasing volume for all temperatures, except at low temperatures when pressure is constant as a function of volume during a phase change. The phase change occupies a region in the plot shaded in blue and labeled Liquid-vapor equilibrium region. Figure b is the same plot, zoomed in to show the p V diagram in and around the shaded liquid vapor region. Above the shaded region, the curves decrease monotonically. The curve that is still outside but just touches the peak of the liquid vapor region is labeled as the critical isotherm, T c. The point at which this curve meets the shaded region is labeled the critical point. The region to the left of the shaded region and at pressures lower than the pressure of the critical point is the liquid region. The region to the right of the shaded region is the vapor region. The right edge of the shaded region is the saturation curve. The region above the critical isotherm is labeled as true but not ideal gas.
pV diagrams. (a) Each curve (isotherm) represents the relationship between p and V at a fixed temperature; the upper curves are at higher temperatures. The lower curves are not hyperbolas because the gas is no longer an ideal gas. (b) An expanded portion of the pV diagram for low temperatures, where the phase can change from a gas to a liquid. The term “vapor” refers to the gas phase when it exists at a temperature below the boiling temperature.

The isotherms above T c do not go through the liquid-gas transition. Therefore, liquid cannot exist above that temperature, which is the critical temperature (described in the chapter on temperature and heat). At sufficiently low pressure above that temperature, the gas has the density of a liquid but will not condense; the gas is said to be supercritical    . At higher pressure, it is solid. Carbon dioxide, for example, has no liquid phase at a temperature above 31.0 ºC . The critical pressure is the maximum pressure at which the liquid can exist. The point on the pV diagram at the critical pressure and temperature is the critical point (which you learned about in the chapter on temperature and heat). [link] lists representative critical temperatures and pressures.

Critical temperatures and pressures for various substances
Substance Critical temperature Critical pressure
K °C Pa atm
Water 647.4 374.3 22.12 × 10 6 219.0
Sulfur dioxide 430.7 157.6 7.88 × 10 6 78.0
Ammonia 405.5 132.4 11.28 × 10 6 111.7
Carbon dioxide 304.2 31.1 7.39 × 10 6 73.2
Oxygen 154.8 –118.4 5.08 × 10 6 50.3
Nitrogen 126.2 –146.9 3.39 × 10 6 33.6
Hydrogen 33.3 –239.9 1.30 × 10 6 12.9
Helium 5.3 –267.9 0.229 × 10 6 2.27

Summary

  • The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
  • A mole of any substance has a number of molecules equal to the number of atoms in a 12-g sample of carbon-12. The number of molecules in a mole is called Avogadro’s number N A ,
    N A = 6.02 × 10 23 mol −1 .
  • A mole of any substance has a mass in grams numerically equal to its molecular mass in unified mass units, which can be determined from the periodic table of elements. The ideal gas law can also be written and solved in terms of the number of moles of gas:
    p V = n R T ,

    where n is the number of moles and R is the universal gas constant,
    R = 8.31 J/mol · K .
  • The ideal gas law is generally valid at temperatures well above the boiling temperature.
  • The van der Waals equation of state for gases is valid closer to the boiling point than the ideal gas law.
  • Above the critical temperature and pressure for a given substance, the liquid phase does not exist, and the sample is “supercritical.”

Conceptual questions

Two H 2 molecules can react with one O 2 molecule to produce two H 2 O molecules. How many moles of hydrogen molecules are needed to react with one mole of oxygen molecules?

2 moles, as that will contain twice as many molecules as the 1 mole of oxygen

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Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

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A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

pressure

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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