1. Plot the Maxwell-Boltzmann speed distributions for He, N₂ and I₂ at 273K on the same graph. Be sure to leave the y axis as the fraction, not some large number of particles. Excel does not have a good trendline (that I could find) to fit this so simply make sure you have enough data points so that the overall shape can be clearly seen. ALWAYS DO A FULL CALCULATION BY HAND ON PAPER WITH FOR EXAMPLE V=100m/s AND GET THE ANSWER FOR THE FRACTION THEN MAKE EXCEL GIVE THE SAME ANSWER! How does the most probable velocity formulas value compare with your graph?

2. Using your graphs from question 1, plot 0 to 200 m/s for each gas. Find the fraction (put your final answer in percent) of molecules with speeds in the range of 100 to 200 m/s. If you use the polynomial fit in excel find the order that best fits the graph between 100 to 200 m/s with scientific notation using 4 decimal places, you simply integrate it with limits of 100 to 200 m/s. To see this clearly plot each of these separately.

3. The Karlsruhe conference of 1860 was called to resolve the problem of determining the molar masses of atoms and molecules. One of the methods presented by Canizzaro uses the following data. Deduce the relation between the pressure and mass density, , of a perfect gas of molar mass M. Confirm graphically, using the following data on dimethyl ether at 25^oC, that perfect gas behavior is reached at low pressures and find the molar mass of the gas.

p/(kPa) 12.223 25.20 36.97 60.37 85.23 101.3

/(kg m^-3) 0.225 0.456 0.664 1.062 1.468 1.734

Hint: You will need to stare at the equation linking density and molar mass thru the ideal gas law to see what quantity to use off your graph. You will ultimately have to graph p/ vs p and extrapolate down to the limit of low pressure.

4a. Find an expression for (d/T)_p,n of an ideal gas. The d is density and the T is temperature. Basically you need to find or make an expression that has density and temperature in it, isolate the d variable then find the derivative of it with respect to T while realizing that p and n are constant.

b. If the temperature is 298 K and the pressure is 1.362 atm what is the value of the slope of a d vs T graph for helium (4.00 g/mol assume ideal gas)?

c. Sketch the experimental apparatus, data chart you would use to collect data and the graph of density vs T. (i.e. what you would do it this was your TR project)

5. Boyles Law for an ideal gas states that the pressure multiplied by the volume is equal to a constant. Graph the volume vs pressure graphs for temperatures of 273 K, 773 K, 1273 and 1773 K on the same graph in excel if the constant is 22.7 dm³bar at 273 K and we assume this constant varies directly with T. Use the power fit for the trendlines and be sure that all your points for your four graphs fit between 0 and 5000 on the volume axis and 0 and 1 bar on the pressure axis. Pick enough points to get nice looking graphs. Then also plot all four on one graph to see them all at once.

Discuss the difference/trends between the graphs.