Ideal Gas Law

Ideal Gas Law

Ideal gas law: pV=mRT

Where p = pressure

           V = volume

           m = mass

           R = gas constant

and     T = temperature

When we allow an ideal gas in a container to expand into a larger volume, we get the following relationship:

                         

Where subscripts 1 denote the initial state and subscripts 2 denote the final state after the expansion.

The Graph of Mass After Mixing, m2 Against Mass Before Mixing, m1

First and foremost, the ideal gas is a type of hypothetical gas which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can think of it as a set of perfectly hard balls that collide but otherwise do not interact with each other. In this gas, all internal energy is in the form of kinetic energy, and any change in internal energy is accompanied by a change in temperature.

            In reality, there is no ideal gas, but many gases behave as if they are ideal at ideal operating temperatures and pressures which are at higher temperature and lower pressure. Higher the potential energy due to intermolecular forces becomes less significant compared with the particle’s kinetic energy. Then, the size of the molecules becomes less significant compared to the empty space between them when lower pressure.

 There are several assumption needed is applied when using the ideal gas law. Firstly, gases molecule is move in the straight line and behave as rigid spheres. Then, pressure is due to collisions between the molecules and the walls of the container. Furthermore, collisions between the molecules themselves and between the molecules and the walls of the container are perfectly elastic. Thus, there is no loss of kinetic energy during the collision. Next, the temperature of the gas is proportional to the average kinetic energy of the molecules. Lastly, intermolecular forces between the gas molecules and the volume occupied by the molecules are negligible.

The ideal gas law can be thought of as derived from the dynamic pressure of the gas molecules colliding with the walls of the vessel according to Newton law. But there are also statistical elements in determining the average kinetic energy of these molecules. The temperature is proportional to the average kinetic energy; this related to the idea of kinetic temperature. One mole of the ideal gas at STP occupies 22.4 liters.

In this experiment, we verified the validity of ideal gas law. Mass after mixing, m2 and before mixing, m1 is calculated to compared the mass of gases. For ideal gas, Mass after mixing, m2 equal to before mixing, m1. From the graph plotted, the experimental mass deviated more greatly from ideal mass line as pressure increasing. This is due to the intermolecular forces becomes more significant compared with the particle’s kinetic energy. Furthermore, at higher pressure the gas molecules are almost in contact, it no longer behaves ideally because molecular volume and intermolecular interactions become significant.

When the valve connected two vessels is opened, the gases flow from higher pressure vessel to lower pressure vessel until equilibrium. After expansion, the temperature for lower pressure vessel increased and the temperature for higher pressure vessel decreased. This show that temperature increased as pressure increased.

Conclusion

From the graph plotted, the deviation is greater at higher pressure due to intermolecular forces becomes more significant compared with the particle’s kinetic energy. Furthermore, at higher pressure the gas molecules are almost in contact, it no longer behaves ideally because molecular volume and intermolecular interactions become significant. In practical, there is no ideal gas, but many gases behave as if they are ideal at ideal operating temperatures and pressures which are at higher temperature and lower pressure. Higher the potential energy due to intermolecular forces becomes less significant compared with the particle’s kinetic energy. Then, the size of the molecules becomes less significant compared to the empty space between them when lower pressure. Thus, ideal gas law is valid if temperature is high enough while pressure is low enough.