The+Ideal+Gas+Law

=**The Ideal Gas Law**=

An ideal gas is a gas filled with molecules that only collide in perfectly elastic collisions with no electromagnetic or gravitational forces present. The ideal gas law helps us describe the characteristics of an ideal gas in a system when pressure or temperature of the gas changes, when the volume of the system changes, or when the number of molecules in the system changes.

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__**Equation**__
PV=nRT
 * === In Chemistry: ===

where: P=Pressure (Pascals) V=Volume (cubic meters) n=moles R=8.31Joules/(moles *K) (universal gas constant) T=temperature (Kelvin) ||< ===In Physics:=== PV=NkT

where: P=Pressure (Pascals) V=Volume (cubic meters) N=number of molecules k=1.38066 x 10 -23 J/K (**Boltzmann's constant**) Temperature (Kelvin). ||

__**Explanation of Variables**__
Before explaining the formula, you should first understand the variables that make up the formula. This will help you conceptualize each variable as it may change in the equation.

Air Pressure
Air Pressure is the force of a gas pushing perpendicular to a surface per unit area. For example, the air pressure exerted by our atmosphere on the Earth's surface is roughly 14.696 pounds per square inch, so 14.696 pounds of force is being exerted on every square inch of the Earth's surface. The standard equation for pressure is

[[image:dvapphysics/Pressure formula.jpg]]
The unit for pressure is the pascal (Pa) which is Newtons of square meters. So for a closed system, let's say an oxygen tank for instance, the air pressure would be the force exerted on the sides of the tank by the air. Instead of using pressure due to the weight of the air, indicated in the picture, it is the pressure due to the collisions of the gas against the walls of the tank. The more collisions the greater the pressure. The faster the molecules are moving (the higher temperature the gas is), the greater the pressure.

Volume
Volume is the amount of space something takes up, regardless of mass. For instance, an inflated balloon has a significantly larger volume than a deflated balloon, but a very similar mass. Various volume formulas can be found on __**[|math.com.]**__ The unit for volume is square meters (m 3 ).

The Mole
A **mole** (variable **n** in the ideal gas law) is a specific number of molecules that was created for convenience. The number of molecules in a mole was accredited to Amedeo Avogadro, and the name of the conversion constant follows so. Moles are especially useful when determining the number of molecules in solutions consisting of the same type of molecular, such as a solid piece of iron. So instead of using incredibly large numbers of molecules, one can simplify it to a much smaller number of moles. The mole variable is usually used in the chemistry application of the ideal gas law. Likewise, in the physics application, we use **N** to represent the number of individual molecules rather than moles.
 * Avogadro's number =** 1 mole = 6.02214x10 23 molecules.

Temperature
The temperature of an ideal gas is the average heat of the gas spread uniformly throughout a closed system. The heat of a gas differs from the temperature of a gas in the way that the heat is the total energy of the gas, while the temperature is the average heat of the gas. One may find the temperature or total heat of a closed system of gas using the formula: Where U is the total internal energy (total heat) of the system (measured in joules), n is the number of moles of gas in that system, R is the universal gas constant, and T is the temperature of the gas (in Kelvin). This formula is only valid for **monatomic gases**, which are gases the are composed of only one type of molecule.

One may also find the **root-mean-square speed** of the molecules using the formula: Where v is the root-mean-square velocity of the molecules, k b is the Boltzmann constant, T is the temperature, and m is the mass of one molecule of gas.

__Explanation of the Ideal Gas Law__
The ideal gas law is best explained using a balloon inflated with an ideal gas. Assuming that the balloon is tied so no air can escape and that the internal air pressure remains the same, common sense would tell us that if we increase the temperature of the air in a balloon, the balloon will expand, and if we decrease the temperature of the air the balloon will shrink. This is supported by PV=nRT. The direct relationship between volume and temperature leads us to conclude that if temperature increases, volume increases, and vice-versa.



Likewise, by holding other variables at a constant value, we can derive more relationships from the equation. For example, if the volume of the balloon and the temperature of the air were held constant, then air pressure and number of moles would have a direct relationship. This means that if you add air, the pressure increases. Take air away, the pressure decreases.

You may fiddle with the program at right to grasp a better understanding of the relationships involved with the ideal gas law. Another useful program can be found on the link found right: http://intro.chem.okstate.edu/1314f00/laboratory/glp.htm

Other than conceptually grasping these concepts, problem solving using this law is essentially plugging-and-chugging.

__Boyle's Law__
Robert Boyle first came up with the relationship that the pressure times the volume (P x V) in a closed system would remain constant despite one variable changing. Thus, we get the equation: where P 1 is the initial pressure and V 1 is the initial volume. P 2 is the pressure after some change and V 2 is the volume after some change.

(1)
A specific water bottle can withstand a maximum internal pressure of 520 KPa before exploding. Jerry wants to know to what temperature to hear the water bottle up to to explode. There are 5 moles of gas contained within the water bottle, which has a volume of 0.002m 2. At what temperature will the water bottle explode (in Kelvin)?

(2)
The internal air pressure of balloons usually reaches equilibrium without the outside environment to cancel out the forces. A balloon with 1000 KPa of internal pressure and a volume of 0.008m 3 is submerged in water. Because the water surrounding the balloon adds additional external pressure on the balloon, the balloon must increase in pressure to counteract it. The external pressure becomes 2000 KPa after the balloon is submerged in water. Assuming the temperature of air inside the balloon remains constant, to what volume must the balloon shrink to to compensate for the increase in external pressure.

(3)
If I have 3 moles of gas contained in a 0.06m 3 container at a temperature of 600K, what is the internal pressure of the gas on the container?

(1)
The first step is establishing the formula. The formula required to solve this is the Ideal gas law formula: PV = nRT

Because we are given the variables for pressure, moles, and volume, we can therefore calculate the pressure.



**(2)**
Boyle's Law

(3)
PV = nRT



__Sources__
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html http://secondarychemistry.com/11u/index/gases/gases05.pdf http://www.eo.ucar.edu/kids/sky/air2.htm http://www.crh.noaa.gov/abr/?n=balloonexp.php http://www.school-for-champions.com/science/pressure.htm http://ygraph.com/chart/1535 http://phet.colorado.edu/en/simulation/gas-properties Serway/Faughn College Physics Seventh Edition textbook pages 334 - 343