Consider the conditions listed in the table below.
Gas
Temperature
Pressure
H2
100 oC
1 atm
CH4
100 oC
20 atm
O2
373 K
1 atm
CO2
373 K
10 atm
Which describes the characteristics of these samples?
I. All molecules have the same kinetic energy
II. The hydrogen molecules have the greatest average molecular velocity
III. The carbon dioxide molecules travel the shortest distances between collisions.
To determine which descriptions in the options best match the characteristics of the given samples, we need to consider the concepts of kinetic energy, average molecular velocity, and molecular motion.
I. All molecules have the same kinetic energy:
The kinetic energy of gas molecules depends on their mass and velocity. The kinetic energy (KE) of a gas molecule can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the molecule and v is its velocity. However, the given table does not provide information about the masses or velocities of the gas molecules. Therefore, we cannot conclude that all molecules have the same kinetic energy.
II. The hydrogen molecules have the greatest average molecular velocity:
The average molecular velocity of a gas depends on its temperature. According to the table, hydrogen (H2) and methane (CH4) both have a temperature of 100°C. Since the temperature is the same, the average molecular velocities of H2 and CH4 can be assumed to be similar. We cannot conclude that hydrogen molecules have the greatest average molecular velocity based on the given information.
III. The carbon dioxide molecules travel the shortest distances between collisions:
The distance between collisions, also called the mean free path, depends on the size and concentration of gas molecules as well as the pressure. The given table indicates that carbon dioxide (CO2) has a higher pressure than hydrogen (H2) or oxygen (O2). Since higher pressure generally means more frequent collisions between gas molecules, it is likely that carbon dioxide molecules will travel shorter distances between collisions compared to hydrogen or oxygen. Therefore, we can conclude that carbon dioxide molecules travel the shortest distances between collisions.
Therefore, the correct description is III. The carbon dioxide molecules travel the shortest distances between collisions.