A centrifuge rotor filled with carbon dioxide rotates

A centrifuge rotor filled with carbon dioxide rotates at a speed of 300 rad/s. In this case, the molar mass of carbon dioxide is 44 * 10-3 kg/mol, the temperature is T = 300 K, and the radius of the rotor is 0.5 m. It is necessary to determine the ratio of the concentrations of molecules at the walls of the rotor and in its center.

To solve this problem, we use the formula for calculating the concentration of gases:

where n/V is the gas concentration, p is the gas pressure, R is the universal gas constant, T is the gas temperature.

Since the gas concentration is proportional to pressure and inversely proportional to temperature, the ratio of the concentrations of molecules at the walls of the rotor and in its center will be determined by the ratio:

Since the centrifugal force acting on gas molecules is proportional to the square of the rotor rotation speed and the radius, the gas pressure at the rotor walls will be higher than at the center. Thus, the ratio of the concentrations of molecules at the walls of the rotor and in its center will be greater than unity.

To calculate the ratio of molecular concentrations, it is necessary to know the values ​​of gas pressure in the walls of the rotor and in its center. Gas pressure can be calculated using the formula:

where p is the gas pressure, ρ is its density, v is the rotor rotation speed, r is the rotor radius.

Gas density can be calculated using the formula:

where P is atmospheric pressure.

Substituting the values ​​into the formulas, we get:

Here we used the fact that the gas density and universal gas constant are the same for both points in the rotor, and the rotation speed at a point on the rotor wall is equal to the rotation speed at the center of the rotor.

Thus, the ratio of the concentrations of molecules at the walls of the rotor and in its center will be equal to the ratio of the squares of the rotor radii:

Thus, the ratio of the concentrations of molecules at the walls of the rotor and in its center will be equal to 4.

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A centrifuge rotor filled with carbon dioxide is a component that is used to generate centrifugal rotation force in various chemical and biological experiments. Carbon dioxide in a centrifuge rotor can act as an inert medium, preventing oxidation or other chemical reactions inside the rotor at high rotation speeds. Spinning the rotor of a carbon dioxide centrifuge can help separate particles, such as cells or molecules, based on their size and density. The carbon dioxide centrifuge rotor can be a useful tool for research in biomedicine, biochemistry, molecular biology and other scientific fields.

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