12, October 2007 Dr. Stevens Gen. Chem. 1 Volume-amt. gas relationship -For 1 mol each at STP => -Ar = 22.09L -O2 = 22.40L -CO2 = 22.26L -Avg molar volume = 22.41L/mol (at STP) -about size of b-ball -if p and T are constant, then equal volumes of diff. gases contain the same moles -ex: find formula of a hydrocarbon if 1L CO2 reacts with 2L H2 to make 1L hydrocarbon + O2. -CO2 + 2H2 H4C + O2 CH4 = methane Empirical relationships: -V is indirectly proportional to p -V is proportional to T -V is proportional to n -therefore: V is proportional to nT/P -V = RnT/P PV = nRT (R = constant) -Ideal Gas Approximation -approximately true if p is low and V is large -R from V/n from Avogadro at STP conditions R = PV/nT V/n = x P/T = 22.414L/mol x 1atm/273K = 0.08206Latm/molK -PV = n(.08206)T -ex: calc. p o 0.010mg N2 in a 5.0L tv tube at rm temp (23C). -p = (.08206)(300)(3.6x10^-7)/5 = 1.6x10^-6atm (near vacuum) -n = 0.010mg = 3.6x10^-7mol Speeds of molecules -Urms = root mean square speed -s = Urms = (u^2)^(1/2) -proportional to T -inversely proportional to MM -s = Urms = (3RT/MM)^(1/2) -on dist. Graph -max = avg. speed -speed most molecules have -KE = .5mv^2 -kinetic energy of gases in same flask is equal -Urms (O2) at SATP -((3x8.314x302)/32)^(1/2) = 482m/s -R = 8.314J/molK
Demo (balloon in N2(l)): -V/T = V/T -V1 = 1L, T = 302 -T2 = -196 + 273 -V2 = .25L -how else could we reduce V to .25L? -change pressure (PV = PV)