The Ideal Gas Law This activity builds on the The Behavior of Gases laboratory activity that you recently completed. There you explored the behavior of gases in mainly a qualitative way, just beginning analysis of quantitative results when you explored the pressure-volume relationship. Now we are going to examine the gas variables (pressure, volume, temperature, and amount as moles) quantitatively in an interactive Excel spreadsheet at http://academic.pgcc.edu/psc/chm101/ideal_gas. 1. On the set-up below the arrow points to a volume of 10 mL of air at 1.0 atm. How will pressure vary when the volume is changed? Now before starting, what is the temperature of the trapped air? Is the amount of air in the syringe constant? Assuming that our syringe does not leak, we have a closed system or a constant amount of air trapped at laboratory temperature (25 oC or 298K). Now, how will pressure vary when the volume is changed? Sketch the relationship and label the axes in the space to the right. Open the Ideal Gas Law spreadsheet and click on the P-V tab. This plot should look familiar. Remember that PV = k. What happens if temperature increases? Try it out and sketch and label on the plot above. What is happening on a microscopic level as the pressure on a gas increases? View animation #1 at http://academic.pgcc.edu/psc/chm101/ideal_gas. CHM 101/Sinex & Gage 1What happens if the number of moles of gas in the syringe decreases? Why? How do the PV values compare when the error is zero? Add a little error to the data using the error slider. What do you notice about the graph? What happens to k (PV)? 2. When you warmed the balloon over the hot water on the hot plate what happened to the balloon? What caused this change? (Consider what is happening on a microscopic level.) View animation #2 at http://academic.pgcc.edu/ psc/chm101/ideal_gas. What variables were constant for the balloon as you heated it? How does volume vary as the temperature is raised? Click on the V-T (C) tab to see the graph of volume as a function of Celsius temperature. Sketch and label the graph. CHM 101/Sinex & Gage 2How does the V/T ratio vary for this plot when the error is zero? How does changing the pressure influence the graph? Sketch and label the effect. What is the numerical value of the x-intercept? What does this mean? This is the basis for the Kelvin temperature scale. When the projected or extrapolated gas volume reaches zero, the temperature at which this occurs is defined as absolute zero. This is how the Kelvin temperature scale was developed. How does error influence the VT result? How could you transform this relationship (have a y-intercept of zero) to determine a direct proportion between volume and temperature with no other factors? Sketch a graph of volume as a function of temperature, where temperature is converted to Kelvin. The transformation of the temperature data is the conversion from Celsius to Kelvin temperature: K = oC + 273. Click on the V-T (K) tab to view this plot. How does the V/T ratio vary for this plot when the error is zero? Why does the data have a lower temperature limit? CHM 101/Sinex & Gage 33. Imagine you blow air into a balloon. What happens to the balloon as the amount of air increases? Is there a direct relationship between volume and amount of air? Click on the V-n tab. Sketch and label the axes for volume as a function of moles. How does changing the pressure influence the graph? Sketch and label the effect. How does changing the temperature influence the graph? Sketch and label the effect. How does the V/n ratio vary for this plot? Why? From the variation of pressure versus volume, volume versus temperature (in Kelvin), and volume versus moles, we can combine these and get the ideal gas law: nRTPV ="knVkTVkPV'===R ''k' let''k'nTPV== where R is referred to as the gas constant. CHM 101/Sinex & Gage 44. We define a reference or standard temperature (0oC or 273.15 K) and pressure (1.00 atmosphere) and refer to these as STP. From experimentation it is found that 1.00 mole of any gas (H2, C4H10, or Rn) occupies a volume of 22.4 L at STP. Using these experimental conditions, find the numerical value of the gas constant, R, and its units. 5. Using the animations and the ideal gas law, explain how pressure and temperature are related. Sketch and label a graph of pressure as a function of temperature (in kelvin) on the axes. What variables must be constant for this relationship to hold? How does changing the volume influence the graph? Sketch and label on the graph. How does changing the number of moles influence the graph? Sketch and label on the graph. Explain on a microscopic level why this relationship exists. How does the P/T ratio vary for this plot? 6. When you warmed the balloon on the hot plate, the volume increased. What about the amount of gas in the balloon, did it change? CHM 101/Sinex & Gage 5If the balloon is a closed system (has no leaks), how did the density change for the balloon as temperature rose? What is the mathematical relationship between gas density and temperature? Explain what is happening on a microscopic level to explain this relationship. 7. Why does a helium-filled balloon rise? Let’s consider how gas density varies as a function of the molar mass of the gas. For the same amount of gas at constant temperature, pressure and volume, how is density going to vary with the molar mass of the gas? Click on the D-MM tab to see the relationship for the Group 8A or noble gases. Sketch and label the graph. How does changing the pressure influence the graph? Sketch and label on the plot. Why does this happen? How does changing the temperature influence the graph? Sketch and label on the plot. How does the D/MM ratio vary? Now derive an equation that expresses density as a function of molar mass and includes the influence of temperature and pressure. CHM 101/Sinex & Gage 6The equation you just derived from the experimental data can be obtained by substituting and manipulating the ideal gas law: VmD MMmnnRTPV=→== RTP(MM)VmD RTMMmPV ==→= 8. Suppose we wanted to calculate the density of air at 1.00 atm and 298K, we would need the molar mass of air. Now air is a mixture, not a compound, so how do we get a molar mass for air? Air, at 1.00 atm of pressure or at sea level, is mixture with a fixed