Question

why does a plastic bottle that is sealed at a high altitude change its shape when it is taken to a low altitude?

• the number of gas molecules that strike the outside of the bottle increases as altitude decreases.
• the number of gas molecules that strike the outside of the bottle decreases as altitude decreases.
• the bonds between the molecules of the plastic bottle become weaker as the altitude decreases.
• the bonds between the molecules of the plastic bottle become stronger as the altitude decreases.

Explanation:

Analyze atmospheric pressure changes with altitude

$$ P_{\text{external}} \propto \text{Density of air} $$

As altitude decreases (moving closer to sea level), the density of the surrounding air increases, which means there are more gas molecules per unit volume.

Relate molecular collisions to pressure

$$ F_{\text{collision}} \propto \text{Number of molecular impacts per unit area} $$

An increase in air density at lower altitudes results in a higher frequency of external gas molecules striking the outside surface of the bottle, increasing the external pressure relative to the sealed internal pressure.

Evaluate the given options

• Option 1 correctly states that the number of gas molecules striking the outside increases as altitude decreases.
• Option 2 is incorrect because the number of striking molecules increases, not decreases.
• Options 3 and 4 are incorrect because the physical bonds between the plastic molecules of the bottle do not change strength due to altitude changes.

Answer:

• (A) The number of gas molecules that strike the outside of the bottle increases as altitude decreases. (Correct answer)
• (B) The number of gas molecules that strike the outside of the bottle decreases as altitude decreases.
• (C) The bonds between the molecules of the plastic bottle become weaker as the altitude decreases.
• (D) The bonds between the molecules of the plastic bottle become stronger as the altitude decreases.