In a cylinder with a capacity of v = 20 liters under a pressure of p = 100 kPa, there is one mole of oxygen.

In a cylinder with a capacity of v = 20 liters under a pressure of p = 100 kPa, there is one mole of oxygen. determine the rms speed of the chaotic movement of oxygen molecules, considering it an ideal gas

Given: V = 20 l = 20 * 10 ^ (- 3) m3; p = 100 kPa = 10 ^ 5 Pa; ν = 1 mol.

Find: <v>.

Decision:

Using the periodic table of chemical elements, we determine the molar mass of oxygen:

M = 2 * 16 = 32 g / mol = 32 * 10 ^ (- 3) kg / mol.

From the Mendeleev-Clapeyron equation, we determine the temperature of oxygen in the cylinder:

pV = νRT;

T = pV / (νR).

The root-mean-square velocity of the chaotic motion of molecules can be found by the formula

<v> = √ (3RT / M) = √ (3RpV / (νR) / M) = √ (3pV / (νM));

<v> = √ (3 * 10 ^ 5 * 20 * 10 ^ (- 3) / (1 * 32 * 10 ^ (- 3))) = 433 m / s.

Answer: <v> = 433 m / s.