Why do gases failed to obey ideal gas equation at high temperature and low pressure?

Answer 1

You have the idea backwards, gases fail to obey the ideal gas laws at low temperatures and high pressures. The ideal gas law assumes the size of a gas molecule to be negligible as well as the naturally occurring attractive forces between molecules in a gas. These difference diminish when the pressure is low or the temperature is high. Low gas pressure suggests the gas molecules are fairly spaced out, so their individual volumes aren't impeeding the other molecules ability to occupy nearby space. With high pressures gas molecules are forced closer together in order to fit the same amount of volume the greater the volume of individual molecules the less volume available fore gas molecules to occupy. Similarly with high temperatures, the average kinetic energy easily overwhelms the intramolecular forces such as london forces and hydrogen bonding, making their presence almost unimportant. In low temperature applications the imfs of the gas molecules are given much more opportunity to interact as the gas molecules have significantly less kinetic energy.

Answer 2

At high temperatures, gas molecules have higher kinetic energy and move faster, leading to increased intermolecular interactions that deviate from ideal behavior. At low pressures, gas molecules are farther apart, reducing the frequency of collisions and interactions among molecules. These factors cause the ideal gas law to break down under these conditions.

Answer 3

high pressure causes the ideal gas law to fail