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B_-_102_F11_Notes

# B_-_102_F11_Notes - B)Gases Petruccietal,10thEdition:6.16.9...

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ChE102 Fall 2011 Class Notes ‐ Gases B‐1 B) Gases Petrucci et al., 10 th Edition: 6.1‐6.9 Definition of Gas Pressure When talking about gases, four properties are often used: amount (moles), temperature, volume & pressure Pressure is the force per unit area = force/area Force resulting from the collision of the gas molecules against the walls of the container Area of the walls of the container holding the gas Understanding Pressure Gas pressure is usually measured indirectly, by comparing it with liquid pressure Liquid pressure is directly proportional to the liquid density and the height of the liquid column = [see Petrucci et al., Figure 6-4] When the pressures are equal: Open‐ended Manometer [see Petrucci et al., Figure 6-5]

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ChE102 Fall 2011 Class Notes ‐ Gases B‐2 Boyle’s Law (1662) [see Petrucci et al., Figure 6-6] “For a fixed amount of gas at a constant temperature, the gas volume is inversely proportional to the gas pressure” PV = constant for a given temperature and given amount of substance Question B1 If gas volume is doubled but the temperature remains constant: A) the pressure stays the same B) the molecules move faster C) the final pressure is 1/2 of the pressure before the volume change D) the final pressure is twice the pressure before the volume change E) none of the above Charles’ Law (1787) [see Petrucci et al., Figure 6-8] “The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin (absolute) temperature” Aside – Definition of Temperature from Charles’s Law Temperature is measured using the ratio of the volume of a gas at the measured temperature to the volume of the same gas at 0ºC (freezing point of water) If T = –273.15°C (absolute zero), then V = 0 Lowest temperature possible before V < 0, which has no physical meaning Kelvin temperature scale is based on this concept: T (K) = T (°C) + 273.15 Substituting this definition into Charles’ law gives: V 0 : volume of the gas at 0ºC T : temperature in ºC c : a constant (for all gases at small pressures, c = 273.15)
ChE102 Fall 2011 Class Notes ‐ Gases B‐3 Avogadro’s Law (1808) “At a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas” STP: Standard Temperature and Pressure Temperature = 0°C = 273.15 K Pressure = 1 atm = 760 mm Hg 1 mol = The Ideal Gas Equation Combining all three gas relationships… Avogadro: Charles: Boyle: Combines to: Or the Ideal Gas Equation: PV = nRT where R = C/c Ideal Gas Constant At STP (1 atm, 0°C) 1 mol of most gases occupies 22.4 L: R can also be given in units of J/(mol·K), since: General Gas Equation (setting R = R):

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ChE102 Fall 2011 Class Notes ‐ Gases B‐4 Gas Laws Gas laws are mathematical equations relating the volume to the number of moles, temperature and pressure of gases: V = f ( n , T , P ) This function is relatively simple because intermolecular forces in gases are generally very weak Sometimes, the ideal gas law is expressed as: PV = nRT or PV m = RT where V m
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B_-_102_F11_Notes - B)Gases Petruccietal,10thEdition:6.16.9...

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