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Unformatted text preview: 12-1 THERMAL PROPERTIES OF MATTER12Q12.1.Reason:The mass of a mole of a substance in grams equals the atomic or molecular mass of the substance. Since neon has an atomic mass of 20, a mole of neon has a mass of 20 g. Since N2has a molecular mass of 28, a mole of N2has a mass of 28 g. Thus a mole of N2has more mass than a mole of neon. Assess:Even though nitrogen atomsare lighter than neon atoms, nitrogen molecules are more massive, so a mole of nitrogen has more mass than a mole of neon. Q12.2.Reason:Hydrogen and helium can escape the atmosphere while heavier elements such as oxygen and nitrogen cannot. This is because hydrogen and helium, being lighter, move faster. From Chapter 11, we know that the root-mean-square speed of a particle is given by the following: vrms=3kBTmIt follows that the lighter a particle is, the greater is its rms speed. Assess:We can be thankful that our Earths gravity holds on to the vital nutrients oxygen and nitrogen. A smaller body than the earth might not be able to hold on to these elements. For example, the moons gravity is too weak for it to have an atmosphere of oxygen or nitrogen. Q12.3.Reason:Since there is almost pure helium in a helium balloon and almost no helium in the outside air, helium tends to diffuse out of the balloon. Similarly, with almost no oxygen or nitrogen in the balloon initially and high concentrations of oxygen and nitrogen in the air, these molecules tend to diffuse into the balloon. However, since helium atoms travel about three times faster than oxygen or nitrogen molecules and since helium atoms are smaller, they diffuse much faster so gas leaves the balloon faster than it enters. An air-filled balloon has the same particles inside as out and so the stated effect does not contribute to the deflation of such balloons. Instead, there is a weaker effect which is also at work for helium balloons: Higher pressure inside the balloon than outside makes the interior air molecules diffuse faster. Assess:Because of the advantages helium atoms have in diffusion, helium balloons deflate faster than air-filled ones. Q12.4.Reason:From the ideal gas law, the lower the pressure of a container of gas, the higher the volume. The pressure inside the bag equals the pressure outside. So when the atmospheric pressure goes down, the pressure in the bag goes down and the volume goes up. Q12.5.Reason:From Equation 12.7, we know that the temperature of a gas is directly proportional to the square of the rms speed of the molecules. Thus, doubling the typical speed of molecules in a gas increases the temperature by a factor of four. We also know, from Equation 12.11, that the pressure of a gas is directly proportional to its temperature, so doubling the typical speed of the molecules must also increase the pressure by 12-2 Chapter 12a factor of four. Increasing the speed of molecules in a gas increases the amount of force a molecule exerts on the wall of the container and the rate of collisions with the walls.wall of the container and the rate of collisions with the walls....
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- Fall '10