Physics 13: 6-13 The Ideal Gas Law
Text Reading: Giancoli, Physics - Principles with Applications, Chapter 13: 6-13
- 13.6: For gases, the rules of thermal expansion don't work very well. For one thing, gases expand to fill their container. We can, however, use the ideal gas law to describe the behavior of gases where the gas is not too dense and not too close to liquefaction. With these provisos, three observations hold:
|Robert Boyle||V ∝ 1/P|
|Jacques Charles||V ∝ T|
|Joseph Gay-Lussac||P ∝ T|
The proportional sign ∝ means that there has to be some other constant factor involved that provides both a scaling component and a units component. Volume is not the same thing as temperature, so V ∝ T means there has to be some proportional constant k that allows us to convert meters3 to Kelvin.
The ideal gas law, PV = nRT = NkT (n = moles, N = number of atoms or molecules), combines the observations of Boyle's, Charles's, and Gay-Lussac's laws. The values for the constant R or k depends on the units of the other factors (i.e., R changes if you measure P in atm instead of Pascal).
- 13.7: When solving gas law problems, you don't always need to know exact values if a particular factor doesn't change. For example, increasing the temperature from T to T' of a gas at pressure P confined to a particular glass container usually means that the volume and number of molecules doesn't change. The before values of pressure and temperature can be set to the fixed values:
P/T = nR/V and these fixed values will equal the final P'/T' calculation. You can then set P/T directly equal to P'/T' and solve for the new pressure P'.
- 13.8: Around 1810, Avogadro proposed that equal volumes of gas held the same number of molecules, regardless of the type of gas: a liter of H2 and a liter of CO2 at the same temperature had equal numbers of molecules. His theory was discounted, and only after his death around 1860 did chemists come to realize that he was correct. When chemists realized the relationship between mass and number of molecules in the mass was governed by a set ratio for each element, they honored Avogadro by naming the number of molecules of H2 gas in a gram (6.02 * 1023) for him; we usually call this value a mole.
- 13.9: Temperature measures average velocity of the individual molecules in a substance, not total heat content of a substance: KEave = ½ mv2 = 3/2 kT.
- 13.10: Average velocities not only go up as temperature goes up, but the distribution of other velocities changes. Since there is a lower limit to velocity (0) but no upper limit, there will be more different velocities exhibited in molecules with velocities higher than average than velocities exhibited in molecules with velocities below average.
- 13.11: Phase status is a function of pressure and temperature: as temperature increases, higher pressures are needed to keep a substance in solid or liquid phase. At some temperature, a substance will shift to the gas phase regardless of the pressure applied: this is the substance's critical point. There often exists a pressure-temperature combination where gas, liquid, and solid phases exists in equilibrium: this is the triple point for the substance (for water, the triple point occurs when P = 0.006 atm and T = 0.01 °C). Below the triple point temperature, the solid sublimates directly to gas without going through a liquid phase.
- 13.12: Vapor pressure is the additional pressure added to the air above a liquid substance by the gas form of the substance escaping from the liquid surface, and usually increases as temperature increases. Saturated vapor pressure occurs when as many molecules are condensing as are evaporating. At the point where vapor pressure equals atmospheric pressure, the liquid will boil. The practical result is that liquid boils at lower temperatures if the atmospheric pressure is lower. For example, water boils below 200 °F in Denver -- which drastically changes its ability to cook food. If several gases are present in a mixture, as in our atmosphere, each gas independently exerts a partial pressure and the sum of the partial pressures equals the total pressure of the gas. The ratio of the partial pressure of water to its saturated vapor pressure at a given temperature is relative humidity; near 100% air holds all the water it can.
- 13.13: Diffusion is the dispersion of molecules from a high concentration area into a volume where the concentration is lower.
- Avogadro's form of the ideal gas law (atoms or molecules instead of moles):
- The universal gas constant has a numerical value based on the units used:
- The Boltzman constant depends on R and Avogadro's number:
Read the following weblecture before chat: The Ideal Gas Law
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