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No. One of the properties of gas is compressibility. Pretend you have a steel box with an open top. You magically find this shape that fits exactly in the opening and completely seals the box so that not even air can escape. You can press down on the lid. It isn't fixed at the top of the box.

Gas particles are so far apart that they feel no intermolecular forces holding them in a relative position to one another. Intermolecular forces are like bonds between different molecules. There are a few different types, but to keep it simple, every type of molecule experiences at least some intermolecular forces in the solid and liquid states.

Solids are non compressible because they experience intermolecular forces that hold the molecules in rigid positions with relationship to one another, and the bond length determines how close they can be. The bonds are non compressible, so solids do have fixed volume. If you have a piece of wood and tried to squish it to fit into a smaller space, it wouldn't work.

Liquid particles also experience intermolecular forces. The molecules are close enough that they are still restricted in terms of compressibility by the molecules nearby but far enough away that they have the ability to move past one another. If you put soup in a container, and it is as full as possible, when you put the lid on, the soup doesn't compress to fit in the container, it spills. Liquid has a fixed volume.

Gas molecules are far enough away from each other that they do not feel intermolecular forces, and the intermolecular bonds are not a limiting factor in how close molecules can come to one another. They can be squished closer. Eventually, if the gas is compressed enough, the molecules will be close enough to feel molecular forces and change to the liquid phase of matter.

So, gas is compressible and does not have fixed volume.

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