Speed Distribution of Ideal Gases Practice Problems

97.9% of oxygen molecules (O₂) in a metallic container have speeds below 1200 m/s. Determine the temperature of this oxygen sample. Hint: v/v_rms = 1.80. O₂ molar mass is 32.00 g/mol.

Oxygen is a diatomic gas with a molar mass of 32.00 g/mol. Determine its average speed (v_av) at 273 K. 

Diatomic nitrogen of molar mass 28.01 g/mol is an inert gas used in bulbs to prevent evaporation and oxidation of the filament. What is the most probable speed of nitrogen at 420 K?

In a competition of thirty athletes, it is seen that three athletes ran at 12.0 km/h, eight at 15.0 km/h, five at 18.0 km/h, four at 21.0 km/h, seven at 24.0 km/h, two at 27.0 km/h, and one at 30.0 km/h. Determine the average speed of the athletes.

A container holds argon gas at a temperature of 500°C. The volume of this container measures around 150 cm³. The pressure exerted by Ar at this temperature equals 25 mm-Hg, and each argon atom's diameter within this gaseous state measures approximately 0.35 nm. Estimate how many times an individual Ar atom collides with other argon atoms every single second. [Hint: The molecular mass of Argon is 39.95 u, 1 mm-Hg ≈ 133.322 Pa and the Boltzmann constant is 1.38 x 10^-23 J/K.]

In a research laboratory, scientists are studying the distribution of particle velocities in a gas sample. The distribution function 𝑓(𝑣) for the velocity 𝑣 of particles is given by the Maxwell-Boltzmann distribution $f(v)=4 \pi N\left(\frac{m}{2 \pi k T}\right)^{3 / 2} v^{2} e^{-\frac{m v^{2}}{2 k T}}$ . Using this distribution function, calculate the value of the integral $\int_{0}^{\infty} f(v) d v$.

Standard pressure conditions require nearly 574 Joules to convert one gram of solid carbon dioxide directly into the gas phase (at a temperature of -78°C). Estimate the mean particle velocity during this process and compare them with carbon dioxide's rms velocity at 25°C.

The distribution of speeds of a gas sample containing 20,000 molecules, each with a mass of 3.00×10⁻²⁶ kg, is given as follows:

Calculate the root-mean-square (rms) speed for this distribution of speeds.