Ideal Gas Model and Behavioral Patterns of Real Gases

Boyles law.Boyles law explains the inverse relationship between the pressure and volume of a gas which is held at a constant temperature. It was discovered by Richard Towneley and Henry Power but was confirmed and published by Robert Boyle.It simply states that when the pressure of gas filled in a container increases the volume decreases.Derivation from the ideal gas equation.Boyles's law is represented by pressure and volume at constant temperature and constant amount of gas. Hence P=1/V.

The ideal gas equation is PV=nRT. It can be represented as Boyle's law by specifying a constant temperature and constant amount of gas. In this case nRT becomes constant and we can represent it as k.So, a change in the volume of gas will result in a change in the pressure. We can say the product of initial pressure and volume of gas is equal to the product of final pressure and volume of gas. Can you imagine some uses of this equation?.This equation is used to predict the decrease in volume or rise in pressure of the gas. Gas quantity and temperature remain constant.

Example 1.When a container filled with gas is being pressed by a piston, its volume decreases. As we make the pressure rise, volume decreases as a consequence of Boyle's law. There is this fact that fish that live in deep sea encounter death if they reach the surface of the water. This happens because of the expansion of gases dissolved in their blood, causing death.Let's see a systematic example. Here a gas exerts 4kpa pressure on the walls of the container. When that container is dumped in a larger container of 15L, pressure exerted by gas increases to 8kpa. Let's find the volume of the first container. We take a constant quantity of gas and constant temperature.So the volume of the container is 30L.

Charles law.It is the law of gas that states the volume of any ideal gas is related to temperature positively. Volume is directly proportional to the absolute temperature of the gas at constant pressure.It was published by Jacques Charles. Because this law explains in detail how volume increases with the rise in temperature, it is referred to as the volumes law.So a rise in temperature leads to a rise in volume or vice versa. That's why Charles law is a special case of ideal gas law.

Derivation from the ideal gas equation.The ideal gas equation is PV=nRT but in the case of constant pressure nR/p=k where k is constant. Then v=kt.V and T are varying directly.in this way, k depends on the pressure, amount, and unit of gas. At the start, V1 is the initial volume and T1 is the initial temperature.After some rise in temperature, it changes to T2 and the rise in volume is V2.Do you think the Charles’s law can be applied in winter and summer?.

Example 1.In winter temperature decreases and as a result, the volume also decreases. This makes the capacity of the human lung shrink. This leads to difficulty for athletes to perform well. It makes the balloons shrink. It is said not to fill diesel tanks of vehicles in hot weather. It is advised to keep the tank a bit empty. That’s because in hot weather, temperature increases, which raises the volume of gases in engines. This is very risky for life. It is a good example of Charles's law.

Let's see a systematic example as gas 250cm³ of volume at the temperature of 10°C and 1 atm pressure. If the temperature increases to 150°C what will be the volume of the gas? First of all, it is clear pressure is constant. So by applying Charles's law. The rise in volume V2 is 373.6cm³.

Avogadro’s law Avogadro's law is the statement that tells that in the same conditions of temperature and pressure, the same volume of different gasses contains an equal number of molecules. It is divided by the kinetic theory of gases with the assumption of the ideal gas. This law is applicable for real gases at low pressure and high temperature. It is represented by NA Avogadro constant 6.02214076x10²³. This law was proposed by Amedeo Avogadro.

Avogadro law derived from ideal gas law asPV=nRT is an ideal gas equation. Here R is the gas constant, T is the temperature in k and P is pressure in pascals. Therefore RT/P = k. k is constant. So V=nk. Volume is directly proportional to moles. V=n which is a mathematical representation of Avogadro law. For example, the molecule's weight of oxygen is 32g/mol which has a mass of 32 grams, containing 6.02214076x10²³ number of particles.

Avogadro law is also indicates that the ideal gas constant is the same value for all gases. Thus the equation for initial and final value is described here.Do you know any example of Avogadro’s law? Let's see a systematic example as a 5L volume of gas contains 1.5 moles of molecules. If the quantity is being increased to 2.7 mol, what will be the new volume of the gas?.We assume pressure and absolute temperature are constant.

Molar volume. It is the volume of 1mole of gas at standard temperature and pressure. It is represented by Vm with m³/mol. It can also be represented as cm⁴/mol and dm⁴/mol unit. It can be calculated by dividing the molar mass M by density.This molar volume of 1 mole of gas at STP has a fixed value of 22.41 liters. It formula is as described.Molar volume is directly proportional to molar mass and inversely proportional to mass density.

Let’s discuss an example. There is oxygen gas with a density of 1.57g/L. What would be its molar volume at standard temperature and pressure? Let’s remind ourselves that Vm=molar mass/density. It would be 10.19L. Experimental determination. Let's find the molar volume of hydrogen at standard temperature and pressure with an experiment. In this experiment, we are going to make hydrogen by the reaction of magnesia metal with hydrochloric acid.

Acids react with metals to form a metal salt and hydrogen gas. Magnesia metal is very reactive metal. It will react with hydrochloric acid to form magnesium chloride and hydrogen gas. We have a small strip of magnesia metal Mg that masses 0.03 for 2 grams. Took the museum ribbon and wrapped it with some copper wire.As copper does not react with hydrochloric acid so it will not produce any hydrogen gas. The role of copper wire is to hold the magnesium ribbon in place during the reaction. We use a gas collection tube that has generated in milliliters and tenths of a milliliter.

Then carefully add about 10 milliliters of 6 molar hydrochloric acids to the tube. The amount of hydrochloric acid is not critical. Then fill the tube with water carefully keeping the tube slanted so that less dense water will be afloat on top of hydrochloric acid. Then place a medium ribbon in the solution and held it in place by copper wire. Then placed a finger over the mouth of the gas collection tube. Then invert the tube in a large beaker of water. The hydrochloric acid will move downward through the water because of its higher density.

When hydrochloric acid reaches the magnesium metal it will produce hydrogen gas. This hydrogen gas will be collected by displacement of water. As the magnesium is completely reacted it will let hydrogen gas stand for a few minutes so that it reaches the same temperature as the surrounding air. Then move the tube to a large water tank. Raise or lower the tube so the water level inside the tube and the water level outside the tube were the same. The outside pressure is equal to biometric pressure or atmospheric pressure, we will take note of the volume of hydrogen gas from the gas collection tube. This volume will be corrected for the pressure of water vapor by measuring the temperature of water in the tank.