Charles' Law
If
Then V= k T (for a constant P and n)
Avogadro Law
If
Then V= kn (for a constant P and T)
The Ideal Gas Law
Avogadro's law V = k1 * n (for a constant P and T)
Charles' law -- V = k2 * T (for a constant P and T)
Boyle's law -- V = k3 / P ( for a constant T and n)
V=( k1 k2 k3 n T) / P
After rearranging and letting the combined proportionality constant R = k1 k2 k3, the equation becomes:
PV= n R T
With the equation in this form, it is possible to determine any one missing variable as long as the other five are know, the number of moles of the gas does not change, and the gas in question acts as an ideal gas at the conditions specified.
Shifting away from a quest to understand elements back to a broader look at how things interact, brings us to the investigation of another gas law. In 1800 Jacques Charles observed that, for a given number of moles of gas, the volume is directly proportional to the absolute temperature if the pressure is held constant.
Charles' law can be expressed in a formula as follows:
P = pressure
V = Volume
T = Temperature0
n = Number of moles of gas
k = constant of proportionality
For comparing the saem gas sample at constant pressure under differing conditions of volume and temperature, Charles' law can be written as follows
T1 V2 = T2V1
The subscripts 1 and 2 represent the different conditions
An Example of Charles' Law
In 1811, Amedeo Avogadro provided the vital third part to the view of gasses and their interactions. He proposed that equal volumes of a gas at constant pressure and temperature have an equal number of molecules.
Avogadro's law can be expressed in a formula as follows:
P = pressure
V = Volume
T = Temperature
n = Number of moles of gas
k = constant of proportionality
At first this may seem like a simple and almost insignificant addition to the body of knowledge. This simple formula, however, allows for the combination of Boyle's and Charles' laws into the ideal gas law.
Start by looking at the three gas laws,
Since the volume V is proportional to the right side of each equation, using algebra to combine and rearrange the equations yields:
This equation is known as the ideal gas law. Though this law can be only used to predict the action of ideal gases, it allows for a better understanding of gasses in general. Most gasses deviate from the results that the equation would predict, but the deviation is so slight that it can be neglected in all but the most critical of calculations.
Using the ideal gas law, many relationships and proportions can be derived. The ideal gas law can be used to give an indication of how a gas will react under changing conditions.
By using simple algebra, the Ideal gas law can be written in a much more useful form.
P1 V1 T2 = P2V2T1
The subscripts 1 and 2 represent the different conditions
More About Ideal Gas
Many other variations of the equation can also be derived. For example, Joseph Gay-Lusac derived and tested a variation of the ideal gas law that correlated pressure and temperature when the volume and number of moles of gas were held constant. He found that as pressure decreased so did temperature. Other experimental verifications of the ideal gas law proved that it worked well for most gasses.
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