Gas
A gas is a state of matter with no fixed shape or volume; its particles move rapidly and independently and spread out to fill any container.
Definition
A gas is a state of matter with neither a definite shape nor a definite volume, because its particles have enough energy to overcome the attractions between them and move freely at high speed, expanding to fill any container and exerting pressure through collisions with its walls. Gas pressure rises with temperature, with the amount of gas present, and when the volume shrinks, and at the molecular level thermal kinetic energy far exceeds intermolecular attractions, so particles travel in straight lines between brief collisions. The ideal gas law, $PV = nRT$, relates pressure, volume, moles, and temperature for gases at low pressure and high temperature, where particle volume and attractions are negligible, the van der Waals equation corrects for both, and kinetic molecular theory derives these laws from particle motion, giving a root-mean-square speed of $v_{rms} = \sqrt{3RT/M}$.
Example
The air in a room fills every corner, and a balloon pushes outward evenly in all directions as the gas inside spreads out; a sealed bag of chips puffs up on a mountain because falling outside pressure lets the gas inside expand, and a bicycle pump warms up as compression squeezes the air inside it. One mole of any ideal gas occupies $22.4\text{ L}$ at $0^\circ\text{C}$ and $1\text{ atm}$, and at $25^\circ\text{C}$ oxygen molecules ($M = 0.032\text{ kg/mol}$) have $v_{rms} \approx 482\text{ m/s}$, faster than the speed of sound, yet a smell still takes minutes to cross a room because of the sheer number of collisions along the way.
Key Insight
Most gases are invisible but still weigh something, which is why a balloon full of air weighs more than an empty one, and liquid water becomes about $1{,}700$ times larger in volume when it boils into steam at $100^\circ\text{C}$, since gas particles occupy mostly empty space. The same $22.4\text{ L}$ holds a mole of any gas regardless of what the gas actually is, because gas volume is set by particle count and motion rather than particle identity, and Avogadro's hypothesis on exactly this point is what finally let chemists work out molecular formulas.