Ideal Gas Laws

1. The ideal gas law is most succinctly stated in the equation: PV = nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant and T is temperature. This law follows logically from the three laws we discussed in class last week. The first of these is Boyle’s Law, which is expressed as
   V = K₁/P       or       P × V = K₁       (K₁ is a constant)
   What does this equation mean, and what conditions must be held constant for it to be true?
2. The second of these laws is Charles’s Law:
   V = K₂ × T       or       V/T = K₂       (K₂ is another constant)
   What does this equation mean, and what conditions must be held constant for it to be true? What units are required for the temperature in this equation?
3. The third law is Avogadro’s Law:
   V = K₃ × n       or       V/n = K₃       (K₃ is a third constant)
   What does this equation mean, and what conditions must be held constant for it to be true?
4. Procedure
   In this lab you are given three sets of experimental data. You will make a graph of each one and from the graph you will derive an equation to describe the physical behavior of the gas. Each one will be a straight line of the algebraic form y = mx + b. For each law, the constant (K_i) will be equal to m, the slope. If the data are ideal the y-intercept b will equal 0. We will make the graphs by hand in class but for extra credit, you may do them on a spreadsheet. Extra credit will consist of a replacement for a poor quiz grade with the grade for your lab.
   
   For full credit on this lab you must hand in your three hand-drawn graphs and the answers to all questions (there are three sections in addition to the pre-lab questions).

Boyle’s Law

•  First, calculate 1000/V and P in atmospheres. 1 atm = 760 mmHg. If graphing using a spreadsheet, enter each column separately with an appropriate heading. You are using a multiple of the reciprocal on the order of 1000 to make the graph easier to draw.
•  Put your name, the date, and the title of the graph at the top of the page, laying the page with the long axis horizontally in front of you.
•  Set up a piece of graph paper with a scale such that the graph will be as large as possible on the page. Place Pressure on the y-axis and 1/V on the x-axis. Label each axis with the proper units and be sure to write the numbers on the scale as neatly as possible.
• Plot each data point on the graph as precisely as possible and use a ruler to find the best-fitting straight line. If using a spreadsheet program, use the chart wizard to create a scatterplot. Then use "Add Trendline" to plot a linear regression (y = mx + b); show the equation and the r² value. This equation will match the following restatement of Boyle’s Law in form: P = K₁ × (1/V). Where y is P, x is 1/V, and K₁ is m. The y-intercept (b) should equal zero).
• Answer the following questions on the back of the graph for data set 1:

1. Should these data fit a straight line? Explain.
2. Suggest reasons the data might not fit the line perfectly.
3. Find the slope of the line you drew to fit the data (K₁ in the following equation: P = K₁ × (1/V). Or, if using a spreadsheet, determine the slope from the equation it provides. What are the units of this slope?
4. Rewrite the equation in the previous question to show how K₁ relates to R (the ideal gas constant). Try comparing P = nRT × 1/V to P = K₁ × 1/V.
5. Use the equation you find to calculate the number of moles in this sample of gas.
6. Should the y-intercept of the line be zero? Why or why not?

Charles’s Law

•  First, calculate T in Kelvin. K = °C + 273. If graphing using a spreadsheet, enter each column separately with an appropriate heading.
•  Put your name, the date, and the title of the graph at the top of the page, laying the page with the long axis horizontally in front of you.
•  Set up a piece of graph paper with a scale such that the graph will be as large as possible on the page. Fill the whole piece of paper! Place Volume on the y-axis and Temperature on the x-axis. Label each axis with the proper units and be sure to write the numbers on the scale as neatly as possible.
• Plot each data point on the graph as precisely as possible and use a ruler to find the best-fitting straight line for each of the two lines. If using a spreadsheet program, use the chart wizard to create a scatterplot. Then use "Add Trendline" to plot a linear regression (y = mx + b); show the equation and the r² value. This equation will match this expression of Charles’s Law: V = K₂ × T. Where y is V, x is T, and K₂ is m. The y-intercept (b) should equal zero).
• Answer the following questions on the back of the graph for data set 2:

1. Find the slope of both lines you drew to fit the data (K₂ in the following equation: V = K₂ × T. Or, if using a spreadsheet, determine the slopes from the equation the trendline provides. What are the units of these slopes?
2. Rewrite the equation in the previous question to show how K₂ relates to R (the ideal gas constant). Rewrite PV = nRT, solving for V/T. Compare this to V/T = K₂.
3. Use the equations you find to calculate the number of moles in both samples of gas. What makes these two samples different?
4. Why are the two lines different if Charles’s Law is true?
5. Do both lines have the same y-intercept? Why or why not?
6. Why is there a long portion of your graph with no data points?
7. Finally, if we were dealing with a real gas, would the gas really have no volume at zero Kelvin? Why or why not?

Avogadro’s Law

•  If graphing using a spreadsheet, enter each column separately with an appropriate heading.
•  Put your name, the date, and the title of the graph at the top of the page, laying the page with the long axis horizontally in front of you.
•  Set up a piece of graph paper with a scale such that the graph will be as large as possible on the page. Fill the whole piece of paper! Place n (moles of gas) on the x-axis and Volume on the y-axis. Label each axis with the proper units and be sure to write the numbers on the scale as neatly as possible.
• Plot each data point on the graph as precisely as possible and use a ruler to find the best-fitting straight line. If using a spreadsheet program, use the chart wizard to create a scatterplot. Then use "Add Trendline" to plot a linear regression (y = mx + b); show the equation and the r² value. This equation will match this expression of Avogardo’s Law: V = K₃ × n. Where y is V, x is n, and K₃ is m. The y-intercept (b) should equal zero).
• Answer the following questions on the back of the graph for data set 3:

1. Find the slope of both lines you drew to fit the data (K₃ in the following equation: V = K₃ × n. Or, if using a spreadsheet, determine the slopes from the equation the trendline provides. What are the units of these slopes?
2. Using the value of K₃ calculate the molar volume of this gas in L/mol at standard temperature and pressure (STP: 0°C and 1 atm).
3. According to your result in the previous question, is the gas behaving ideally? Explain.