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Chapter 10 - Gases

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Chapter 10 - Gases ١٤٣٧/٢٦/٢ CHAPTER 10 - GASES Prof. Dr. Nizam M. El-Ashgar CHARACTERISTICS OF GASES Air is a complex mixture of several substances, primarily N2 (78%) and O2 (21%), with small amounts of several other gases (1.0%) ١ ١٤٣٧/٢٦/٢ GGASES Most compounds that exist as gases are molecular , have low molar masses, and made of only nonmetals. Ex: Elements: monoatomic: He, Ne, Ar, Kr, Xe Diatomic: H2,N2,O2, Cl 2 Compounds: CO, CO 2, CH 4, NO 2, and SO 2. A vapor is a substance in the gaseous state that exists as a liquid or solid under ordinary conditions. Ex: O2 = gas H2O = vapor PROPERTIES OF GASES A gas expands to fill its container, so the volume of a gas always equals the volume of the container. Gases are highly compressible. Gases form homogeneous mixtures with each other regardless of the identities or relative proportions of the component gases. Gas particles are far apart and act independently of one another. ٢ ١٤٣٧/٢٦/٢ SECTION 10.2 - PRESSURE Gas molecules are constantly in motion. As they move and strike a surface, they push on that surface. push = force Pressure is a force that acts on a given area. P = Pressure (Pa) F = force (N) A = area (m 2) Atmospheric pressure: is the weight of air per unit of area. ٣ ١٤٣٧/٢٦/٢ PPRESSURE UUNITS The SI unit for pressure is: Pascal (Pa). 1 Pa = 1 N/m 2 1 N = 1 kg-m/s 2 Other Units: Bar 1 bar = 1.013 x10 5 Pa = 101.3 kPa The atmospheric pressure (atm): 1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 1 bar STANDARD PRESSURE • Normal atmospheric pressure at sea level. It is equal to – 1.00 atm – 14.7 psi (Ib/in 2) pound per square inch – 760 torr (760 mmHg) – 101.325 kPa – 1 bar ٤ ١٤٣٧/٢٦/٢ BAROMETER A barometer: is a device used to measure atmospheric pressure. Standard atmospheric pressure: is the pressure at sea level and can support a column of mercury (h) = 76 cm Hg = 760mmHg = 760 torr Hg SAMPLE EXERCISE 10.1 a. Convert 0.357 atm to torr. b. Convert 6.6 x 10 -2 torr to atm. c. Convert 147.2 kPa to torr. ٥ ١٤٣٧/٢٦/٢ PRACTICE EXERCISE a) In countries that use the metric system, atmospheric pressure in weather reports is given in kPa. Convert a pressure of 745 torr to kPa. Answers: 99.3 KPa b) An English unit of pressure used in engineering is pounds per square inch or psi: 1atm = 14.7 lb/in 2. If a pressure is reported as 91.5 psi, express the measurement in atm. Answers: 0.890 atm MANOMETERS A manometer is a device that we use in the lab to measure gas pressure. Pressure is based on the difference in the heights of the two arms. Pgas = Patm + Ph ٦ ١٤٣٧/٢٦/٢ SAMPLE EXERCISE 10.2 A sample of gas is placed in a flask attached to a manometer and the level of mercury in the open-end arm has a height of 136.4 mm, and the are that is in contact with the gas has a height of 103.8 mm. What is the pressure of the gas in atm if the atmospheric pressure was 764.7 torr? Solution: CLOSED -END MANOMETER When gas sample has P < atm Hg in arm ↓, as not enough P to hold up Hg. Patm = 0 ∴ Pgas = PHg So directly read off P of gas 14 ٧ ١٤٣٧/٢٦/٢ PPRACTICE EEXERCISE Convert a pressure of 0.975 atm into Pa and kPa. Answer: 9.88 x 10 4 Pa and 98.8 kPa THE GAS LAWS Gas laws relates 4 variables of gases to each other: 1. Pressure , P 2. Temperature , T (must be in kelvin) 3. Volume , V 4. Amount of gas , n (must be in moles) ٨ ١٤٣٧/٢٦/٢ BOYLE ’S LAW States that: the volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure. At constant T and n: V ∝ 1/P PV = K P1 × V1 = P 2 × V2 CHARLES ’ L AW States that: the volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute (Kelvin) temperature. At constant P and n: V∝ T ٩ ١٤٣٧/٢٦/٢ If you plot volume vs. temperature for any gas at constant pressure, the points will all fall on a straight line. If the lines are extrapolated back to a volume of “0,” they all show the same temperature, –273.15 °C, called absolute zero . AVOGADRO ’S LAW States that: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Note: 1 mole of any gas a 0oC and 1 atm will contain 6.02 x 10 23 particles and will occupy a volume of 22.4L. At constant P and T: V∝ n ١٠ ١٤٣٧/٢٦/٢ AVOGADRO ’S LAW Equal volume of gases at constant P and T have same number of moles of gas SAMPLE EXERCISE 10.3 Suppose we have a gas confined to a cylinder with a piston and inlet valve. Consider the following changes: a. Heat the gas from 298 K to 360 K at constant pressure. The volume increases but the pressure will not change. The total number of moles of gas remains the same. b. Move the piston to reduce the volume of gas from 1L to 0.5L. The pressure increases. c. Inject additional gas through the gas inlet valve while keeping the volume and temperature constant. The number of moles of gas increases and the average distance between molecules must decrease and the pressure will increase in the cylinder. ١١ ١٤٣٧/٢٦/٢ PRACTICE EXERCISE What happens to the density of a gas as: a. The gas is heated in a constant-volume container? b. The gas is compressed at constant temperature? c. Additional gas is added to a constant-volume container? Answers: (a) no change, (b) increases, (c) increases THE IDEAL GAS EQUATION : (T HE IDEAL -GAS LAW ) The ideal gas equation related all of the calculated values of a gas: pressure, temperature, volume, and number of moles. V ∝ 1/P (Boyle’s law) V ∝ T (Charles’s law) V ∝ n (Avogadro’s law) Combining these, we get nT nT V ∝ then V = R P P R = 0.0821 L.atm/mol .K (8.31 L.kPa/mol .K) ١٢ ١٤٣٧/٢٦/٢ IDEAL GAS LAW PV = nRT P = pressure in atm V = volume in liters n = moles R = proportionality constant = 0.08206 L· atm/ mol·K T = temperature in Kelvin AN IDEAL GAS A hypothetical gas whose pressure, volume, and temperature relationships are described completely by the ideal-gas equation. Assuming: (a) The molecules of an ideal gas do not interact with one another. (b) The combined volume of the molecules is much smaller than the volume the gas occupies (molecules taking up no space in the container). In many cases, the small error introduced by these assumptions is acceptable. If more accurate calculations are needed: If we know the attraction forces between molecules . If we know the diameter of the molecules. ١٣ ١٤٣٧/٢٦/٢ IDEAL -GAS C0NSTANT R The constant of proportionality is known as R, the gas constant. Note: 1 J = 101.3 L.atm STP STP means standard temperature and pressure. The values for STP are 0oC and 1 atm. ١٤ ١٤٣٧/٢٦/٢ SAMPLE EXERCISE 10.4 A sample of CaCO 3 is decomposed, and the carbon dioxide is collected in a 250mL flask. After the decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31 oC. How many moles of CO 2 gas were generated? PRACTICE EXERCISE Tennis balls are usually filled with air or N2 gas to a pressure above atmospheric pressure to increase their bounce. If a particular tennis ball has a volume of 144 cm 3 and contains 0.33g of N2 gas, what is the pressure inside the ball at 24 oC? Answer: 2.0 atm ١٥ ١٤٣٧/٢٦/٢ THE COMBINED GAS LAW The combined gas law combines pressure, volume, and temperature for a gas with a constant number of particles. Any variable that constant can be cancelled from the previous law. SAMPLE EXERCISE 10.5 The gas pressure in an aerosol can is 1.5 atm at 25 oC. Assuming that the gas inside obeys the ideal gas equation, what would the pressure be if the can were heated to 450 oC? ١٦ ١٤٣٧/٢٦/٢ PRACTICE EXERCISE A large natural gas storage tank is arranged so that the pressure is maintained at 2.20 atm. On a cold day in December when the temperature is -15 oC, the volume of gas in the tank is 3.25 x 10 3 m3. What is the volume of the same quantity of gas on a warm July day when the temperature is 31 oC? Answer: 3.83 * 103 m3 SAMPLE EXERCISE 10.6 An inflated balloon has a volume of 6.0L at sea level (1 atm) and is allowed to ascend in altitude until the pressure is 0.45 atm. During ascent the temperature of the gas falls from 22 oC to -21 oC. Calculate the volume of the balloon at its final altitude. ١٧ ١٤٣٧/٢٦/٢ SAMPLE EXERCISE A 0.50 mol sample of oxygen gas is confined at 0oC in a cylinder with a moveable piston. The gas has an initial pressure of 1.0 atm.
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