22P2Q04

4a)

The gas consists of large number of molecules moving randomly at high speed.

When these gas molecules collide elastically with the walls of the vessel, they undergo changes in momentum.

By newton’s 2nd and 3rd laws, this implies a force and thus pressure is exerted on the walls.

4bi)

The volume of the gas particles is negligible compared to the volume of the gas.

4bii)

\displaystyle \begin{aligned}   (pV&=NkT) \\  (180)(3.2\times {{10}^{-4}})&=N(1.38\times {{10}^{-23}})(298) \\  N&=1.401\times {{10}^{14}} \end{aligned}

\displaystyle \sqrt[3]{\frac{V}{N}}=\sqrt[3]{\frac{3.2\times {{10}^{-4}}}{1.401\times {{10}^{14}}}}=2.84\times {{10}^{-8}}\text{ m}

4biii)

Since the separation (\displaystyle 2.84\times {{10}^{-8}}\text{ m}) is >100 times the diameter of \displaystyle 1\times {{10}^{-10}}\text{ m}, the assumption is valid.

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