Gas particles travel at speeds of up to 500 m/s. Why, then, does it take so long for gas molecules to travel the length of a room?

My answer would be that the molecules still have a weak attraction to each other and, in addition, the friction of the molecules surrounding the gas, which are in the atmosphere, impede the gaseous molecules' movement across the room. Is this correct?

I think everything you say is true; however, I think you are hitting around the answer and not hitting the answer on the nose. I think the primary reason is that the gas molecules bump into oxygen and nitrogen molecules of the air and that keeps them from being able to move directly from one side of the room to the other. I think friction and the weak attraction for the molecules for each other are so small that those forces are negligible when compared to the main problem. The gas molecules can't travel more than a few nanometers (if that much) without hitting an oxygen or nitrogen molecule of the air.

Your answer is partially correct. While intermolecular attractions and friction with other molecules in the atmosphere do play a role, there are a few other factors to consider.

Firstly, gas molecules move randomly in all directions. While some of the molecules may be moving quickly, others may be moving slowly or even in the opposite direction. This contributes to the overall slower net movement of the gas in a particular direction.

Secondly, collisions between gas molecules themselves and with the walls of the room can cause them to change direction and lose some of their kinetic energy. These collisions tend to randomize the movement of the gas molecules even further.

Additionally, the density of the gas also affects its rate of diffusion. In a typical room, the gas particles are relatively spread out, reducing the chances of frequent collisions and thus slowing down the overall movement.

Lastly, the size of the room also plays a role. Even though gas particles are moving at high speeds, the distance they need to travel to cover the length of a room can still take time. Considering the average molecular speed of 500 m/s, it would take a considerable amount of time to cross a room that may be several meters in length.

So, while the individual gas particles may be moving at high speeds, the combination of these factors - random motion, collisions, density, and distance - results in the relatively slow movement observed in gases across a room.