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Observations: Reported Air Pressure: 102.8 kPa Correction for Altitude: 102.8 kPa - 1.2(85/100)=101.6kPa Mass of Mg used (g) Moles of Mg used Room Temp. (oC) Room Press. (kPa) Water Temp (oC) Vol. of Gas Collected (mL) .04 .04/24.31 = .00165 22 101.6 22 = 295 K 25 = 0.025 L Calculations: 1) Write the balanced chemical equation for this lab: Mg(s) + 2HCl(aq) —> MgCl2(aq) + H2(g) 2) Based on the equation, what is the theoretical yield, in moles, of H2 gas for your reaction? 0.00165 mol Mg(s) /2 x1 = 0.000825 mol H2(g) 3) a) What is the partial pressure of water in the cylinder (PH2O) based on room temperature? 2.3 kPa Look up the value for 22 oC in the table on page 464 in the text book (2.3 is what I remember) b) If no gases except H2 and H2O are present, what is the partial pressure of Hydrogen gas (PH2)? PT = PH2 + PH2O thus, PH2 = PT - PH2O = 101.6 - 2.3 = 99.3 kPa Discussion: 1. For what two reasons must you wait 5 minutes before measuring the gas volume in the cylinder? Several reasons: 1) let the gas temperature in the tube to equilibrate with the room temperature, 2) let the gas in the tube reach 100% humidity, and, as one of you pointed out, 3) make sure the reaction really is over (and all the gas has collected at the top of the tube) 2. Use the combined gas law to calculate the volume your hydrogen gas by itself would have occupied at SATP? (P1 is PH2 from data, V1 is from the data table, and T1 is the room temperature) P1V1/(n1T1)=P2V2/(n2T2) therefore: V2 = n2T2P1V1/(P2n1T1) = T2P1V1/(P2T1) since n is not changing = 298K x 99.3kPa x 0.025L /(100kPa x 295K) = 0.0251 L Not much of a difference since we already were close to SATP conditions during the lab. 3) a) Should one mole of any ideal gas have the same volume at SATP? Yes. b) What is the accepted value of the ideal gas constant (R)? 8.31 kPaL/molK 4) a) Use the ideal gas equation, PV=nRT, to calculate your experimental value for R Use the volume that you calculated for SATP in question 2 R = PV/nT = (100 kPa)(0.0251)/((0.00165 mol)(298 K)) = 2.51/.4917 = 5.10 b) Calculate the percent discrepancy between your molar volume at SATP and the theoretical one 100% (5.10 - 8.31)/8.31 = -39% not so great! 5) Use the ideal gas law and the accepted value of R to calculate what volume 1 mole of ideal gas should have at SATP. V = nRT/P = 1(8.31)(298)/100 = 24.71 L Gas Concepts Ideal gas molecules have large kinetic energies such that the intermolecular forces have virtually zero effectiveness at holding molecules together. Thus: 1) molecules move in straight lines in random directions unless they collide with something. 2) all collisions are elastic - no kinetic energy is lost. 3) the volume of the molecules is insignificant compared to the total volume of the gas. Properties needed to calculate the number of moles of a gas: Volume Temperature: a measure of the average internal kinetic energy of the particles in an object A given temperature actually corresponds to a distribution of kinetic energies. Note just how fast air molecules move on average, even at room temperature (300 K): 500 m/s or 0.5 km/s. Higher temperatures mean higher average speed. However, temperature is proportional to kinetic energy, not speed. Ek = .5 m v2 At the same temperature, molecules with larger molar masses are moving more slowly. You can measure this by releasing two gases at the same moment and timing how long it takes for their odours to be detected at some distance away. v12/v22 = m2/m1 = t22/t12 Pressure: pressure is calculated as a force divided by the area over which it is applied in a gas: the force is the sum of the collisions happening at any given moment they are small, but as noted above, they move fast and they are many the area is the internal surface area of the container More moles of gas molecules means more collisions per second = higher pressure Higher temperature, the faster the molecules, the more often collisions occur and the greater the force of the collisions = higher pressure With some simple experiments, we can derive a mathematical relationship between moles, temperature, pressure, and volume that we can use. Real gases condense as pressure increases or temperature decreases. At that point, they stop behaving in an ideal fashion. Since direct relationships can be described between all four of these properties, we can derive: P1V1 n 1 T1 = P2V2 n 2 T2 P1V1/(n1T1) = P2V2/(n2T2) or Temperature must be in Kelvins, or the equation will not work. Kelvin = oC + 273 The gas also must be approximately ideal. P1V1/(n1T1) = P2V2/(n2T2) can be used to calculate how any one of these properties changes if you know how the other three have changed. E.g., if the pressure, temperature, and number of moles of gas change, what is the new volume? V2 = n2T2P1V1 / (P2n1T1) However, the equation P1V1/(n1T1) = P2V2/(n2T2) means that PV / (nT) = a constant With experiments, we find that it is the same constant not matter what gas is used, as long as it behaves as an ideal gas: PV / (nT) = R = 8.31 kPaL/molK Pressure must be in kPa, volume in L, temperature in Kelvins, and the gas is ideal. Mixtures of Gases Since all ideal gases behave ideally, they all contribute to pressure in the same way at the same temperature. So, at a give temperature in the same container, we would get the same pressure from 5 moles of Nitrogen gas as we would from 2 moles of Nitrogen gas and 3 moles of Oxygen gas. In the second case, the nitrogen would account for 40% of the pressure (2/5) and the Oxygen would account for 60% of the pressure. The pressure produced by just one gas in a mixture (its part) is called Partial Pressure. Partial pressure is shown with a subscript denoting the particular gas: PN2 and PO2 in the example above. Total pressure is just P In general: Px = (nx/ntotal)P P = Px + Py + Pz... (the total pressure is the sum of all the partial pressures in a mixture) Water Vapour This is not an ideal gas at room temperature, since it is well below its boiling point. There are tables (see page 464) that tell us what the partial pressure of water vapour is at certain temperatures when the humidity is 100% (a saturated solution of water vapour in air). We encounter this when we are collecting gases by downward displacement of water. If we collect 0.05 L of H2 gas at 25 oC and a pressure of 105 kPa by downward displacement of water in a tube, we can find that the PH O is 3.17 kPa. We know that P = PH + PH O so PH = P - PH O = 105 - 3.17 = 101.83 kPa 2 2 2 2 2 I can now use the ideal gas equation to calculate the number of moles of hydrogen gas collected PV=nRT nH = PH V/RT = 101.83 x 0.05 / (8.31 x (25 + 273)) = 0.0021 moles 2 2