Chapter 11 - lecture notes PDF

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Chapter 11 Gases Physical Properties of Gases 1) Gases have no definite shape or volume. They will expand to fill any container (expand infinitely) 2) Gases are highly compressible. 3) Gases have low densities (especially compared to liquids and solids) 4) Gases in a closed container exert uniform pressure on all walls. 5) Gases mix spontaneously and completely with each other at constant pressure (diffusion). The Kinetic Molecular Theory 1) Gas particles move continuously, rapidly, randomly in straight lines, and in all directions. 2) Gas particles are tiny and the distances between them are great. 3) For gases, both gravitational forces and forces of attraction between gas particles are negligible. 4) When gas particles collide with one another, or with the walls of the container, no energy is lost (perfectly elastic collisions). 5) The average kinetic energy is the same for all gases at the same temperature; it varies with the temperature in kelvins. Atmospheric Pressure Pressure is the force per unit area. Pressure is the result of the constant collisions between the atoms or molecules in the gas and the surfaces around them. The atmospheric pressure is the total force exerted by the molecules of air on each unit of area on the surface of the Earth. At sea level the atmospheric pressure is 760 mmHg as measured in a device called a barometer. A barometer uses a closed tube filled with mercury (Hg) to measure the air pressure. On average the height of the mercury in the tube is 760 millimeters. See page 363, Table 11.10. 1 atmosphere (atm) = 760 mmHg = 760 torr 1 mmHg = 1 torr The SI unit of pressure is the Pascal (Pa), defined as 1 newton (N) per square meter. 1 Pa = 1 N/m2 1 atm = 101,325 Pa 1 atm = 14.7 psi

Boyle’s Law

At constant temperature, the volume, V, occupied by a gas sample is inversely proportional to the pressure, P. P1V1 = P2V2 P1 = initial pressure, V1 = initial volume, P2 = final pressure, V2 = final volume As the volume increases, the pressure will decrease. The reverse is also true. As pressure increases then volume will decrease.

Charles’s Law At constant pressure, the volume occupied by a gas sample is directly proportional to its Kelvin temperature. V1T2 = V2T1 V1 = initial volume, T2 = final temperature, V2 = final volume, T1 = initial temp. As temperature increase the volume will increase. As temperature decreases then the volume decreases. Gay-Lussac’s Law At constant volume, the pressure exerted by a specific gas sample is directly proportional to its Kelvin temperature. P1T2 = P2T1 P1 = initial pressure, T2 = final temperature, P2 = final pressure, T1 = initial temp. In a fixed volume, as the pressure increases so does the temperature. As the pressure decreases, the temperature decreases. Standard Temperature and Pressure (STP) 1 atmosphere (atm) and 273 Kelvin (0oC) Combined Gas Law The other gas laws depend on having a fixed variable (pressure, temperature, or volume). P1V1 = P2V2 T1 T2 There are six variables in this equation as long as you know five of the variables you can find the sixth.

Now, what if the changing variable is not pressure, temperature, or volume? What if the variable is the number of gas molecules in the sample? Avogadro’s Hypothesis Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. If you double the volume of the gas, you double the number of gas molecules. Avogadro’s Law The volume of gas at constant temperature and pressure is proportional to the number of moles (n) of the gas. V1n2 = V2n1 Molar Volume and Gas Density at STP The volume occupied by a mole of any gas at STP will always be 22.4L. This is called the molar volume. To find the density of any gas at STP all you have to do is multiply the molar mass of the gas (grams per mole) by 1 over the molar volume. Grams x 1 mole = grams /Liter Mole 22.4 L Ideal Gas Law It is possible to relate the pressure (P), the volume (V), the temperature (T), and the number of moles of a gas (n). To do this you need a universal gas constant (R). R is equal to 0.0821 liter- atmosphere per mole-Kelvin. PV = nRT This is a very useful equation, but it assumes an ideal gas. An ideal gas conforms perfectly to all the gas laws we have mentioned. This, alas, does not exist. But, the ideal gas law allows you to estimate fairly close. Dalton’s Law of Partial Pressures In a mixture of gases, each individual gas acts as if it were alone. The molecules of the gases are so far apart that they have minimal influence on each other. The total pressure that the mixture exerts on the vessel is the sum of the partial pressures exerted by the separate gases. PTotal = P1 + P2 + P3 + …………… The vapor pressure of a substance is the partial pressure exerted by the molecules of the substance that are in gas phase above the liquid phase of the substance.

The various gas laws are summarized on page 380, Table 11.2....