1!#15: The Ideal Gas Law and the Determination of the Gas Constant, R Gases defined by 4 properties:  P = pressure  V = volume  n = number of moles of gas  T = temperature (Kelvin) Gas Simulation http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm!V ∝1PV ∝ TV ∝ nV ∝nTPV =nRTPPV = nRTR = ideal gas constant for 1 mole of gas at STP: P = 1 atm V = 22.414 L T = 273.15 K R =PVnT=1atm( )22.414 L( )1mol( )273.15K( )= 0.0821L ⋅ atmmol ⋅ KAn ideal gas behaves according to the assumptions of kinetic-molecular theory2!Gas Simulation http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm!Deviations from ideality low temperature high pressure Our goal in lab this week:  measure the properties of a sample of oxygen (not at STP)  verify the value of R  Is R constant (within the limits of experimental error)? Oxygen boiling point = -183°C Do you expect it to behave ideally? decompose potassium chlorate to generate oxygen gas:!2KClO3(s)  2KCl(s) + 3O2(g)!KClO3 + MnO2!O2!O2!2KClO3(s)  2KCl(s) + 3O2(g)!Goal: determine n, V, P, T and calculate R 1. Calculate n: weigh solid before and after heating before = mass KClO3 + MnO2 after = mass KClO3 + MnO2 + KCl 2KClO3(s)  2KCl(s) + 3O2(g)!n = mass loss( )molO232.00 g⎛⎝⎜⎞⎠⎟-!difference = mass O23!KClO3 + MnO2!O2!O2!2. Determine Volume: Volume H2O displaced = Volume O2 generated for volume determination, weigh beaker empty and with water d =massvolumetherefore,volume =mass H2OdensityAppendix A!3. Determine temperature: measure temperature of the water assume T(O2) = T(H2O) 4. Determine pressure:  atmospheric pressure gauge in lab  Be sure to record the pressure before leaving lab - it can change quickly. but, the gas contains water vapor too: Patm = PO2 + PH2O Patm - PH2O = PO2 Appendix B!Calculate R:!R =PVnTBut, how much confidence do you have in your answer? Is the calculated value the same as the literature value, within the range of expected uncertainty? What do we mean by experimental uncertainty? A C!A and C are measured values!standard deviation reflects the uncertainty in the mean!B = mean or average!B!4!But, all data values also have an associated uncertainty A C!B!indeterminate error - the range a value has due to the need to estimate the last digit being reported Uncertainty is not the same as error A C!B! D!D is the true value. (Recall, distance from the true value reflects the error.) to summarize: A C!B! D!Precision: closeness of A and C to each other (scatter) Accuracy (error): distance from B to D Uncertainty: bands around A and C Measured values: reporting uncertainty  last digit in recorded values is the uncertain digit  convention: +/- 1 in the last digit speed = 251 mph range: 250 - 252 Calculated values: determining uncertainty How does uncertainty in recorded values propagate through to final calculated value? R =PVnTMathematical process: propagation of error tricky, involves multi-variable calculus!“Max - Best - Min” method  Calculate maximum value, with maximum error = “Max”  Calculate minimum value, with maximum error = “Min” Best = (Max + Min)/2 , or the average Max - Min = range Uncertainty = range/25!Example: 2 solids mass 1 = 17.2 +/- 0.2 g mass 2 = 12.5 +/- 0.1 g What is the sum of the masses? Max: 17.4 + 12.6 = 30.0 Min: 17.0 + 12.4 = 29.4 Best: (30.0 + 29.4)/2 = 29.7 Uncertainty = (30.0 - 29.4)/2 = 0.3 Sum = 29.7 +/- 0.3 g General rule for addition and subtraction: For addition and subtraction, the uncertainty is the sum of all the uncertainties being added or subtracted. How about multiplication and division? mass = 1.19 +/- 0.01 g volume = 0.286 +/- 0.002 mL What is the density? Max: 1.20/0.284 = 4.225 Min: 1.18/0.288 = 4.097 Best: (4.225 + 4.097)/2 = 4.161 g/mL Uncertainty = (4.225 - 4.097)/2 = 0.064 Density = 4.16 +/- 0.06 g/mL General rule for multiplication and division: For addition and subtraction, set up the calculation to maximize and minimize and calculate the uncertainty. For this week’s lab:  One trial, so you won’t calculate std. dev.  Instead, calculate best value of R and uncertainty using “Max-Best-Min” method.  Does the accepted value of R fall within the range of your experimental uncertainty?  If not,