# The concentration of gas molecules in the vessel has decreased by 2 times, and the average square of the molecular velocity

August 24, 2021 | education

| **The concentration of gas molecules in the vessel has decreased by 2 times, and the average square of the molecular velocity has increased by 4 times. Has the gas pressure changed?**

The basic equation of the molecular kinetic theory of gas:

P = (1/3) * m0 * n * v², where m0 is the mass of one gas molecule, n is the gas concentration, v is the average velocity of the molecule.

Expression to determine the pressure before the change:

P1 = (1/3) * m0 * n1 * v1²

After changing the speed of the molecules:

P2 = (1/3) * m0 * n2 * v2²

By condition: n1 = 2 * n2 = n; v2² = 4v1².

Find the ratio P2 / P1:

P2 / P1 = ((1/3) * m0 * n * v2²) / (1/3) * m0 * n * v1² = n2 * v2² / (n1 * v1²) = n2 * 4v1² / (2 * n2 * v1² ) = 4/2 = 2

Answer: the pressure has doubled.

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