Chapter 18

The size of an oxygen molecule is about 2.0 $\times$ 10${}^{-}{}^1{}^0$ m. Make a rough estimate of the pressure at which the finite volume of the molecules should cause noticeable deviations from ideal gas behavior at ordinary temperatures ($T$ = 300 K).

A sealed box contains a monatomic ideal gas. The number of gas atoms per unit volume is 5.00 $\times$ 10${}^2{}^0$ atoms/cm${}^3$, and the average translational kinetic energy of each atom is 1.80 $\times$ 10${}^{-}{}^2{}^3$ $J$. (a) What is the gas pressure? (b) If the gas is neon (molar mass 20.18 g/mol), what is $\upsilon {}_r{}_m{}_s$ for the gas atoms?

Helium gas is in a cylinder that has rigid walls. If the pressure of the gas is 2.00 atm, then the root-mean-square speed of the helium atoms is $\upsilon {}_r{}_m{}_s$ = 176 m/s. By how much (in atmospheres) must the pressure be increased to increase the $\upsilon {}_r{}_m{}_s$ of the He atoms by 100 m/s? Ignore any change in the volume of the cylinder.

You blow up a spherical balloon to a diameter of 50.0 cm until the absolute pressure inside is 1.25 atm and the temperature is 22.0${}^{\circ }$C. Assume that all the gas is N${}_2$, of molar mass 28.0 g/mol. (a) Find the mass of a single N${}_2$ molecule. (b) How much translational kinetic energy does an average N${}_2$ molecule have? (c) How many N${}_2$ molecules are in this balloon? (d) What is the $total$ translational kinetic energy of all the molecules in the balloon?

What is one reason the noble gases are $preferable$ to air (which is mostly nitrogen and oxygen) as an insulating material? (a) Noble gases are monatomic, so no rotational modes contribute to their molar heat capacity; (b) noble gases are monatomic, so they have lower molecular masses than do nitrogen and oxygen; (c) molecular radii in noble gases are much larger than those of gases that consist of diatomic molecules; (d) because noble gases are monatomic, they have many more degrees of freedom than do diatomic molecules, and their molar heat capacity is reduced by the number of degrees of freedom.

The rate of $effusion$-that is, leakage of a gas through tiny cracks-is proportional to $v_{rms}$ . If tiny cracks exist in the material that's used to seal the space between two glass panes, how many times greater is the rate of $He$ leakage out of the space between the panes than the rate of $Xe$ leakage at the same temperature? (a) 370 times; (b) 19 times; (c) 6 times; (d) no greater-the $He$ leakage rate is the same as for $Xe$.