The discovery of natural law is a scientific achievement. In terms of science, we are interested in the laws as well as the strategy leading to discovery. Science is the study of these laws and the development of scientific methods for discovery.
The discoveries of gas laws represent some major breakthroughs in our understanding of the gases in the material world. At the dawn of science, experiments were performed on gases at specific conditions. Under these conditions, gas laws were formulated.
A law is a model that mimics the behavior of a system. By applying a gas law, we can predict the outcome of certain parameters when a set of condition is understood or given.
The ABCD laws of gases refers to four gas laws:
These laws were not discovered in the above order, but we review them in this order. Since you also have some concept of the ideal gas law, we show how they are related to the ideal gas law,
The ideal gas law is easy to remember and apply in solving problems, as long as you get the proper values and units for the gas constant, R.
Of course, this law can be and has been stated in many ways. Equal numbers of molecules means equal amount in moles.
The Avogadro's law is part of the ideal gas law, P V = n R T, which can be written in the following form:
R T V = ---- n PAt some specific T and P, the volume is proportional to the amount, n, in moles (a fun link). Amounts of two gases at the same T and P are, of course, proportional to their volumes. Thus, when 2 L of hydrogen reacts with 1 L of O2, the number of hydrogen molecules are twice those of oxygen molecules. Observations like these led Avogadro to propose the diatomic molecules for these elements, and formulate the chemical reaction as:
Robert Boyles (1627-1691), experimented with gas at constant temperature. Using Torricelli discovery, Boyle measured the variation of pressure when the volume changes, and discovered that volume is inversely proportional to the pressure, and vice versa.
Again, the Charles's law is also part of the ideal gas law, and the relationship between V and T is obvious:
By now, you can see that the ideal gas law combines the ABC laws of gases.
Well, there are four quantities in dealing with gases, amount n, volume V, pressure P, and temperature T. The ABC laws of gases give the relationship of any two of these quantities when the other two of them are held constant.
The partial pressure is the pressure due to a particular gas as if it is in the container by itself. Avogadro's law implies that gas molecule of any gas behave exactly the same way. Thus, the pressure exerted by n mole of any gas, or n mole of a gas mixture has the same pressure.
The ideal gas law includes the law of partial pressures, because the total number of moles is the sum of moles of all the components in the mixture.
Later, these laws are integrated into a simple ideal gas law for the calculation of gas properties. At temperatures much higher than the critical temperature of the gas, and when the pressure is not very high, the ideal gas law is adquate to predict the gas properties. However, for industrial and other applications accurate predictions are required, and corrections due to non-ideal behavior must be made.
One of the applicatons of Dalton's law is for the correction of pressure when a gas is collected by displacement of water. During this process, the gas collected is saturated by water vapor. Water vapor pressure or partial pressure depends on temperature.
The partial pressure of O2 is total pressure minus the partial pressure of water vapor.
PO2 = (759 - 12) torr = 747 torr.
By the ideal gas law, n = P V / R T, we have,
(747/760 atm) * 0.250 L n = ---------------------------- 0.08205 L atm/K.mol * 287 K = 0.0104 mol.Discussion
Note that 1 atm = 760 torr (or mm Hg). The units used in the formulation requires R = 0.08205 L atm / (mol.K).
Formulate the calculation for n.
(12/760 atm) * 0.250 L n = ---------------------------- 0.08205 L atm/K.mol * 287 K