Which of the following statements is incorrect about `H_(2)" and "CO_(2)` gas considering them as ideal gases?

Options

A. The average kinetic energies of `H_(2)" and "CO_(2)` molecules are the same at a given temperature.
B. The root mean square velocities of `H_(2)" and CO_(2)` molecules are the same at a given temperature
C. The fraction of `H_(2)" and "CO_(2)` molecules with the most probable velocity decreases with increase in temperature.
D. The density of `H_(2)` is less than `CO_(2)` at a given temperature and pressure

Answer

B

Explanation

Average kinetic energy per mole is equal to kinetic energy per molecule multiplied by Avogadro number, `E_("avg")= N_(A)xx (3)/(2)kT= (3)/(2)RT" "therefore E_("avg") propto T`
Since, for any ideal gas, average kinetic energy depends only on the température, `SO_2` at a given temperature it is equal for every ideal gas. The root mean square velocity depends on temperature as well as on molar mass, so, fortwo different ideal gases, it is different at a given temperature.
`v_(rms)= sqrt((3RT)/(M))" or "v_(rms) propto sqrt((T)/(M))`
Maxwell.s distribution curve of velocity graph flattens on increasing temperature, so, the most probable velocity fraction is decreased. Since density is directly proportional to the molar mass, and molar mass of hydrogen is lower than carbon dioxide, so, density of hydrogen is less than carbon dioxide.