Question

(V) H20 and CH4 are gases at 150°C. Which exhibits more ideal behavior? Why? (VI) Assume that you have a cylinder with a movable piston. What would happen to the gas pressure inside the cylinder if you were to do the following? (a) Triple the Kelvin temperature while holding the volume constant (b) Reduce the amount of gas by 1/3 while holding the temperature and volume constant (c) Decrease the volume by 45% at constant T (d) Halve the Kelvin temperature, and triple the volume

Answer 1

V. CH_{​​​​​4} shows more ideal gas behaviour at 150^oC. This is because the gas molecules of methane have very little interaction among themselves as compared to water molecules at the same temperature. And an ideal gas should have very low interaction among its particles.

As we all know methane is already a gas at room temperature while water is liquid. This means that the intermolecular forces of attraction are stronger in water than in methane. So as temperature increases, the individual molecules gain energy. Thus the intermolecular forces become even lower. Thus distance between molecules increases along with lowering of intermolecular force of attraction. But as methane is already a gas and increasing any temperature further increases the intermolecular gap and lowers intermolecular forces. Thus it behaves as an ideal gas more than water.

VI. Ideal gas law states that PV = nRT

Where P = pressure, V = Volume, n= number of moles, T = temperature, R= gas constant

a. If temperature is tripled while keeping the volume constant, then the pressure will also be tripled. This is because number of moles of gas in the container is constant as no molecule can get in or out of the system.

b. If amount of gas i,e n is made 1/3 keeping temperature and volume constant, then pressure will also become 1/3.

c. If volume is decreased by 45%, then the actual Volume is 100% - 45% = 55% of original. So pressure will be 100/55 of original pressure. This is because pressure and Volume are inversely proportional to each other. This means pressure will increase.

d. So pressure is directly proportional to temperature and inversely proportional to volume. If temperature is halved and volume is tripled, then the new pressure will become 3/2 times the original pressure. This means pressure will increase.