At 298K and 1 atm, a 0.5 mol sample of O2 and a separate 0.75 mol sample of CO2 gas have the same:

A. mass
B. density
C. average molecular speed
D. average molecular kinetic energy
E. number of atoms
Please explain, and thanks for helping!

To determine which of the given options are the same for the 0.5 mol sample of O2 and the 0.75 mol sample of CO2 gas at 298K and 1 atm, we will need to consider the properties of gases and use the ideal gas law.

The ideal gas law relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas using the equation PV = nRT, where R is the ideal gas constant.

In this case, both gases are at the same temperature and pressure, so from the ideal gas law we can see that the number of moles is directly proportional to the volume of the gas.

Now let's go through each option and determine if it's the same for both gases:

A. Mass:
The mass of a gas is directly proportional to the number of moles. Since the number of moles is different for the two gases, the mass will also be different. Therefore, option A is not correct.

B. Density:
Density is defined as mass per unit volume. Since the mass is different for the two gases (as determined in option A), the density will also be different. Therefore, option B is not correct.

C. Average molecular speed:
The average molecular speed of a gas is directly proportional to the square root of the temperature. Since both gases are at the same temperature, their average molecular speeds will be the same. Therefore, option C is correct.

D. Average molecular kinetic energy:
The average molecular kinetic energy of a gas is directly proportional to the temperature. Since both gases are at the same temperature, their average molecular kinetic energies will be the same. Therefore, option D is correct.

E. Number of atoms:
The number of atoms in a gas sample is directly proportional to the number of moles. Since the number of moles is different for the two gases, the number of atoms will also be different. Therefore, option E is not correct.

In conclusion, the correct answers are options C and D. The 0.5 mol sample of O2 and the 0.75 mol sample of CO2 gas will have the same average molecular speed and average molecular kinetic energy at 298K and 1 atm.