Name Gas Unit Activity Modeling Gas Behavior PART 1 Background Information Please Read The combined gas law or ideal gas law can be arrived at from trying to find a mathematical relationship between the properties of volume temperature and pressure for a gas It is important to realize that many scientific models arrive at physical insight by simplifying the behaviors observed in the real world As such there are often limits to their applicability Today we will examine some real data to figure out under what conditions the ideal gas law best models real gas behavior and under which conditions it does not Below is a table with some P T V data for molecular hydrogen H2 gas For each data point find the volume that the ideal gas law would yield and compare it to that of the actual volume of the gas The data is all for 1 mole of gas Temperature Pressure K bar Volume L Volume L Difference real ideal measured measured calculated minus ideal 100 0 100 0 100 0 100 0 300 0 300 0 300 0 300 0 500 0 500 0 500 0 500 0 8 313 8301 08767 02425 24 96 2 509 0 2644 04095 41 59 4 174 0 4321 0 05763 1 000 10 00 100 0 1000 1 000 10 00 100 0 1000 1 000 10 00 100 0 1000 8 314 0 8314 0 08314 0 008314 24 94 2 494 0 2494 0 02494 41 57 4 157 0 4157 0 04157 0 001 0 0013 0 0045 0 01593 0 02 0 015 0 0149 0 01600 0 02 0 016 0 0163 0 01605 Difference Difference divided by Real Volume 0 02 0 16 5 16 65 7 0 06 0 58 5 64 39 1 0 04 0 39 3 78 28 9 1 Referring to the data table under what conditions does the Ideal Gas equation best model the real gas behavior BE ABLE TO EXPLAIN YOUR ANSWER A high pressure B low pressure C high temperature D low temperature Revised SH 6 17 13 LaBrake Vanden Bout 2013 Name Explanation Clearly as the pressure increases the percentage error starts to get very very bad For P 1atm the IG is less than 0 1 error at every temperature It is also sometimes better at low T and sometime better at high T The really trend is clearly that as P increases the error increases 2 From the molecular perspective what is changing as the pressure is increased at constant temperature A The molecules get closer together B The space between the molecules does not change but the molecules are moving faster C The measured pressure increases D The measured volume decreases E A C and D are all an acceptable answer for this question 3 What does the ideal gas law predict for the volume in the limit that the pressure goes to infinity Does this make physical sense It goes to ZERO It is impossible for something that takes up space and has volume to no longer take up space and have volume PART 2 THE HARD SPHERE MODEL The volume of the molecules can t go to zero Only the volume between the molecules can go to zero in which case one would be describing a condensed phase Explain the reality is that gases do take up space and they can be described with a new model This is done by replacing the volume which represents ideally the volume in space in which the gas can move which is approximated at the volume of the container in the ideal gas equation by the volume minus a constant The constant is essentially the volume occupied by the gas particles This would give an equation like the following P V nb nRT where b is a constant with units of L mol 1 If we re arrange this equation to solve for the volume we find V nRT P nb That is V VIG nb OR V VIG nb So if this model were to work we would expect that the real volume and the ideal volume would always be different by a constant The constant is unique to the gas because it is dependent on the size of the gas particle Revised SH 6 17 13 LaBrake Vanden Bout 2013 Name 1 Look back in the data table at the difference between the measured volume and the calculated volume Is this difference a consistent value for the majority of the data points Yes 2 If so what value do you think you would get for the constant b for the data that is given Looking at the data b 0 015 L mol 1 or 0 016 Revised SH 6 17 13 LaBrake Vanden Bout 2013
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