.
Recall:
We were talking about:
Properties of Gases
In order to describe or discuss the properties of gases we must know the variables which determine the state of a gas. These variables are,
Pressure
The SI unit of pressure is the Paschal (Pa), but we commonly use other units. The most common pressure units are:
1 atm = 101325 Pa.Volume1 bar = 105 Pa.
1 atm = 760 Torr.
The SI unit of volume is the m3. We will usually use the metric unit of volume the liter (L),
1 L = 10-3 m3.
Temperature
The SI unit of temperature is the Kelvin. The Kelvin has the same size "degree" as the Celsius scale, but the origin of the Kelvin scale is at absolute zero.
0o C = 273.15 K.Temperature measurements for use in the gas laws will always be in Kelvin (K).
The Gas Laws
Beginning in the middle 17th century many scientists
were experimenting to determine the properties of gases. These experiments
spanned nearly 200 years and resulted in a set of equations (gas laws)
which describe to good accuracy the properties of gases. Mainly these gas
laws showed how the variables, p, V, T, and n,
were related to each other in the description of gases.
Boyle's Law
Around 1660 Robert Boyle was experimenting with the properties of gases under conditions where the temperature was held constants. He would take a sample of gas and measure the volume of the gas at different pressures (without changing the temperature).
Boyle found that, at constant temperature, the volume of the gas was inversely proportional to the pressure on the gas. That is, at constant T,
We usually write Boyle's law in the form,
At the beginning of the 19th century the French chemist Joseph Gay-Lussac made several contributions to the understanding of the properties of Gases. The law, called Gay-Lussac's law, concerned the behavior of gases at constant volume. That is, how does the pressure depend on temperature if the volume is held constant. He found, by experiment, that
In words, at constant volume the pressure of a gas is proportional to the absolute temperature. (By the way, this kind of experiment is one way to determine that there is such a thing as an absolute temperature. According to Gay-Lussac's law absolute zero is the temperature at which p = 0.)
Example calculation:
In 1787 French scientist Jacques Charles was studying the properties of gases at constant pressure. He found that,
(This is another equation that suggests that there is an absolute zero of temperature. The absolute zero is the temperature at which the pressure of the gas would go to zero.)
Example problem:
The Combined Gas Law
If we multiply Boyle's law, Gay-Lussac's law and Charles' law together and take the square root we arrive at the combined gas law,
That is, for a given sample of gas
This equation allows us to do calculations in which two variables change at the same time.
Example problem:
Gay-Lussac conducted other experiments on gases, in particular, on the volumes of gases involved in chemical reactions.
He found that the ratio of the volumes of gases involved in chemical reactions (at the same temperature and pressure) were always simple fractions (fractions composed of small whole numbers).
For example, in the reaction
at constant temperature and pressure, Gay-Lussac found that the ratio of the volume of H2(g) to the volume of N2(g) was always 3 to 1, regardless of the initial volumes used. Likewise, the ratio of the volume of H2(g) to the volume of NH3(g) was always 3 to 2.N2(g) + 3 H2(g) ® 2 NH3(g),
This lead Amedeo Avogadro to postulate ,
Avogadro's Law
Avogadro's law states that, at the same temperature and
pressure, equal volumes of gases contain the same number of molecules.
This law provides an explanation for why Gay-Lussac's law of combining
volumes works.
The Ideal Gas Law
Going back to the combined gas law
it was easily seen that from experiments that the constant in this equation depended on the quantity of gas. In fact, the constant is proportional to the number of moles, n, of gas. If we call the proportionality constant R, we get
The latter of these two equations is known as the ideal gas law. (There are logical reasons why this equation should be called the "perfect gas law," and it was called this for a while, but the name "perfect gas law" has lost favor in recent times. We will call it simply the ideal gas law.)
(A more accurate name for this equation would be "the ideal gas equation of state." That is because it provides a relationship between the state variables p, V, T, and n. We can't pick arbitrary values for these four variables. If we select the values of any three variables the fourth is fixed by the equation.)
