A. Romero 2007 Gas Laws and the Molar Mass of Butane CHEM 30A The Erlenmeyer flask is initially full of water. The butane gas bubbles released from the butane cylinder displace the water in the flask, lowering the water level inside the flask (and raising the water level in the beaker). When the water level in the flask reaches the neck of the flask, we stop releasing gas, and can make the two water levels equal by adjusting the height of the metal ring supporting the flask. At this point, the pressure of the gas inside the flask is equal to the pressure of the air in the room which can be measured using a barometer. We can also mark the position of the water level on the tape along the neck of the flask so that we can determine the volume of the butane gas in the flask. If we measure the temperature of the water (and gas), and we find the mass of the butane gas released by difference, we now have all the information that is needed to calculate the molar mass of butane. Partial Pressure: The pressure due to one individual gas within a mixture of gases. Dalton’s Law of Partial Pressures: The total pressure of a mixture of gases is the sum of the partial pressures of all the individual gases. Ptotal = PA + PB + PC… Dalton’s Law applied to the collection of butane gas over water in a pneumatic trough: Because the water levels are equal, the total pressure inside the Erlenmeyer flask is equal to the atmospheric pressure in the lab room. According to Dalton’s law, the total pressure inside the Erlenmeyer flask is the sum of the partial pressures of the two gases it contains, butane and water vapor. Substitution and algebraic rearrangement give us our final equation (bold). Patm (outside) = Ptotal (inside) Ptotal (inside) = Pbutane + PH2O Patm (outside): the atmospheric pressure in the lab room P total (inside): the total pressure inside the Erlenmeyer flask therefore, Pbutane: the partial pressure of the butane gas collected inside the Erlenmeyer flask Pbutane = Patm (outside) – PH2O PH2O: the partial pressure of the water vapor inside the Erlenmeyer flask The atmospheric pressure can be measured with a barometer (ask your instructor for the current value), and the vapor pressure of the water at the current temperature can be found in the attached table (see Table 1 below). Units of pressure: The following definitions and conversion factors are useful Barometer: A device used to measure the current pressure of the Earth’s atmosphere (which varies from day to day and decreases with increasing altitude). The pressure is measured by the height of a column of mercury that can be supported by the atmospheric pressure. The higher the column of mercury is, the higher the pressure is. Barometer readings usually have units of millimeters of mercury (mm Hg) or inches of mercury (in Hg). Torr: A torr is a unit of pressure named after Evangelista Torricelli, the Italian scientist who invented the barometer in 1643. 1 torr = 1 mm Hg (original definition of a torr) 1 torr = 1 atm (current revised definition) 760 Still approximately true (to six decimal places) Atmosphere: An atmosphere is a unit of pressure representing the average pressure of the Earth’s atmosphere at sea level. An atmosphere is officially defined as 101,325 Pa (pascal = Newton of force per square meter), but more useful to us is the relationship below: 1 atm = 760 torr (exact, by definition of a torr) The Ideal Gas Law: This law relates the four variable properties of a gas (the pressure, volume, number of moles, and temperature) with a proportionality constant (the Ideal Gas constant). PV = nRT Note: all values must be in the correct units P = pressure in atmospheres (atm) V = volume in liters (L) n = number of moles of gas (mol) R = Ideal gas constant (0.08206 L·atm K·mol T = temperature in Kelvin (K) Sample calculation of the molar mass of butane: Your original data will differ, but the conversions and calculations should be similar. Original Data: Mass butane cylinder (initial): Mass butane cylinder (final): Volume of Erlenmeyer flask (to line): Temperature: Atmospheric pressure: 87.63 g 86.98 g 276.1 mL 21.6 °C 30.05 in Hg Conversions and Calculations: Mass of butane gas: 87.63 g (initial mass butane cylinder) − 86.98 g (final mass butane cylinder) 0.65 g (mass butane gas) Temperature of water and butane gas (in Kelvin): K = °C + 273.15 21.6 °C + 273.15 294.75 K Volume of butane gas in the Erlenmeyer flask (in liters): 276.1 mL 10−3 L 1 mL = 0.2761 L ) Atmospheric pressure (Patm): (exact) 30.05 in Hg 2.54 cm 10−2 m 1 mm 1 torr 1 in 1 cm 10−3 m 1 mm Hg = 763.27 torr Partial pressure of butane (Pbutane): at 21.6 °C (see Table 1 below) Pbutane = Patm – PH2O Pbutane = 763.27 torr – 19.359 torr Pbutane = 743.911 torr 743.911 torr 1 atm = 0.9788302632 atm 760 torr Molar mass of butane (using the ideal gas law and the definition of molar mass): PV = nRT nbutane = PbutaneV RT (0.9788302632 atm) (0.2761 L) = (0.08206 L·atm/K·mol) (294.75 K) = 0.0111734803 mol butane g 0.65 g butane molar = = 58.17345905 g/mol mass = mol 0. 0111734803 mol butane molar mass butane = 58 g/mol Note: The accepted value for the molar mass of butane (C4H10) is: 58.123 g/mol C4H10 = 4(12.011 g/mol) + 10(1.0079 g/mol)

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