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Questions asked by users might not always be phrased in the clearest way.
Statement I and II are not true. Here's why:
Statement I: As the density of a gas increases, the molecules become more crowded, leading to more frequent collisions. This decreases the mean free path, not increases it.
Statement II: The mean free path is dependent on the molecular size. Larger molecules have a greater cross-sectional area, leading to more frequent collisions and a shorter mean free path.
Statement III: This statement is true. Increased density leads to more frequent collisions, thus decreasing the average distance a molecule travels before colliding (the mean free path).