Question

a meteorologist is measuring air samples (a gas sample) taken from different locations on the same day. the air samples all contain the same 22 l volume of air with a measure of the place, temperature, and pressure conditions under which it was taken. how would the density of the air samples likely differ? (note: a typo/irrelevant reference to hardy - weinberg may be present.) select the statement that best applies.
options (paraphrased from image):

• the air sample from the mountaintop would be less dense...
• both air samples would have similar densities...
• the air sample from the mountaintop would be more dense...
• the air sample from the mountaintop would be more dense... (lower temperature...

Explanation:

To solve this, we analyze the effect of altitude (location: mountaintop vs. city) on air sample properties (volume, temperature, pressure, conditions).

Key Concept: Gas Laws (e.g., Ideal Gas Law \( PV = nRT \))

• At higher altitudes (mountaintop), atmospheric pressure is lower (since pressure decreases with increasing altitude).
• The air samples have the same volume (\( V \)), amount of gas (\( n \)), and were collected on the same day (so \( T \) might vary slightly, but the main difference is pressure).

Analyzing Each Option:

1. “The air sample from the mountaintop would be less dense... more air molecules... making the air less dense.”

• Density of a gas is \(

ho = \frac{PM}{RT} \) (from \( PV = nRT \) and \( n = \frac{m}{M} \), so \(
ho = \frac{PM}{RT} \)). At lower pressure (\( P \)) on the mountaintop, density (\(
ho \)) decreases. But “more air molecules” contradicts lower pressure (lower \( P \) means fewer molecules per volume, if \( T \) is constant). Eliminate.

1. “Both air samples would have similar compositions... same volume, temperature, pressure (the volume is the same).”

• Pressure differs (mountaintop has lower pressure). So this is incorrect. Eliminate.

1. “The air sample from the mountaintop would be less dense... lower pressure at the mountaintop means that the molecules would be further apart... fewer air particles would be in a given volume.”

• Lower pressure at higher altitudes means gas molecules are more spread out (fewer per unit volume). From \(

ho = \frac{PM}{RT} \), lower \( P \) (with constant \( T \), \( M \), \( R \)) reduces density. This matches gas behavior. Correct.

1. “The air sample from the mountaintop would be more dense... lower temperature at the mountaintop means that the air...”

• Lower temperature (if true) would increase density (since \(

ho \propto \frac{1}{T} \) from \(
ho = \frac{PM}{RT} \)). But the primary factor here is pressure (altitude), not temperature. Also, “more dense” contradicts lower pressure. Eliminate.

Answer:

The option stating: "The air sample from the mountaintop would be less dense. The lower pressure at the mountaintop means that the molecules would be further apart. Therefore, fewer air particles would be in a given volume." (the third option, depending on formatting)