A rigid steel sphere at a temperature of is evacuated and then sequentially filled…

CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance

Problem

A rigid

5.0\,\text{L}

steel sphere at a temperature of

350\,\text{K}

is evacuated and then sequentially filled with two noble gases while the temperature is held constant. First,

1.5\times10^{24}

helium atoms are injected. Second,

0.40\,\text{g}

of neon gas (molar mass

20.2\,\text{g\,mol}^{-1}

) is added. Assume ideal behavior for both gases. Constants:

R=0.0821\,\text{L\,atm\,mol}^{-1}\text{K}^{-1}

k_B=1.38\times10^{-23}\,\text{J\,K}^{-1}

. (a) Calculate the partial pressure of the helium after its addition but before any neon is introduced. (b) Determine the number of moles of neon placed in the sphere. (c) After the neon is added, compute the total pressure inside the sphere. (d) Find the average translational kinetic energy of a single gas atom in the final mixture and explain why this value is the same for both types of atoms.

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