A 0.10- gas tank holds 5.0 moles of nitrogen gas (N₂), at a temperature of 370 K. The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 × 10^-10 m, and the Boltzmann constant is 1.38 × 10^-23 J/K. The root-mean-square speed (thermal speed) of the molecules is closest to A) 570 m/s. B) 810 m/s. C) 410 m/s. D) 22 m/s. E) 99 m/s.

Question

Quizplus · Accepted Answer

The root-mean-square speed of the molecules is given by the equation:

v(rms) = sqrt((3kT)/m)

where k is the Boltzmann constant, T is the temperature, and m is the molecular mass.

First, we need to calculate the mass of 5.0 moles of nitrogen gas:

mass = 5.0 mol x 14 g/mol = 70 g

Next, we need to convert the temperature from Celsius to Kelvin:

T = 370 K

Now we can calculate the root-mean-square speed:

v(rms) = sqrt((3 x 1.38 x 10^-23 J/K x 370 K)/(0.070 kg))

v(rms) = 570 m/s

Therefore, the closest answer choice is A) 570 m/s.

A 010- Gas Tank Holds 5