Use the kinetic-molecular theory to explain the following: Why the pressure of a

Question

Use the kinetic-molecular theory to explain the following: Why the pressure of a gas doubles if its volume is reduced to half at constant temperature? Why the pressure of a gas is increased if the gas is heated in a closed, rigid container? Why oxygen can be added to a rigid container which is filled with nitrogen? Why a helium filled rubber balloon will collapse quicker than if it was filled with nitrogen? Why some gases will liquefy more readily than others? Why gases deviate from the gas laws at low temperature and high pressure?

Explanation / Answer

2. a. According to Boyle's law,

PV = constant, at constant temperature.

So, P1V1 = P2V2

P1/P2 = V2/V1

If V1 = V, and V2 = V/2

then, V2/V1 = (V/2)/V = 1/2

P1/P2 = V2/V1 = 1/2

P1/P2 = 1/2

P2 = 2P1

This explains that pressure doubles.

b. According to Gay-Lussac's law,

At constant volume, P/T = constant

So, this means that P is proportional to T.

If the gas is heated, it means that the temperature of the gas is increased. and as shown in above equation if T is increased, P will also increase. So, pressure of the gas also increases.

c. A rigid container means the volume is constant. According to ideal gas equation, PV =nRT

If V and T are constant, P is proportional to n. So, if the oxygen is added to the container containing nitrogen gas, pressure will increase but volume and temperature will remain constant. So, oxygen can be added to the rigid container having nitrogen. Only pressure will increase due to this addition.

d. In the balloons filled with helium or nitrogen, the balloons with helium will collapse easily because He is smaller in size than nitrogen. So, helium can easily leak from the balloon as compared to nitrogen. Helium can diffuse through the balloon rubber. Thus, it will shrink before that of nitrogen balloon.

e. The liquification of gases takes place above a certain temperature and pressure, which are known as critical temperature and critical pressure. Above these values of temperature and pressure, the gases liquify. All the gases have different critical temperature and pressure. So, depending on those values, the liquification of gases can be done. The gases having lesser critical temperature and pressure liquify easily, while the gases having higher critical temperature and pressure liquify with difficulty.

f. The gases deviate from the gas laws at low temperature and high pressure, because gas laws are valid for high temperatures and low pressure only. In gas laws, two assumption are done, first one is that the gas particles will occupy negligible fraction of total volume and second assumption is there is no attraction between the gas molecules. The first assumption is not true for high pressures. When the pressure is high, the gas is compressed and gas particles occupy a significant volume. The second assumption is not true for low temperature, because at low temperature, the gases change into liquid form and there has to be some attraction between them to hold molecules together. Thus gases deviate from gas laws at low temperature and high pressure.

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