Question

Describe why high pressures but low temperatures cause substances to deviate from ideal gas conditions. Make sure to discuss the assumptions we made to come to the ideal gas law and how high pressures and low temperatures negate those assumptions.

Answer 1

According to Ideal gas law,

PV = nRT

with,

P = pressure; V = volume; R = gas constant; T = temperature and n = moles of gas

the ideal gas law works on the basic assumption that the volume of gas under normal standard pressure occupy very less volume of the total volume of system. Also gases are non-interactive with each other. At low pressures this assumption works alright, But at higher pressure the voume the gases occupy become more significant. Van-der Waal introduced a term for this volume correction as b which is the volume occupied by gases at high pressure. Making the ideal gas equation term,

P(V-nb) = nRT

Now, gases do not interact with each other works good at high temperature where degree of freedom is maximum, however at low temperatures gases tend to condense and this is due to interaction of gaseous molecules with each other. The attractive forces between the gas molecules lowers the pressure from the ideal gas state, this fact is corrected by an^2/V^2 term in the ideal gas equation, with a being the constant.

the final Van-der Waals equation thus beocmes,

(P+an^2/V)(V-nb) = nRT

thus, taking care of the pressure and temperature and the attractive forces between the gaseous molecules in the real gas condition.