Final answer:
The speeds of nitrogen molecules at 295 K can be calculated using equations from kinetic theory, with the rms speed being the greatest, followed by the average speed, and then the most probable speed.
Step-by-step explanation:
The question deals with finding various speeds of nitrogen molecules at a given temperature using the principles of kinetic theory of gases. Specifically, we need to find the most probable speed, average speed, and the root-mean-square (rms) speed of nitrogen molecules at 295 K.
For nitrogen (N₂) with a molar mass (M) of 28.0 g/mol, the speeds can be calculated using the following equations from the kinetic theory of gases:
- The most probable speed (vmp) is given by the equation: vmp = √((2*k*T)/m)
- The average speed (α) can be approximated by: α = √((8*k*T)/(pi*m))
- The rms speed (vrms) can be calculated using: vrms = √((3*k*T)/m)
Here, k is the Boltzmann constant (1.38 x 10-23 J/K), T is the absolute temperature in kelvins (295 K in this case), and m is the mass of one molecule of nitrogen. The mass m can be determined from the molar mass (M) by converting it to kilograms and then dividing by Avogadro's number (6.022 x 1023 mol-1) to get the mass per molecule.
To answer the multiple-choice part of the question, the relationship among these speeds for any ideal gas is always: (c) rms speed (vrms) > average speed (α) > most probable speed (vmp). Therefore, the correct answer is the third option (c).