### Find the root-mean-square speed of brownian motion

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1. A container with volume 1.68L is initially evacuated. Then it is filled with 0.240g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy.

a) If the root-mean-square speed of the gas molecules is 167m/s , what is the pressure of the gas?

2. Smoke particles in the air typically have masses of the order of 10^-16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope.

a) Find the root-mean-square speed of Brownian motion for a particle with a mass of 3.00 x 10^-16kg in air at 300K.

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